2 * Resizable, Scalable, Concurrent Hash Table
4 * Copyright (c) 2015 Herbert Xu <herbert@gondor.apana.org.au>
5 * Copyright (c) 2014-2015 Thomas Graf <tgraf@suug.ch>
6 * Copyright (c) 2008-2014 Patrick McHardy <kaber@trash.net>
8 * Code partially derived from nft_hash
9 * Rewritten with rehash code from br_multicast plus single list
10 * pointer as suggested by Josh Triplett
12 * This program is free software; you can redistribute it and/or modify
13 * it under the terms of the GNU General Public License version 2 as
14 * published by the Free Software Foundation.
17 #include <linux/atomic.h>
18 #include <linux/kernel.h>
19 #include <linux/init.h>
20 #include <linux/log2.h>
21 #include <linux/sched.h>
22 #include <linux/slab.h>
23 #include <linux/vmalloc.h>
25 #include <linux/jhash.h>
26 #include <linux/random.h>
27 #include <linux/rhashtable.h>
28 #include <linux/err.h>
29 #include <linux/export.h>
31 #define HASH_DEFAULT_SIZE 64UL
32 #define HASH_MIN_SIZE 4U
33 #define BUCKET_LOCKS_PER_CPU 128UL
35 static u32
head_hashfn(struct rhashtable
*ht
,
36 const struct bucket_table
*tbl
,
37 const struct rhash_head
*he
)
39 return rht_head_hashfn(ht
, tbl
, he
, ht
->p
);
42 #ifdef CONFIG_PROVE_LOCKING
43 #define ASSERT_RHT_MUTEX(HT) BUG_ON(!lockdep_rht_mutex_is_held(HT))
45 int lockdep_rht_mutex_is_held(struct rhashtable
*ht
)
47 return (debug_locks
) ? lockdep_is_held(&ht
->mutex
) : 1;
49 EXPORT_SYMBOL_GPL(lockdep_rht_mutex_is_held
);
51 int lockdep_rht_bucket_is_held(const struct bucket_table
*tbl
, u32 hash
)
53 spinlock_t
*lock
= rht_bucket_lock(tbl
, hash
);
55 return (debug_locks
) ? lockdep_is_held(lock
) : 1;
57 EXPORT_SYMBOL_GPL(lockdep_rht_bucket_is_held
);
59 #define ASSERT_RHT_MUTEX(HT)
63 static int alloc_bucket_locks(struct rhashtable
*ht
, struct bucket_table
*tbl
,
67 #if defined(CONFIG_PROVE_LOCKING)
68 unsigned int nr_pcpus
= 2;
70 unsigned int nr_pcpus
= num_possible_cpus();
73 nr_pcpus
= min_t(unsigned int, nr_pcpus
, 32UL);
74 size
= roundup_pow_of_two(nr_pcpus
* ht
->p
.locks_mul
);
76 /* Never allocate more than 0.5 locks per bucket */
77 size
= min_t(unsigned int, size
, tbl
->size
>> 1);
79 if (sizeof(spinlock_t
) != 0) {
81 if (size
* sizeof(spinlock_t
) > PAGE_SIZE
&&
83 tbl
->locks
= vmalloc(size
* sizeof(spinlock_t
));
86 tbl
->locks
= kmalloc_array(size
, sizeof(spinlock_t
),
90 for (i
= 0; i
< size
; i
++)
91 spin_lock_init(&tbl
->locks
[i
]);
93 tbl
->locks_mask
= size
- 1;
98 static void bucket_table_free(const struct bucket_table
*tbl
)
106 static void bucket_table_free_rcu(struct rcu_head
*head
)
108 bucket_table_free(container_of(head
, struct bucket_table
, rcu
));
111 static struct bucket_table
*bucket_table_alloc(struct rhashtable
*ht
,
115 struct bucket_table
*tbl
= NULL
;
119 size
= sizeof(*tbl
) + nbuckets
* sizeof(tbl
->buckets
[0]);
120 if (size
<= (PAGE_SIZE
<< PAGE_ALLOC_COSTLY_ORDER
) ||
122 tbl
= kzalloc(size
, gfp
| __GFP_NOWARN
| __GFP_NORETRY
);
123 if (tbl
== NULL
&& gfp
== GFP_KERNEL
)
128 tbl
->size
= nbuckets
;
130 if (alloc_bucket_locks(ht
, tbl
, gfp
) < 0) {
131 bucket_table_free(tbl
);
135 INIT_LIST_HEAD(&tbl
->walkers
);
137 get_random_bytes(&tbl
->hash_rnd
, sizeof(tbl
->hash_rnd
));
139 for (i
= 0; i
< nbuckets
; i
++)
140 INIT_RHT_NULLS_HEAD(tbl
->buckets
[i
], ht
, i
);
145 static struct bucket_table
*rhashtable_last_table(struct rhashtable
*ht
,
146 struct bucket_table
*tbl
)
148 struct bucket_table
*new_tbl
;
152 tbl
= rht_dereference_rcu(tbl
->future_tbl
, ht
);
158 static int rhashtable_rehash_one(struct rhashtable
*ht
, unsigned int old_hash
)
160 struct bucket_table
*old_tbl
= rht_dereference(ht
->tbl
, ht
);
161 struct bucket_table
*new_tbl
= rhashtable_last_table(ht
,
162 rht_dereference_rcu(old_tbl
->future_tbl
, ht
));
163 struct rhash_head __rcu
**pprev
= &old_tbl
->buckets
[old_hash
];
165 struct rhash_head
*head
, *next
, *entry
;
166 spinlock_t
*new_bucket_lock
;
167 unsigned int new_hash
;
169 rht_for_each(entry
, old_tbl
, old_hash
) {
171 next
= rht_dereference_bucket(entry
->next
, old_tbl
, old_hash
);
173 if (rht_is_a_nulls(next
))
176 pprev
= &entry
->next
;
182 new_hash
= head_hashfn(ht
, new_tbl
, entry
);
184 new_bucket_lock
= rht_bucket_lock(new_tbl
, new_hash
);
186 spin_lock_nested(new_bucket_lock
, SINGLE_DEPTH_NESTING
);
187 head
= rht_dereference_bucket(new_tbl
->buckets
[new_hash
],
190 RCU_INIT_POINTER(entry
->next
, head
);
192 rcu_assign_pointer(new_tbl
->buckets
[new_hash
], entry
);
193 spin_unlock(new_bucket_lock
);
195 rcu_assign_pointer(*pprev
, next
);
201 static void rhashtable_rehash_chain(struct rhashtable
*ht
,
202 unsigned int old_hash
)
204 struct bucket_table
*old_tbl
= rht_dereference(ht
->tbl
, ht
);
205 spinlock_t
*old_bucket_lock
;
207 old_bucket_lock
= rht_bucket_lock(old_tbl
, old_hash
);
209 spin_lock_bh(old_bucket_lock
);
210 while (!rhashtable_rehash_one(ht
, old_hash
))
213 spin_unlock_bh(old_bucket_lock
);
216 static int rhashtable_rehash_attach(struct rhashtable
*ht
,
217 struct bucket_table
*old_tbl
,
218 struct bucket_table
*new_tbl
)
220 /* Protect future_tbl using the first bucket lock. */
221 spin_lock_bh(old_tbl
->locks
);
223 /* Did somebody beat us to it? */
224 if (rcu_access_pointer(old_tbl
->future_tbl
)) {
225 spin_unlock_bh(old_tbl
->locks
);
229 /* Make insertions go into the new, empty table right away. Deletions
230 * and lookups will be attempted in both tables until we synchronize.
232 rcu_assign_pointer(old_tbl
->future_tbl
, new_tbl
);
234 spin_unlock_bh(old_tbl
->locks
);
239 static int rhashtable_rehash_table(struct rhashtable
*ht
)
241 struct bucket_table
*old_tbl
= rht_dereference(ht
->tbl
, ht
);
242 struct bucket_table
*new_tbl
;
243 struct rhashtable_walker
*walker
;
244 unsigned int old_hash
;
246 new_tbl
= rht_dereference(old_tbl
->future_tbl
, ht
);
250 for (old_hash
= 0; old_hash
< old_tbl
->size
; old_hash
++)
251 rhashtable_rehash_chain(ht
, old_hash
);
253 /* Publish the new table pointer. */
254 rcu_assign_pointer(ht
->tbl
, new_tbl
);
256 spin_lock(&ht
->lock
);
257 list_for_each_entry(walker
, &old_tbl
->walkers
, list
)
259 spin_unlock(&ht
->lock
);
261 /* Wait for readers. All new readers will see the new
262 * table, and thus no references to the old table will
265 call_rcu(&old_tbl
->rcu
, bucket_table_free_rcu
);
267 return rht_dereference(new_tbl
->future_tbl
, ht
) ? -EAGAIN
: 0;
271 * rhashtable_expand - Expand hash table while allowing concurrent lookups
272 * @ht: the hash table to expand
274 * A secondary bucket array is allocated and the hash entries are migrated.
276 * This function may only be called in a context where it is safe to call
277 * synchronize_rcu(), e.g. not within a rcu_read_lock() section.
279 * The caller must ensure that no concurrent resizing occurs by holding
282 * It is valid to have concurrent insertions and deletions protected by per
283 * bucket locks or concurrent RCU protected lookups and traversals.
285 static int rhashtable_expand(struct rhashtable
*ht
)
287 struct bucket_table
*new_tbl
, *old_tbl
= rht_dereference(ht
->tbl
, ht
);
290 ASSERT_RHT_MUTEX(ht
);
292 old_tbl
= rhashtable_last_table(ht
, old_tbl
);
294 new_tbl
= bucket_table_alloc(ht
, old_tbl
->size
* 2, GFP_KERNEL
);
298 err
= rhashtable_rehash_attach(ht
, old_tbl
, new_tbl
);
300 bucket_table_free(new_tbl
);
306 * rhashtable_shrink - Shrink hash table while allowing concurrent lookups
307 * @ht: the hash table to shrink
309 * This function shrinks the hash table to fit, i.e., the smallest
310 * size would not cause it to expand right away automatically.
312 * The caller must ensure that no concurrent resizing occurs by holding
315 * The caller must ensure that no concurrent table mutations take place.
316 * It is however valid to have concurrent lookups if they are RCU protected.
318 * It is valid to have concurrent insertions and deletions protected by per
319 * bucket locks or concurrent RCU protected lookups and traversals.
321 static int rhashtable_shrink(struct rhashtable
*ht
)
323 struct bucket_table
*new_tbl
, *old_tbl
= rht_dereference(ht
->tbl
, ht
);
327 ASSERT_RHT_MUTEX(ht
);
329 size
= roundup_pow_of_two(atomic_read(&ht
->nelems
) * 3 / 2);
330 if (size
< ht
->p
.min_size
)
331 size
= ht
->p
.min_size
;
333 if (old_tbl
->size
<= size
)
336 if (rht_dereference(old_tbl
->future_tbl
, ht
))
339 new_tbl
= bucket_table_alloc(ht
, size
, GFP_KERNEL
);
343 err
= rhashtable_rehash_attach(ht
, old_tbl
, new_tbl
);
345 bucket_table_free(new_tbl
);
350 static void rht_deferred_worker(struct work_struct
*work
)
352 struct rhashtable
*ht
;
353 struct bucket_table
*tbl
;
356 ht
= container_of(work
, struct rhashtable
, run_work
);
357 mutex_lock(&ht
->mutex
);
359 tbl
= rht_dereference(ht
->tbl
, ht
);
360 tbl
= rhashtable_last_table(ht
, tbl
);
362 if (rht_grow_above_75(ht
, tbl
))
363 rhashtable_expand(ht
);
364 else if (ht
->p
.automatic_shrinking
&& rht_shrink_below_30(ht
, tbl
))
365 rhashtable_shrink(ht
);
367 err
= rhashtable_rehash_table(ht
);
369 mutex_unlock(&ht
->mutex
);
372 schedule_work(&ht
->run_work
);
375 static bool rhashtable_check_elasticity(struct rhashtable
*ht
,
376 struct bucket_table
*tbl
,
379 unsigned int elasticity
= ht
->elasticity
;
380 struct rhash_head
*head
;
382 rht_for_each(head
, tbl
, hash
)
389 int rhashtable_insert_rehash(struct rhashtable
*ht
,
390 struct bucket_table
*tbl
)
392 struct bucket_table
*old_tbl
;
393 struct bucket_table
*new_tbl
;
397 old_tbl
= rht_dereference_rcu(ht
->tbl
, ht
);
403 if (rht_grow_above_75(ht
, tbl
))
405 /* Do not schedule more than one rehash */
406 else if (old_tbl
!= tbl
)
411 new_tbl
= bucket_table_alloc(ht
, size
, GFP_ATOMIC
);
415 err
= rhashtable_rehash_attach(ht
, tbl
, new_tbl
);
417 bucket_table_free(new_tbl
);
421 schedule_work(&ht
->run_work
);
426 /* Do not fail the insert if someone else did a rehash. */
427 if (likely(rcu_dereference_raw(tbl
->future_tbl
)))
430 /* Schedule async rehash to retry allocation in process context. */
432 schedule_work(&ht
->run_work
);
436 EXPORT_SYMBOL_GPL(rhashtable_insert_rehash
);
438 struct bucket_table
*rhashtable_insert_slow(struct rhashtable
*ht
,
440 struct rhash_head
*obj
,
441 struct bucket_table
*tbl
)
443 struct rhash_head
*head
;
447 tbl
= rhashtable_last_table(ht
, tbl
);
448 hash
= head_hashfn(ht
, tbl
, obj
);
449 spin_lock_nested(rht_bucket_lock(tbl
, hash
), SINGLE_DEPTH_NESTING
);
452 if (key
&& rhashtable_lookup_fast(ht
, key
, ht
->p
))
456 if (unlikely(rht_grow_above_max(ht
, tbl
)))
460 if (rhashtable_check_elasticity(ht
, tbl
, hash
) ||
461 rht_grow_above_100(ht
, tbl
))
466 head
= rht_dereference_bucket(tbl
->buckets
[hash
], tbl
, hash
);
468 RCU_INIT_POINTER(obj
->next
, head
);
470 rcu_assign_pointer(tbl
->buckets
[hash
], obj
);
472 atomic_inc(&ht
->nelems
);
475 spin_unlock(rht_bucket_lock(tbl
, hash
));
479 else if (err
== -EAGAIN
)
484 EXPORT_SYMBOL_GPL(rhashtable_insert_slow
);
487 * rhashtable_walk_init - Initialise an iterator
488 * @ht: Table to walk over
489 * @iter: Hash table Iterator
491 * This function prepares a hash table walk.
493 * Note that if you restart a walk after rhashtable_walk_stop you
494 * may see the same object twice. Also, you may miss objects if
495 * there are removals in between rhashtable_walk_stop and the next
496 * call to rhashtable_walk_start.
498 * For a completely stable walk you should construct your own data
499 * structure outside the hash table.
501 * This function may sleep so you must not call it from interrupt
502 * context or with spin locks held.
504 * You must call rhashtable_walk_exit if this function returns
507 int rhashtable_walk_init(struct rhashtable
*ht
, struct rhashtable_iter
*iter
)
514 iter
->walker
= kmalloc(sizeof(*iter
->walker
), GFP_KERNEL
);
518 spin_lock(&ht
->lock
);
520 rcu_dereference_protected(ht
->tbl
, lockdep_is_held(&ht
->lock
));
521 list_add(&iter
->walker
->list
, &iter
->walker
->tbl
->walkers
);
522 spin_unlock(&ht
->lock
);
526 EXPORT_SYMBOL_GPL(rhashtable_walk_init
);
529 * rhashtable_walk_exit - Free an iterator
530 * @iter: Hash table Iterator
532 * This function frees resources allocated by rhashtable_walk_init.
534 void rhashtable_walk_exit(struct rhashtable_iter
*iter
)
536 spin_lock(&iter
->ht
->lock
);
537 if (iter
->walker
->tbl
)
538 list_del(&iter
->walker
->list
);
539 spin_unlock(&iter
->ht
->lock
);
542 EXPORT_SYMBOL_GPL(rhashtable_walk_exit
);
545 * rhashtable_walk_start - Start a hash table walk
546 * @iter: Hash table iterator
548 * Start a hash table walk. Note that we take the RCU lock in all
549 * cases including when we return an error. So you must always call
550 * rhashtable_walk_stop to clean up.
552 * Returns zero if successful.
554 * Returns -EAGAIN if resize event occured. Note that the iterator
555 * will rewind back to the beginning and you may use it immediately
556 * by calling rhashtable_walk_next.
558 int rhashtable_walk_start(struct rhashtable_iter
*iter
)
561 struct rhashtable
*ht
= iter
->ht
;
565 spin_lock(&ht
->lock
);
566 if (iter
->walker
->tbl
)
567 list_del(&iter
->walker
->list
);
568 spin_unlock(&ht
->lock
);
570 if (!iter
->walker
->tbl
) {
571 iter
->walker
->tbl
= rht_dereference_rcu(ht
->tbl
, ht
);
577 EXPORT_SYMBOL_GPL(rhashtable_walk_start
);
580 * rhashtable_walk_next - Return the next object and advance the iterator
581 * @iter: Hash table iterator
583 * Note that you must call rhashtable_walk_stop when you are finished
586 * Returns the next object or NULL when the end of the table is reached.
588 * Returns -EAGAIN if resize event occured. Note that the iterator
589 * will rewind back to the beginning and you may continue to use it.
591 void *rhashtable_walk_next(struct rhashtable_iter
*iter
)
593 struct bucket_table
*tbl
= iter
->walker
->tbl
;
594 struct rhashtable
*ht
= iter
->ht
;
595 struct rhash_head
*p
= iter
->p
;
598 p
= rht_dereference_bucket_rcu(p
->next
, tbl
, iter
->slot
);
602 for (; iter
->slot
< tbl
->size
; iter
->slot
++) {
603 int skip
= iter
->skip
;
605 rht_for_each_rcu(p
, tbl
, iter
->slot
) {
612 if (!rht_is_a_nulls(p
)) {
615 return rht_obj(ht
, p
);
623 /* Ensure we see any new tables. */
626 iter
->walker
->tbl
= rht_dereference_rcu(tbl
->future_tbl
, ht
);
627 if (iter
->walker
->tbl
) {
630 return ERR_PTR(-EAGAIN
);
635 EXPORT_SYMBOL_GPL(rhashtable_walk_next
);
638 * rhashtable_walk_stop - Finish a hash table walk
639 * @iter: Hash table iterator
641 * Finish a hash table walk.
643 void rhashtable_walk_stop(struct rhashtable_iter
*iter
)
646 struct rhashtable
*ht
;
647 struct bucket_table
*tbl
= iter
->walker
->tbl
;
654 spin_lock(&ht
->lock
);
655 if (tbl
->rehash
< tbl
->size
)
656 list_add(&iter
->walker
->list
, &tbl
->walkers
);
658 iter
->walker
->tbl
= NULL
;
659 spin_unlock(&ht
->lock
);
666 EXPORT_SYMBOL_GPL(rhashtable_walk_stop
);
668 static size_t rounded_hashtable_size(const struct rhashtable_params
*params
)
670 return max(roundup_pow_of_two(params
->nelem_hint
* 4 / 3),
671 (unsigned long)params
->min_size
);
674 static u32
rhashtable_jhash2(const void *key
, u32 length
, u32 seed
)
676 return jhash2(key
, length
, seed
);
680 * rhashtable_init - initialize a new hash table
681 * @ht: hash table to be initialized
682 * @params: configuration parameters
684 * Initializes a new hash table based on the provided configuration
685 * parameters. A table can be configured either with a variable or
688 * Configuration Example 1: Fixed length keys
692 * struct rhash_head node;
695 * struct rhashtable_params params = {
696 * .head_offset = offsetof(struct test_obj, node),
697 * .key_offset = offsetof(struct test_obj, key),
698 * .key_len = sizeof(int),
700 * .nulls_base = (1U << RHT_BASE_SHIFT),
703 * Configuration Example 2: Variable length keys
706 * struct rhash_head node;
709 * u32 my_hash_fn(const void *data, u32 len, u32 seed)
711 * struct test_obj *obj = data;
713 * return [... hash ...];
716 * struct rhashtable_params params = {
717 * .head_offset = offsetof(struct test_obj, node),
719 * .obj_hashfn = my_hash_fn,
722 int rhashtable_init(struct rhashtable
*ht
,
723 const struct rhashtable_params
*params
)
725 struct bucket_table
*tbl
;
728 size
= HASH_DEFAULT_SIZE
;
730 if ((!params
->key_len
&& !params
->obj_hashfn
) ||
731 (params
->obj_hashfn
&& !params
->obj_cmpfn
))
734 if (params
->nulls_base
&& params
->nulls_base
< (1U << RHT_BASE_SHIFT
))
737 memset(ht
, 0, sizeof(*ht
));
738 mutex_init(&ht
->mutex
);
739 spin_lock_init(&ht
->lock
);
740 memcpy(&ht
->p
, params
, sizeof(*params
));
742 if (params
->min_size
)
743 ht
->p
.min_size
= roundup_pow_of_two(params
->min_size
);
745 if (params
->max_size
)
746 ht
->p
.max_size
= rounddown_pow_of_two(params
->max_size
);
748 if (params
->insecure_max_entries
)
749 ht
->p
.insecure_max_entries
=
750 rounddown_pow_of_two(params
->insecure_max_entries
);
752 ht
->p
.insecure_max_entries
= ht
->p
.max_size
* 2;
754 ht
->p
.min_size
= max(ht
->p
.min_size
, HASH_MIN_SIZE
);
756 if (params
->nelem_hint
)
757 size
= rounded_hashtable_size(&ht
->p
);
759 /* The maximum (not average) chain length grows with the
760 * size of the hash table, at a rate of (log N)/(log log N).
761 * The value of 16 is selected so that even if the hash
762 * table grew to 2^32 you would not expect the maximum
763 * chain length to exceed it unless we are under attack
764 * (or extremely unlucky).
766 * As this limit is only to detect attacks, we don't need
767 * to set it to a lower value as you'd need the chain
768 * length to vastly exceed 16 to have any real effect
771 if (!params
->insecure_elasticity
)
774 if (params
->locks_mul
)
775 ht
->p
.locks_mul
= roundup_pow_of_two(params
->locks_mul
);
777 ht
->p
.locks_mul
= BUCKET_LOCKS_PER_CPU
;
779 ht
->key_len
= ht
->p
.key_len
;
780 if (!params
->hashfn
) {
781 ht
->p
.hashfn
= jhash
;
783 if (!(ht
->key_len
& (sizeof(u32
) - 1))) {
784 ht
->key_len
/= sizeof(u32
);
785 ht
->p
.hashfn
= rhashtable_jhash2
;
789 tbl
= bucket_table_alloc(ht
, size
, GFP_KERNEL
);
793 atomic_set(&ht
->nelems
, 0);
795 RCU_INIT_POINTER(ht
->tbl
, tbl
);
797 INIT_WORK(&ht
->run_work
, rht_deferred_worker
);
801 EXPORT_SYMBOL_GPL(rhashtable_init
);
804 * rhashtable_free_and_destroy - free elements and destroy hash table
805 * @ht: the hash table to destroy
806 * @free_fn: callback to release resources of element
807 * @arg: pointer passed to free_fn
809 * Stops an eventual async resize. If defined, invokes free_fn for each
810 * element to releasal resources. Please note that RCU protected
811 * readers may still be accessing the elements. Releasing of resources
812 * must occur in a compatible manner. Then frees the bucket array.
814 * This function will eventually sleep to wait for an async resize
815 * to complete. The caller is responsible that no further write operations
816 * occurs in parallel.
818 void rhashtable_free_and_destroy(struct rhashtable
*ht
,
819 void (*free_fn
)(void *ptr
, void *arg
),
822 const struct bucket_table
*tbl
;
825 cancel_work_sync(&ht
->run_work
);
827 mutex_lock(&ht
->mutex
);
828 tbl
= rht_dereference(ht
->tbl
, ht
);
830 for (i
= 0; i
< tbl
->size
; i
++) {
831 struct rhash_head
*pos
, *next
;
833 for (pos
= rht_dereference(tbl
->buckets
[i
], ht
),
834 next
= !rht_is_a_nulls(pos
) ?
835 rht_dereference(pos
->next
, ht
) : NULL
;
836 !rht_is_a_nulls(pos
);
838 next
= !rht_is_a_nulls(pos
) ?
839 rht_dereference(pos
->next
, ht
) : NULL
)
840 free_fn(rht_obj(ht
, pos
), arg
);
844 bucket_table_free(tbl
);
845 mutex_unlock(&ht
->mutex
);
847 EXPORT_SYMBOL_GPL(rhashtable_free_and_destroy
);
849 void rhashtable_destroy(struct rhashtable
*ht
)
851 return rhashtable_free_and_destroy(ht
, NULL
, NULL
);
853 EXPORT_SYMBOL_GPL(rhashtable_destroy
);