#include <stdio.h>

#define frost_warning printf
/*
 * This code requires a typedef named 'list_node' for the list node.  It
 * is assumed that the list type is the type of a pointer to a list
 * node, and that the node has a field named 'next' that implements to
 * the linked list.  No additional invariant is maintained (e.g. the
 * 'prev' pointer of a doubly-linked list node is _not_ updated).  Any
 * invariant would require a post-processing pass to fix matters if
 * necessary.
 */
typedef list_node *digit;

/*
 * The maximum possible depth of the merge tree
 *   = ceiling (log2 (maximum number of list nodes))
 *   = ceiling (log2 (maximum possible memory size/size of each list node))
 *   = number of bits in 'size_t' - floor (log2 (sizeof digit))
 * Also, each list in sort_info is at least 2 nodes long: we can reduce the depth by 1
 */
#define FLOOR_LOG2(x) (((x)>=2) + ((x)>=4) + ((x)>=8) + ((x)>=16) + ((x)>=32) + ((x)>=64) + ((x)>=128))
#define MAX_RANKS ((sizeof (size_t) * 8) - FLOOR_LOG2(sizeof (list_node)) - 1)

struct sort_info
{
    int min_rank, n_ranks;
    FROSTCompareFunc func;

    /* Invariant: ranks[i] == NULL || length(ranks[i]) >= 2**(i+1) */
    list_node *ranks [MAX_RANKS]; /* ~ 128 bytes on 32bit, ~ 512 bytes on 64bit */
};

static inline void
init_sort_info (struct sort_info *si, FROSTCompareFunc func)
{
    si->min_rank = si->n_ranks = 0;
    si->func = func;
    /* we don't need to initialize si->ranks, since we never lookup past si->n_ranks.  */
}

static inline list_node *
merge_lists (list_node *first, list_node *second, FROSTCompareFunc func)
{
    /* merge the two lists */
    list_node *list = NULL;
    list_node **pos = &list;
    while (first && second) {
        if (func (first->data, second->data) > 0) {
            *pos = second;
            second = second->next;
        } else {
            *pos = first;
            first = first->next;
        }
        pos = &((*pos)->next);
    }
    *pos = first ? first : second;
    return list;
}

/* Pre-condition: upto <= si->n_ranks, list == NULL || length(list) == 1 */
static inline list_node *
sweep_up (struct sort_info *si, list_node *list, int upto)
{
    int i;
    for (i = si->min_rank; i < upto; ++i) {
        list = merge_lists (si->ranks [i], list, si->func);
        si->ranks [i] = NULL;
    }
    return list;
}

/*
 * The 'ranks' array essentially captures the recursion stack of a mergesort.
 * The merge tree is built in a bottom-up manner.  The control loop for
 * updating the 'ranks' array is analogous to incrementing a binary integer,
 * and the O(n) time for counting upto n translates to O(n) merges when
 * inserting rank-0 lists.  When we plug in the sizes of the lists involved in
 * those merges, we get the O(n log n) time for the sort.
 *
 * Inserting higher-ranked lists reduce the height of the merge tree, and also
 * eliminate a lot of redundant comparisons when merging two lists that would've
 * been part of the same run.  Adding a rank-i list is analogous to incrementing
 * a binary integer by 2**i in one operation, thus sharing a similar speedup.
 *
 * When inserting higher-ranked lists, we choose to clear out the lower ranks
 * in the interests of keeping the sort stable, but this makes analysis harder.
 * Note that clearing the lower-ranked lists is O(length(list))-- thus it
 * shouldn't affect the O(n log n) behaviour.  IOW, inserting one rank-i list
 * is equivalent to inserting 2**i rank-0 lists, thus even if we do i additional
 * merges in the clearing-out (taking at most 2**i time) we are still fine.
 */

#define stringify2(x) #x
#define stringify(x) stringify2(x)

/* Pre-condition: 2**(rank+1) <= length(list) < 2**(rank+2) (therefore: length(list) >= 2) */
static inline void
insert_list (struct sort_info *si, list_node* list, int rank)
{
    int i;

    if (rank > si->n_ranks) {
        if (rank > MAX_RANKS) {
            frost_warning ("Rank '%d' should not exceed " stringify (MAX_RANKS), rank);
            rank = MAX_RANKS;
        }
        list = merge_lists (sweep_up (si, NULL, si->n_ranks), list, si->func);
        for (i = si->n_ranks; i < rank; ++i)
            si->ranks [i] = NULL;
    } else {
        if (rank)
            list = merge_lists (sweep_up (si, NULL, rank), list, si->func);
        for (i = rank; i < si->n_ranks && si->ranks [i]; ++i) {
            list = merge_lists (si->ranks [i], list, si->func);
            si->ranks [i] = NULL;
        }
    }

    if (i == MAX_RANKS) /* Will _never_ happen: so we can just devolve into quadratic ;-) */
        --i;
    if (i >= si->n_ranks)
        si->n_ranks = i + 1;
    si->min_rank = i;
    si->ranks [i] = list;
}

#undef stringify2
#undef stringify
#undef MAX_RANKS
#undef FLOOR_LOG2

/* A non-recursive mergesort */
static inline digit
do_sort (list_node* list, FROSTCompareFunc func)
{
    struct sort_info si;

    init_sort_info (&si, func);

    while (list && list->next) {
        list_node* next = list->next;
        list_node* tail = next->next;

        if (func (list->data, next->data) > 0) {
            next->next = list;
            next = list;
            list = list->next;
        }
        next->next = NULL;

        insert_list (&si, list, 0);

        list = tail;
    }

    return sweep_up (&si, list, si.n_ranks);
}
