/*
 * lib/prio_tree.c - priority search tree
 *
 * Copyright (C) 2004, Rajesh Venkatasubramanian <vrajesh@umich.edu>
 *
 * This file is released under the GPL v2.
 *
 * Based on the radix priority search tree proposed by Edward M. McCreight
 * SIAM Journal of Computing, vol. 14, no.2, pages 257-276, May 1985
 *
 * 02Feb2004    Initial version
 */

#include <linux/init.h>
#include <linux/mm.h>
#include <linux/prio_tree.h>

/*
 * A clever mix of heap and radix trees forms a radix priority search tree (PST)
 * which is useful for storing intervals, e.g, we can consider a vma as a closed
 * interval of file pages [offset_begin, offset_end], and store all vmas that
 * map a file in a PST. Then, using the PST, we can answer a stabbing query,
 * i.e., selecting a set of stored intervals (vmas) that overlap with (map) a
 * given input interval X (a set of consecutive file pages), in "O(log n + m)"
 * time where 'log n' is the height of the PST, and 'm' is the number of stored
 * intervals (vmas) that overlap (map) with the input interval X (the set of
 * consecutive file pages).
 *
 * In our implementation, we store closed intervals of the form [radix_index,
 * heap_index]. We assume that always radix_index <= heap_index. McCreight's PST
 * is designed for storing intervals with unique radix indices, i.e., each
 * interval have different radix_index. However, this limitation can be easily
 * overcome by using the size, i.e., heap_index - radix_index, as part of the
 * index, so we index the tree using [(radix_index,size), heap_index].
 *
 * When the above-mentioned indexing scheme is used, theoretically, in a 32 bit
 * machine, the maximum height of a PST can be 64. We can use a balanced version
 * of the priority search tree to optimize the tree height, but the balanced
 * tree proposed by McCreight is too complex and memory-hungry for our purpose.
 */

/*
 * The following macros are used for implementing prio_tree for i_mmap
 */

#define RADIX_INDEX(vma)  ((vma)->vm_pgoff)
#define VMA_SIZE(vma)     (((vma)->vm_end - (vma)->vm_start) >> PAGE_SHIFT)
/* avoid overflow */
#define HEAP_INDEX(vma)   ((vma)->vm_pgoff + (VMA_SIZE(vma) - 1))


static void get_index(const struct prio_tree_root *root,
    const struct prio_tree_node *node,
    unsigned long *radix, unsigned long *heap)
{
        if (root->raw) {
                struct vm_area_struct *vma = prio_tree_entry(
                    node, struct vm_area_struct, shared.prio_tree_node);

                *radix = RADIX_INDEX(vma);
                *heap = HEAP_INDEX(vma);
        }
        else {
                *radix = node->start;
                *heap = node->last;
        }
}

static unsigned long index_bits_to_maxindex[BITS_PER_LONG];

void __init prio_tree_init(void)
{
        unsigned int i;

        for (i = 0; i < ARRAY_SIZE(index_bits_to_maxindex) - 1; i++)
                index_bits_to_maxindex[i] = (1UL << (i + 1)) - 1;
        index_bits_to_maxindex[ARRAY_SIZE(index_bits_to_maxindex) - 1] = ~0UL;
}

/*
 * Maximum heap_index that can be stored in a PST with index_bits bits
 */
static inline unsigned long prio_tree_maxindex(unsigned int bits)
{
        return index_bits_to_maxindex[bits - 1];
}

/*
 * Extend a priority search tree so that it can store a node with heap_index
 * max_heap_index. In the worst case, this algorithm takes O((log n)^2).
 * However, this function is used rarely and the common case performance is
 * not bad.
 */
static struct prio_tree_node *prio_tree_expand(struct prio_tree_root *root,
                struct prio_tree_node *node, unsigned long max_heap_index)
{
        struct prio_tree_node *first = NULL, *prev, *last = NULL;

        if (max_heap_index > prio_tree_maxindex(root->index_bits))
                root->index_bits++;

        while (max_heap_index > prio_tree_maxindex(root->index_bits)) {
                root->index_bits++;

                if (prio_tree_empty(root))
                        continue;

                if (first == NULL) {
                        first = root->prio_tree_node;
                        prio_tree_remove(root, root->prio_tree_node);
                        INIT_PRIO_TREE_NODE(first);
                        last = first;
                } else {
                        prev = last;
                        last = root->prio_tree_node;
                        prio_tree_remove(root, root->prio_tree_node);
                        INIT_PRIO_TREE_NODE(last);
                        prev->left = last;
                        last->parent = prev;
                }
        }

        INIT_PRIO_TREE_NODE(node);

        if (first) {
                node->left = first;
                first->parent = node;
        } else
                last = node;

        if (!prio_tree_empty(root)) {
                last->left = root->prio_tree_node;
                last->left->parent = last;
        }

        root->prio_tree_node = node;
        return node;
}

/*
 * Replace a prio_tree_node with a new node and return the old node
 */
struct prio_tree_node *prio_tree_replace(struct prio_tree_root *root,
                struct prio_tree_node *old, struct prio_tree_node *node)
{
        INIT_PRIO_TREE_NODE(node);

        if (prio_tree_root(old)) {
                BUG_ON(root->prio_tree_node != old);
                /*
                 * We can reduce root->index_bits here. However, it is complex
                 * and does not help much to improve performance (IMO).
                 */
                node->parent = node;
                root->prio_tree_node = node;
        } else {
                node->parent = old->parent;
                if (old->parent->left == old)
                        old->parent->left = node;
                else
                        old->parent->right = node;
        }

        if (!prio_tree_left_empty(old)) {
                node->left = old->left;
                old->left->parent = node;
        }

        if (!prio_tree_right_empty(old)) {
                node->right = old->right;
                old->right->parent = node;
        }

        return old;
}

/*
 * Insert a prio_tree_node @node into a radix priority search tree @root. The
 * algorithm typically takes O(log n) time where 'log n' is the number of bits
 * required to represent the maximum heap_index. In the worst case, the algo
 * can take O((log n)^2) - check prio_tree_expand.
 *
 * If a prior node with same radix_index and heap_index is already found in
 * the tree, then returns the address of the prior node. Otherwise, inserts
 * @node into the tree and returns @node.
 */
struct prio_tree_node *prio_tree_insert(struct prio_tree_root *root,
                struct prio_tree_node *node)
{
        struct prio_tree_node *cur, *res = node;
        unsigned long radix_index, heap_index;
        unsigned long r_index, h_index, index, mask;
        int size_flag = 0;

        get_index(root, node, &radix_index, &heap_index);

        if (prio_tree_empty(root) ||
                        heap_index > prio_tree_maxindex(root->index_bits))
                return prio_tree_expand(root, node, heap_index);

        cur = root->prio_tree_node;
        mask = 1UL << (root->index_bits - 1);

        while (mask) {
                get_index(root, cur, &r_index, &h_index);

                if (r_index == radix_index && h_index == heap_index)
                        return cur;

                if (h_index < heap_index ||
                    (h_index == heap_index && r_index > radix_index)) {
                        struct prio_tree_node *tmp = node;
                        node = prio_tree_replace(root, cur, node);
                        cur = tmp;
                        /* swap indices */
                        index = r_index;
                        r_index = radix_index;
                        radix_index = index;
                        index = h_index;
                        h_index = heap_index;
                        heap_index = index;
                }

                if (size_flag)
                        index = heap_index - radix_index;
                else
                        index = radix_index;

                if (index & mask) {
                        if (prio_tree_right_empty(cur)) {
                                INIT_PRIO_TREE_NODE(node);
                                cur->right = node;
                                node->parent = cur;
                                return res;
                        } else
                                cur = cur->right;
                } else {
                        if (prio_tree_left_empty(cur)) {
                                INIT_PRIO_TREE_NODE(node);
                                cur->left = node;
                                node->parent = cur;
                                return res;
                        } else
                                cur = cur->left;
                }

                mask >>= 1;

                if (!mask) {
                        mask = 1UL << (BITS_PER_LONG - 1);
                        size_flag = 1;
                }
        }
        /* Should not reach here */
        BUG();
        return NULL;
}

/*
 * Remove a prio_tree_node @node from a radix priority search tree @root. The
 * algorithm takes O(log n) time where 'log n' is the number of bits required
 * to represent the maximum heap_index.
 */
void prio_tree_remove(struct prio_tree_root *root, struct prio_tree_node *node)
{
        struct prio_tree_node *cur;
        unsigned long r_index, h_index_right, h_index_left;

        cur = node;

        while (!prio_tree_left_empty(cur) || !prio_tree_right_empty(cur)) {
                if (!prio_tree_left_empty(cur))
                        get_index(root, cur->left, &r_index, &h_index_left);
                else {
                        cur = cur->right;
                        continue;
                }

                if (!prio_tree_right_empty(cur))
                        get_index(root, cur->right, &r_index, &h_index_right);
                else {
                        cur = cur->left;
                        continue;
                }

                /* both h_index_left and h_index_right cannot be 0 */
                if (h_index_left >= h_index_right)
                        cur = cur->left;
                else
                        cur = cur->right;
        }

        if (prio_tree_root(cur)) {
                BUG_ON(root->prio_tree_node != cur);
                __INIT_PRIO_TREE_ROOT(root, root->raw);
                return;
        }

        if (cur->parent->right == cur)
                cur->parent->right = cur->parent;
        else
                cur->parent->left = cur->parent;

        while (cur != node)
                cur = prio_tree_replace(root, cur->parent, cur);
}

/*
 * Following functions help to enumerate all prio_tree_nodes in the tree that
 * overlap with the input interval X [radix_index, heap_index]. The enumeration
 * takes O(log n + m) time where 'log n' is the height of the tree (which is
 * proportional to # of bits required to represent the maximum heap_index) and
 * 'm' is the number of prio_tree_nodes that overlap the interval X.
 */

static struct prio_tree_node *prio_tree_left(struct prio_tree_iter *iter,
                unsigned long *r_index, unsigned long *h_index)
{
        if (prio_tree_left_empty(iter->cur))
                return NULL;

        get_index(iter->root, iter->cur->left, r_index, h_index);

        if (iter->r_index <= *h_index) {
                iter->cur = iter->cur->left;
                iter->mask >>= 1;
                if (iter->mask) {
                        if (iter->size_level)
                                iter->size_level++;
                } else {
                        if (iter->size_level) {
                                BUG_ON(!prio_tree_left_empty(iter->cur));
                                BUG_ON(!prio_tree_right_empty(iter->cur));
                                iter->size_level++;
                                iter->mask = ULONG_MAX;
                        } else {
                                iter->size_level = 1;
                                iter->mask = 1UL << (BITS_PER_LONG - 1);
                        }
                }
                return iter->cur;
        }

        return NULL;
}

static struct prio_tree_node *prio_tree_right(struct prio_tree_iter *iter,
                unsigned long *r_index, unsigned long *h_index)
{
        unsigned long value;

        if (prio_tree_right_empty(iter->cur))
                return NULL;

        if (iter->size_level)
                value = iter->value;
        else
                value = iter->value | iter->mask;

        if (iter->h_index < value)
                return NULL;

        get_index(iter->root, iter->cur->right, r_index, h_index);

        if (iter->r_index <= *h_index) {
                iter->cur = iter->cur->right;
                iter->mask >>= 1;
                iter->value = value;
                if (iter->mask) {
                        if (iter->size_level)
                                iter->size_level++;
                } else {
                        if (iter->size_level) {
                                BUG_ON(!prio_tree_left_empty(iter->cur));
                                BUG_ON(!prio_tree_right_empty(iter->cur));
                                iter->size_level++;
                                iter->mask = ULONG_MAX;
                        } else {
                                iter->size_level = 1;
                                iter->mask = 1UL << (BITS_PER_LONG - 1);
                        }
                }
                return iter->cur;
        }

        return NULL;
}

static struct prio_tree_node *prio_tree_parent(struct prio_tree_iter *iter)
{
        iter->cur = iter->cur->parent;
        if (iter->mask == ULONG_MAX)
                iter->mask = 1UL;
        else if (iter->size_level == 1)
                iter->mask = 1UL;
        else
                iter->mask <<= 1;
        if (iter->size_level)
                iter->size_level--;
        if (!iter->size_level && (iter->value & iter->mask))
                iter->value ^= iter->mask;
        return iter->cur;
}

static inline int overlap(struct prio_tree_iter *iter,
                unsigned long r_index, unsigned long h_index)
{
        return iter->h_index >= r_index && iter->r_index <= h_index;
}

/*
 * prio_tree_first:
 *
 * Get the first prio_tree_node that overlaps with the interval [radix_index,
 * heap_index]. Note that always radix_index <= heap_index. We do a pre-order
 * traversal of the tree.
 */
static struct prio_tree_node *prio_tree_first(struct prio_tree_iter *iter)
{
        struct prio_tree_root *root;
        unsigned long r_index, h_index;

        INIT_PRIO_TREE_ITER(iter);

        root = iter->root;
        if (prio_tree_empty(root))
                return NULL;

        get_index(root, root->prio_tree_node, &r_index, &h_index);

        if (iter->r_index > h_index)
                return NULL;

        iter->mask = 1UL << (root->index_bits - 1);
        iter->cur = root->prio_tree_node;

        while (1) {
                if (overlap(iter, r_index, h_index))
                        return iter->cur;

                if (prio_tree_left(iter, &r_index, &h_index))
                        continue;

                if (prio_tree_right(iter, &r_index, &h_index))
                        continue;

                break;
        }
        return NULL;
}

/*
 * prio_tree_next:
 *
 * Get the next prio_tree_node that overlaps with the input interval in iter
 */
struct prio_tree_node *prio_tree_next(struct prio_tree_iter *iter)
{
        unsigned long r_index, h_index;

        if (iter->cur == NULL)
                return prio_tree_first(iter);

repeat:
        while (prio_tree_left(iter, &r_index, &h_index))
                if (overlap(iter, r_index, h_index))
                        return iter->cur;

        while (!prio_tree_right(iter, &r_index, &h_index)) {
                while (!prio_tree_root(iter->cur) &&
                                iter->cur->parent->right == iter->cur)
                        prio_tree_parent(iter);

                if (prio_tree_root(iter->cur))
                        return NULL;

                prio_tree_parent(iter);
        }

        if (overlap(iter, r_index, h_index))
                return iter->cur;

        goto repeat;
}