#ifndef JEMALLOC_INTERNAL_PH_H
#define JEMALLOC_INTERNAL_PH_H

/*
 * A Pairing Heap implementation.
 *
 * "The Pairing Heap: A New Form of Self-Adjusting Heap"
 * https://www.cs.cmu.edu/~sleator/papers/pairing-heaps.pdf
 *
 * With auxiliary twopass list, described in a follow on paper.
 *
 * "Pairing Heaps: Experiments and Analysis"
 * http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.106.2988&rep=rep1&type=pdf
 *
 *******************************************************************************
 *
 * We include a non-obvious optimization:
 * - First, we introduce a new pop-and-link operation; pop the two most
 *   recently-inserted items off the aux-list, link them, and push the resulting
 *   heap.
 * - We maintain a count of the number of insertions since the last time we
 *   merged the aux-list (i.e. via first() or remove_first()).  After N inserts,
 *   we do ffs(N) pop-and-link operations.
 *
 * One way to think of this is that we're progressively building up a tree in
 * the aux-list, rather than a linked-list (think of the series of merges that
 * will be performed as the aux-count grows).
 *
 * There's a couple reasons we benefit from this:
 * - Ordinarily, after N insertions, the aux-list is of size N.  With our
 *   strategy, it's of size O(log(N)).  So we decrease the worst-case time of
 *   first() calls, and reduce the average cost of remove_min calls.  Since
 *   these almost always occur while holding a lock, we practically reduce the
 *   frequency of unusually long hold times.
 * - This moves the bulk of the work of merging the aux-list onto the threads
 *   that are inserting into the heap.  In some common scenarios, insertions
 *   happen in bulk, from a single thread (think tcache flushing; we potentially
 *   move many slabs from slabs_full to slabs_nonfull).  All the nodes in this
 *   case are in the inserting threads cache, and linking them is very cheap
 *   (cache misses dominate linking cost).  Without this optimization, linking
 *   happens on the next call to remove_first.  Since that remove_first call
 *   likely happens on a different thread (or at least, after the cache has
 *   gotten cold if done on the same thread), deferring linking trades cheap
 *   link operations now for expensive ones later.
 *
 * The ffs trick keeps amortized insert cost at constant time.  Similar
 * strategies based on periodically sorting the list after a batch of operations
 * perform worse than this in practice, even with various fancy tricks; they
 * all took amortized complexity of an insert from O(1) to O(log(n)).
 */

typedef int (*ph_cmp_t)(void *, void *);

/* Node structure. */
typedef struct phn_link_s phn_link_t;
struct phn_link_s {
	void *prev;
	void *next;
	void *lchild;
};

typedef struct ph_s ph_t;
struct ph_s {
	void *root;
	/*
	 * Inserts done since the last aux-list merge.  This is not necessarily
	 * the size of the aux-list, since it's possible that removals have
	 * happened since, and we don't track whether or not those removals are
	 * from the aux list.
	 */
	size_t auxcount;
};

JEMALLOC_ALWAYS_INLINE phn_link_t *
phn_link_get(void *phn, size_t offset) {
	return (phn_link_t *)(((uintptr_t)phn) + offset);
}

JEMALLOC_ALWAYS_INLINE void
phn_link_init(void *phn, size_t offset) {
	phn_link_get(phn, offset)->prev = NULL;
	phn_link_get(phn, offset)->next = NULL;
	phn_link_get(phn, offset)->lchild = NULL;
}

/* Internal utility helpers. */
JEMALLOC_ALWAYS_INLINE void *
phn_lchild_get(void *phn, size_t offset) {
	return phn_link_get(phn, offset)->lchild;
}

JEMALLOC_ALWAYS_INLINE void
phn_lchild_set(void *phn, void *lchild, size_t offset) {
	phn_link_get(phn, offset)->lchild = lchild;
}

JEMALLOC_ALWAYS_INLINE void *
phn_next_get(void *phn, size_t offset) {
	return phn_link_get(phn, offset)->next;
}

JEMALLOC_ALWAYS_INLINE void
phn_next_set(void *phn, void *next, size_t offset) {
	phn_link_get(phn, offset)->next = next;
}

JEMALLOC_ALWAYS_INLINE void *
phn_prev_get(void *phn, size_t offset) {
	return phn_link_get(phn, offset)->prev;
}

JEMALLOC_ALWAYS_INLINE void
phn_prev_set(void *phn, void *prev, size_t offset) {
	phn_link_get(phn, offset)->prev = prev;
}

JEMALLOC_ALWAYS_INLINE void
phn_merge_ordered(void *phn0, void *phn1, size_t offset,
    ph_cmp_t cmp) {
	void *phn0child;

	assert(phn0 != NULL);
	assert(phn1 != NULL);
	assert(cmp(phn0, phn1) <= 0);

	phn_prev_set(phn1, phn0, offset);
	phn0child = phn_lchild_get(phn0, offset);
	phn_next_set(phn1, phn0child, offset);
	if (phn0child != NULL) {
		phn_prev_set(phn0child, phn1, offset);
	}
	phn_lchild_set(phn0, phn1, offset);
}

JEMALLOC_ALWAYS_INLINE void *
phn_merge(void *phn0, void *phn1, size_t offset, ph_cmp_t cmp) {
	void *result;
	if (phn0 == NULL) {
		result = phn1;
	} else if (phn1 == NULL) {
		result = phn0;
	} else if (cmp(phn0, phn1) < 0) {
		phn_merge_ordered(phn0, phn1, offset, cmp);
		result = phn0;
	} else {
		phn_merge_ordered(phn1, phn0, offset, cmp);
		result = phn1;
	}
	return result;
}

JEMALLOC_ALWAYS_INLINE void *
phn_merge_siblings(void *phn, size_t offset, ph_cmp_t cmp) {
	void *head = NULL;
	void *tail = NULL;
	void *phn0 = phn;
	void *phn1 = phn_next_get(phn0, offset);

	/*
	 * Multipass merge, wherein the first two elements of a FIFO
	 * are repeatedly merged, and each result is appended to the
	 * singly linked FIFO, until the FIFO contains only a single
	 * element.  We start with a sibling list but no reference to
	 * its tail, so we do a single pass over the sibling list to
	 * populate the FIFO.
	 */
	if (phn1 != NULL) {
		void *phnrest = phn_next_get(phn1, offset);
		if (phnrest != NULL) {
			phn_prev_set(phnrest, NULL, offset);
		}
		phn_prev_set(phn0, NULL, offset);
		phn_next_set(phn0, NULL, offset);
		phn_prev_set(phn1, NULL, offset);
		phn_next_set(phn1, NULL, offset);
		phn0 = phn_merge(phn0, phn1, offset, cmp);
		head = tail = phn0;
		phn0 = phnrest;
		while (phn0 != NULL) {
			phn1 = phn_next_get(phn0, offset);
			if (phn1 != NULL) {
				phnrest = phn_next_get(phn1, offset);
				if (phnrest != NULL) {
					phn_prev_set(phnrest, NULL, offset);
				}
				phn_prev_set(phn0, NULL, offset);
				phn_next_set(phn0, NULL, offset);
				phn_prev_set(phn1, NULL, offset);
				phn_next_set(phn1, NULL, offset);
				phn0 = phn_merge(phn0, phn1, offset, cmp);
				phn_next_set(tail, phn0, offset);
				tail = phn0;
				phn0 = phnrest;
			} else {
				phn_next_set(tail, phn0, offset);
				tail = phn0;
				phn0 = NULL;
			}
		}
		phn0 = head;
		phn1 = phn_next_get(phn0, offset);
		if (phn1 != NULL) {
			while (true) {
				head = phn_next_get(phn1, offset);
				assert(phn_prev_get(phn0, offset) == NULL);
				phn_next_set(phn0, NULL, offset);
				assert(phn_prev_get(phn1, offset) == NULL);
				phn_next_set(phn1, NULL, offset);
				phn0 = phn_merge(phn0, phn1, offset, cmp);
				if (head == NULL) {
					break;
				}
				phn_next_set(tail, phn0, offset);
				tail = phn0;
				phn0 = head;
				phn1 = phn_next_get(phn0, offset);
			}
		}
	}
	return phn0;
}

JEMALLOC_ALWAYS_INLINE void
ph_merge_aux(ph_t *ph, size_t offset, ph_cmp_t cmp) {
	ph->auxcount = 0;
	void *phn = phn_next_get(ph->root, offset);
	if (phn != NULL) {
		phn_prev_set(ph->root, NULL, offset);
		phn_next_set(ph->root, NULL, offset);
		phn_prev_set(phn, NULL, offset);
		phn = phn_merge_siblings(phn, offset, cmp);
		assert(phn_next_get(phn, offset) == NULL);
		ph->root = phn_merge(ph->root, phn, offset, cmp);
	}
}

JEMALLOC_ALWAYS_INLINE void *
ph_merge_children(void *phn, size_t offset, ph_cmp_t cmp) {
	void *result;
	void *lchild = phn_lchild_get(phn, offset);
	if (lchild == NULL) {
		result = NULL;
	} else {
		result = phn_merge_siblings(lchild, offset, cmp);
	}
	return result;
}

JEMALLOC_ALWAYS_INLINE void
ph_new(ph_t *ph) {
	ph->root = NULL;
	ph->auxcount = 0;
}

JEMALLOC_ALWAYS_INLINE bool
ph_empty(ph_t *ph) {
	return ph->root == NULL;
}

JEMALLOC_ALWAYS_INLINE void *
ph_first(ph_t *ph, size_t offset, ph_cmp_t cmp) {
	if (ph->root == NULL) {
		return NULL;
	}
	ph_merge_aux(ph, offset, cmp);
	return ph->root;
}

JEMALLOC_ALWAYS_INLINE void *
ph_any(ph_t *ph, size_t offset) {
	if (ph->root == NULL) {
		return NULL;
	}
	void *aux = phn_next_get(ph->root, offset);
	if (aux != NULL) {
		return aux;
	}
	return ph->root;
}

/* Returns true if we should stop trying to merge. */
JEMALLOC_ALWAYS_INLINE bool
ph_try_aux_merge_pair(ph_t *ph, size_t offset, ph_cmp_t cmp) {
	assert(ph->root != NULL);
	void *phn0 = phn_next_get(ph->root, offset);
	if (phn0 == NULL) {
		return true;
	}
	void *phn1 = phn_next_get(phn0, offset);
	if (phn1 == NULL) {
		return true;
	}
	void *next_phn1 = phn_next_get(phn1, offset);
	phn_next_set(phn0, NULL, offset);
	phn_prev_set(phn0, NULL, offset);
	phn_next_set(phn1, NULL, offset);
	phn_prev_set(phn1, NULL, offset);
	phn0 = phn_merge(phn0, phn1, offset, cmp);
	phn_next_set(phn0, next_phn1, offset);
	if (next_phn1 != NULL) {
		phn_prev_set(next_phn1, phn0, offset);
	}
	phn_next_set(ph->root, phn0, offset);
	phn_prev_set(phn0, ph->root, offset);
	return next_phn1 == NULL;
}

JEMALLOC_ALWAYS_INLINE void
ph_insert(ph_t *ph, void *phn, size_t offset, ph_cmp_t cmp) {
	phn_link_init(phn, offset);

	/*
	 * Treat the root as an aux list during insertion, and lazily merge
	 * during a_prefix##remove_first().  For elements that are inserted,
	 * then removed via a_prefix##remove() before the aux list is ever
	 * processed, this makes insert/remove constant-time, whereas eager
	 * merging would make insert O(log n).
	 */
	if (ph->root == NULL) {
		ph->root = phn;
	} else {
		/*
		 * As a special case, check to see if we can replace the root.
		 * This is practically common in some important cases, and lets
		 * us defer some insertions (hopefully, until the point where
		 * some of the items in the aux list have been removed, savings
		 * us from linking them at all).
		 */
		if (cmp(phn, ph->root) < 0) {
			phn_lchild_set(phn, ph->root, offset);
			phn_prev_set(ph->root, phn, offset);
			ph->root = phn;
			ph->auxcount = 0;
			return;
		}
		ph->auxcount++;
		phn_next_set(phn, phn_next_get(ph->root, offset), offset);
		if (phn_next_get(ph->root, offset) != NULL) {
			phn_prev_set(phn_next_get(ph->root, offset), phn,
			    offset);
		}
		phn_prev_set(phn, ph->root, offset);
		phn_next_set(ph->root, phn, offset);
	}
	if (ph->auxcount > 1) {
		unsigned nmerges = ffs_zu(ph->auxcount - 1);
		bool done = false;
		for (unsigned i = 0; i < nmerges && !done; i++) {
			done = ph_try_aux_merge_pair(ph, offset, cmp);
		}
	}
}

JEMALLOC_ALWAYS_INLINE void *
ph_remove_first(ph_t *ph, size_t offset, ph_cmp_t cmp) {
	void *ret;

	if (ph->root == NULL) {
		return NULL;
	}
	ph_merge_aux(ph, offset, cmp);
	ret = ph->root;
	ph->root = ph_merge_children(ph->root, offset, cmp);

	return ret;

}

JEMALLOC_ALWAYS_INLINE void
ph_remove(ph_t *ph, void *phn, size_t offset, ph_cmp_t cmp) {
	void *replace;
	void *parent;

	if (ph->root == phn) {
		/*
		 * We can delete from aux list without merging it, but we need
		 * to merge if we are dealing with the root node and it has
		 * children.
		 */
		if (phn_lchild_get(phn, offset) == NULL) {
			ph->root = phn_next_get(phn, offset);
			if (ph->root != NULL) {
				phn_prev_set(ph->root, NULL, offset);
			}
			return;
		}
		ph_merge_aux(ph, offset, cmp);
		if (ph->root == phn) {
			ph->root = ph_merge_children(ph->root, offset, cmp);
			return;
		}
	}

	/* Get parent (if phn is leftmost child) before mutating. */
	if ((parent = phn_prev_get(phn, offset)) != NULL) {
		if (phn_lchild_get(parent, offset) != phn) {
			parent = NULL;
		}
	}
	/* Find a possible replacement node, and link to parent. */
	replace = ph_merge_children(phn, offset, cmp);
	/* Set next/prev for sibling linked list. */
	if (replace != NULL) {
		if (parent != NULL) {
			phn_prev_set(replace, parent, offset);
			phn_lchild_set(parent, replace, offset);
		} else {
			phn_prev_set(replace, phn_prev_get(phn, offset),
			    offset);
			if (phn_prev_get(phn, offset) != NULL) {
				phn_next_set(phn_prev_get(phn, offset), replace,
				    offset);
			}
		}
		phn_next_set(replace, phn_next_get(phn, offset), offset);
		if (phn_next_get(phn, offset) != NULL) {
			phn_prev_set(phn_next_get(phn, offset), replace,
			    offset);
		}
	} else {
		if (parent != NULL) {
			void *next = phn_next_get(phn, offset);
			phn_lchild_set(parent, next, offset);
			if (next != NULL) {
				phn_prev_set(next, parent, offset);
			}
		} else {
			assert(phn_prev_get(phn, offset) != NULL);
			phn_next_set(
			    phn_prev_get(phn, offset),
			    phn_next_get(phn, offset), offset);
		}
		if (phn_next_get(phn, offset) != NULL) {
			phn_prev_set(
			    phn_next_get(phn, offset),
			    phn_prev_get(phn, offset), offset);
		}
	}
}

#define ph_structs(a_prefix, a_type)					\
typedef struct {							\
	phn_link_t link;						\
} a_prefix##_link_t;							\
									\
typedef struct {							\
	ph_t ph;							\
} a_prefix##_t;

/*
 * The ph_proto() macro generates function prototypes that correspond to the
 * functions generated by an equivalently parameterized call to ph_gen().
 */
#define ph_proto(a_attr, a_prefix, a_type)				\
									\
a_attr void a_prefix##_new(a_prefix##_t *ph);				\
a_attr bool a_prefix##_empty(a_prefix##_t *ph);				\
a_attr a_type *a_prefix##_first(a_prefix##_t *ph);			\
a_attr a_type *a_prefix##_any(a_prefix##_t *ph);			\
a_attr void a_prefix##_insert(a_prefix##_t *ph, a_type *phn);		\
a_attr a_type *a_prefix##_remove_first(a_prefix##_t *ph);		\
a_attr void a_prefix##_remove(a_prefix##_t *ph, a_type *phn);		\
a_attr a_type *a_prefix##_remove_any(a_prefix##_t *ph);

/* The ph_gen() macro generates a type-specific pairing heap implementation. */
#define ph_gen(a_attr, a_prefix, a_type, a_field, a_cmp)		\
JEMALLOC_ALWAYS_INLINE int						\
a_prefix##_ph_cmp(void *a, void *b) {					\
	return a_cmp((a_type *)a, (a_type *)b);				\
}									\
									\
a_attr void								\
a_prefix##_new(a_prefix##_t *ph) {					\
	ph_new(&ph->ph);						\
}									\
									\
a_attr bool								\
a_prefix##_empty(a_prefix##_t *ph) {					\
	return ph_empty(&ph->ph);					\
}									\
									\
a_attr a_type *								\
a_prefix##_first(a_prefix##_t *ph) {					\
	return ph_first(&ph->ph, offsetof(a_type, a_field),		\
	    &a_prefix##_ph_cmp);					\
}									\
									\
a_attr a_type *								\
a_prefix##_any(a_prefix##_t *ph) {					\
	return ph_any(&ph->ph, offsetof(a_type, a_field));		\
}									\
									\
a_attr void								\
a_prefix##_insert(a_prefix##_t *ph, a_type *phn) {			\
	ph_insert(&ph->ph, phn, offsetof(a_type, a_field),		\
	    a_prefix##_ph_cmp);						\
}									\
									\
a_attr a_type *								\
a_prefix##_remove_first(a_prefix##_t *ph) {				\
	return ph_remove_first(&ph->ph, offsetof(a_type, a_field),	\
	    a_prefix##_ph_cmp);						\
}									\
									\
a_attr void								\
a_prefix##_remove(a_prefix##_t *ph, a_type *phn) {			\
	ph_remove(&ph->ph, phn, offsetof(a_type, a_field),		\
	    a_prefix##_ph_cmp);						\
}									\
									\
a_attr a_type *								\
a_prefix##_remove_any(a_prefix##_t *ph) {				\
	a_type *ret = a_prefix##_any(ph);				\
	if (ret != NULL) {						\
		a_prefix##_remove(ph, ret);				\
	}								\
	return ret;							\
}

#endif /* JEMALLOC_INTERNAL_PH_H */