summaryrefslogtreecommitdiff
path: root/include/linux/radix-tree.h
blob: 11c8e7cc392007811b5d673972af08056f9098a6 (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
524
525
526
527
528
529
530
531
532
533
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
/*
 * Copyright (C) 2001 Momchil Velikov
 * Portions Copyright (C) 2001 Christoph Hellwig
 * Copyright (C) 2006 Nick Piggin
 * Copyright (C) 2012 Konstantin Khlebnikov
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License as
 * published by the Free Software Foundation; either version 2, or (at
 * your option) any later version.
 * 
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 * 
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
 */
#ifndef _LINUX_RADIX_TREE_H
#define _LINUX_RADIX_TREE_H

#include <linux/bitops.h>
#include <linux/preempt.h>
#include <linux/types.h>
#include <linux/bug.h>
#include <linux/kernel.h>
#include <linux/rcupdate.h>

/*
 * Entries in the radix tree have the low bit set if they refer to a
 * radix_tree_node.  If the low bit is clear then the entry is user data.
 *
 * We also use the low bit to indicate that the slot will be freed in the
 * next RCU idle period, and users need to re-walk the tree to find the
 * new slot for the index that they were looking for.  See the comment in
 * radix_tree_shrink() for details.
 */
#define RADIX_TREE_INTERNAL_NODE	1

/*
 * A common use of the radix tree is to store pointers to struct pages;
 * but shmem/tmpfs needs also to store swap entries in the same tree:
 * those are marked as exceptional entries to distinguish them.
 * EXCEPTIONAL_ENTRY tests the bit, EXCEPTIONAL_SHIFT shifts content past it.
 */
#define RADIX_TREE_EXCEPTIONAL_ENTRY	2
#define RADIX_TREE_EXCEPTIONAL_SHIFT	2

#define RADIX_DAX_MASK	0xf
#define RADIX_DAX_SHIFT	4
#define RADIX_DAX_PTE  (0x4 | RADIX_TREE_EXCEPTIONAL_ENTRY)
#define RADIX_DAX_PMD  (0x8 | RADIX_TREE_EXCEPTIONAL_ENTRY)
#define RADIX_DAX_TYPE(entry) ((unsigned long)entry & RADIX_DAX_MASK)
#define RADIX_DAX_SECTOR(entry) (((unsigned long)entry >> RADIX_DAX_SHIFT))
#define RADIX_DAX_ENTRY(sector, pmd) ((void *)((unsigned long)sector << \
		RADIX_DAX_SHIFT | (pmd ? RADIX_DAX_PMD : RADIX_DAX_PTE)))

static inline int radix_tree_is_internal_node(void *ptr)
{
	return (int)((unsigned long)ptr & RADIX_TREE_INTERNAL_NODE);
}

/*** radix-tree API starts here ***/

#define RADIX_TREE_MAX_TAGS 3

#ifndef RADIX_TREE_MAP_SHIFT
#define RADIX_TREE_MAP_SHIFT	(CONFIG_BASE_SMALL ? 4 : 6)
#endif

#define RADIX_TREE_MAP_SIZE	(1UL << RADIX_TREE_MAP_SHIFT)
#define RADIX_TREE_MAP_MASK	(RADIX_TREE_MAP_SIZE-1)

#define RADIX_TREE_TAG_LONGS	\
	((RADIX_TREE_MAP_SIZE + BITS_PER_LONG - 1) / BITS_PER_LONG)

#define RADIX_TREE_INDEX_BITS  (8 /* CHAR_BIT */ * sizeof(unsigned long))
#define RADIX_TREE_MAX_PATH (DIV_ROUND_UP(RADIX_TREE_INDEX_BITS, \
					  RADIX_TREE_MAP_SHIFT))

/* Internally used bits of node->count */
#define RADIX_TREE_COUNT_SHIFT	(RADIX_TREE_MAP_SHIFT + 1)
#define RADIX_TREE_COUNT_MASK	((1UL << RADIX_TREE_COUNT_SHIFT) - 1)

struct radix_tree_node {
	unsigned char	shift;	/* Bits remaining in each slot */
	unsigned char	offset;	/* Slot offset in parent */
	unsigned int	count;
	union {
		struct {
			/* Used when ascending tree */
			struct radix_tree_node *parent;
			/* For tree user */
			void *private_data;
		};
		/* Used when freeing node */
		struct rcu_head	rcu_head;
	};
	/* For tree user */
	struct list_head private_list;
	void __rcu	*slots[RADIX_TREE_MAP_SIZE];
	unsigned long	tags[RADIX_TREE_MAX_TAGS][RADIX_TREE_TAG_LONGS];
};

/* root tags are stored in gfp_mask, shifted by __GFP_BITS_SHIFT */
struct radix_tree_root {
	gfp_t			gfp_mask;
	struct radix_tree_node	__rcu *rnode;
};

#define RADIX_TREE_INIT(mask)	{					\
	.gfp_mask = (mask),						\
	.rnode = NULL,							\
}

#define RADIX_TREE(name, mask) \
	struct radix_tree_root name = RADIX_TREE_INIT(mask)

#define INIT_RADIX_TREE(root, mask)					\
do {									\
	(root)->gfp_mask = (mask);					\
	(root)->rnode = NULL;						\
} while (0)

static inline bool radix_tree_empty(struct radix_tree_root *root)
{
	return root->rnode == NULL;
}

/**
 * Radix-tree synchronization
 *
 * The radix-tree API requires that users provide all synchronisation (with
 * specific exceptions, noted below).
 *
 * Synchronization of access to the data items being stored in the tree, and
 * management of their lifetimes must be completely managed by API users.
 *
 * For API usage, in general,
 * - any function _modifying_ the tree or tags (inserting or deleting
 *   items, setting or clearing tags) must exclude other modifications, and
 *   exclude any functions reading the tree.
 * - any function _reading_ the tree or tags (looking up items or tags,
 *   gang lookups) must exclude modifications to the tree, but may occur
 *   concurrently with other readers.
 *
 * The notable exceptions to this rule are the following functions:
 * __radix_tree_lookup
 * radix_tree_lookup
 * radix_tree_lookup_slot
 * radix_tree_tag_get
 * radix_tree_gang_lookup
 * radix_tree_gang_lookup_slot
 * radix_tree_gang_lookup_tag
 * radix_tree_gang_lookup_tag_slot
 * radix_tree_tagged
 *
 * The first 8 functions are able to be called locklessly, using RCU. The
 * caller must ensure calls to these functions are made within rcu_read_lock()
 * regions. Other readers (lock-free or otherwise) and modifications may be
 * running concurrently.
 *
 * It is still required that the caller manage the synchronization and lifetimes
 * of the items. So if RCU lock-free lookups are used, typically this would mean
 * that the items have their own locks, or are amenable to lock-free access; and
 * that the items are freed by RCU (or only freed after having been deleted from
 * the radix tree *and* a synchronize_rcu() grace period).
 *
 * (Note, rcu_assign_pointer and rcu_dereference are not needed to control
 * access to data items when inserting into or looking up from the radix tree)
 *
 * Note that the value returned by radix_tree_tag_get() may not be relied upon
 * if only the RCU read lock is held.  Functions to set/clear tags and to
 * delete nodes running concurrently with it may affect its result such that
 * two consecutive reads in the same locked section may return different
 * values.  If reliability is required, modification functions must also be
 * excluded from concurrency.
 *
 * radix_tree_tagged is able to be called without locking or RCU.
 */

/**
 * radix_tree_deref_slot	- dereference a slot
 * @pslot:	pointer to slot, returned by radix_tree_lookup_slot
 * Returns:	item that was stored in that slot with any direct pointer flag
 *		removed.
 *
 * For use with radix_tree_lookup_slot().  Caller must hold tree at least read
 * locked across slot lookup and dereference. Not required if write lock is
 * held (ie. items cannot be concurrently inserted).
 *
 * radix_tree_deref_retry must be used to confirm validity of the pointer if
 * only the read lock is held.
 */
static inline void *radix_tree_deref_slot(void **pslot)
{
	return rcu_dereference(*pslot);
}

/**
 * radix_tree_deref_slot_protected	- dereference a slot without RCU lock but with tree lock held
 * @pslot:	pointer to slot, returned by radix_tree_lookup_slot
 * Returns:	item that was stored in that slot with any direct pointer flag
 *		removed.
 *
 * Similar to radix_tree_deref_slot but only used during migration when a pages
 * mapping is being moved. The caller does not hold the RCU read lock but it
 * must hold the tree lock to prevent parallel updates.
 */
static inline void *radix_tree_deref_slot_protected(void **pslot,
							spinlock_t *treelock)
{
	return rcu_dereference_protected(*pslot, lockdep_is_held(treelock));
}

/**
 * radix_tree_deref_retry	- check radix_tree_deref_slot
 * @arg:	pointer returned by radix_tree_deref_slot
 * Returns:	0 if retry is not required, otherwise retry is required
 *
 * radix_tree_deref_retry must be used with radix_tree_deref_slot.
 */
static inline int radix_tree_deref_retry(void *arg)
{
	return unlikely(radix_tree_is_internal_node(arg));
}

/**
 * radix_tree_exceptional_entry	- radix_tree_deref_slot gave exceptional entry?
 * @arg:	value returned by radix_tree_deref_slot
 * Returns:	0 if well-aligned pointer, non-0 if exceptional entry.
 */
static inline int radix_tree_exceptional_entry(void *arg)
{
	/* Not unlikely because radix_tree_exception often tested first */
	return (unsigned long)arg & RADIX_TREE_EXCEPTIONAL_ENTRY;
}

/**
 * radix_tree_exception	- radix_tree_deref_slot returned either exception?
 * @arg:	value returned by radix_tree_deref_slot
 * Returns:	0 if well-aligned pointer, non-0 if either kind of exception.
 */
static inline int radix_tree_exception(void *arg)
{
	return unlikely((unsigned long)arg &
		(RADIX_TREE_INTERNAL_NODE | RADIX_TREE_EXCEPTIONAL_ENTRY));
}

/**
 * radix_tree_replace_slot	- replace item in a slot
 * @pslot:	pointer to slot, returned by radix_tree_lookup_slot
 * @item:	new item to store in the slot.
 *
 * For use with radix_tree_lookup_slot().  Caller must hold tree write locked
 * across slot lookup and replacement.
 */
static inline void radix_tree_replace_slot(void **pslot, void *item)
{
	BUG_ON(radix_tree_is_internal_node(item));
	rcu_assign_pointer(*pslot, item);
}

int __radix_tree_create(struct radix_tree_root *root, unsigned long index,
			unsigned order, struct radix_tree_node **nodep,
			void ***slotp);
int __radix_tree_insert(struct radix_tree_root *, unsigned long index,
			unsigned order, void *);
static inline int radix_tree_insert(struct radix_tree_root *root,
			unsigned long index, void *entry)
{
	return __radix_tree_insert(root, index, 0, entry);
}
void *__radix_tree_lookup(struct radix_tree_root *root, unsigned long index,
			  struct radix_tree_node **nodep, void ***slotp);
void *radix_tree_lookup(struct radix_tree_root *, unsigned long);
void **radix_tree_lookup_slot(struct radix_tree_root *, unsigned long);
bool __radix_tree_delete_node(struct radix_tree_root *root,
			      struct radix_tree_node *node);
void *radix_tree_delete_item(struct radix_tree_root *, unsigned long, void *);
void *radix_tree_delete(struct radix_tree_root *, unsigned long);
struct radix_tree_node *radix_tree_replace_clear_tags(
				struct radix_tree_root *root,
				unsigned long index, void *entry);
unsigned int radix_tree_gang_lookup(struct radix_tree_root *root,
			void **results, unsigned long first_index,
			unsigned int max_items);
unsigned int radix_tree_gang_lookup_slot(struct radix_tree_root *root,
			void ***results, unsigned long *indices,
			unsigned long first_index, unsigned int max_items);
int radix_tree_preload(gfp_t gfp_mask);
int radix_tree_maybe_preload(gfp_t gfp_mask);
void radix_tree_init(void);
void *radix_tree_tag_set(struct radix_tree_root *root,
			unsigned long index, unsigned int tag);
void *radix_tree_tag_clear(struct radix_tree_root *root,
			unsigned long index, unsigned int tag);
int radix_tree_tag_get(struct radix_tree_root *root,
			unsigned long index, unsigned int tag);
unsigned int
radix_tree_gang_lookup_tag(struct radix_tree_root *root, void **results,
		unsigned long first_index, unsigned int max_items,
		unsigned int tag);
unsigned int
radix_tree_gang_lookup_tag_slot(struct radix_tree_root *root, void ***results,
		unsigned long first_index, unsigned int max_items,
		unsigned int tag);
unsigned long radix_tree_range_tag_if_tagged(struct radix_tree_root *root,
		unsigned long *first_indexp, unsigned long last_index,
		unsigned long nr_to_tag,
		unsigned int fromtag, unsigned int totag);
int radix_tree_tagged(struct radix_tree_root *root, unsigned int tag);
unsigned long radix_tree_locate_item(struct radix_tree_root *root, void *item);

static inline void radix_tree_preload_end(void)
{
	preempt_enable();
}

/**
 * struct radix_tree_iter - radix tree iterator state
 *
 * @index:	index of current slot
 * @next_index:	one beyond the last index for this chunk
 * @tags:	bit-mask for tag-iterating
 * @shift:	shift for the node that holds our slots
 *
 * This radix tree iterator works in terms of "chunks" of slots.  A chunk is a
 * subinterval of slots contained within one radix tree leaf node.  It is
 * described by a pointer to its first slot and a struct radix_tree_iter
 * which holds the chunk's position in the tree and its size.  For tagged
 * iteration radix_tree_iter also holds the slots' bit-mask for one chosen
 * radix tree tag.
 */
struct radix_tree_iter {
	unsigned long	index;
	unsigned long	next_index;
	unsigned long	tags;
#ifdef CONFIG_RADIX_TREE_MULTIORDER
	unsigned int	shift;
#endif
};

static inline unsigned int iter_shift(struct radix_tree_iter *iter)
{
#ifdef CONFIG_RADIX_TREE_MULTIORDER
	return iter->shift;
#else
	return 0;
#endif
}

#define RADIX_TREE_ITER_TAG_MASK	0x00FF	/* tag index in lower byte */
#define RADIX_TREE_ITER_TAGGED		0x0100	/* lookup tagged slots */
#define RADIX_TREE_ITER_CONTIG		0x0200	/* stop at first hole */

/**
 * radix_tree_iter_init - initialize radix tree iterator
 *
 * @iter:	pointer to iterator state
 * @start:	iteration starting index
 * Returns:	NULL
 */
static __always_inline void **
radix_tree_iter_init(struct radix_tree_iter *iter, unsigned long start)
{
	/*
	 * Leave iter->tags uninitialized. radix_tree_next_chunk() will fill it
	 * in the case of a successful tagged chunk lookup.  If the lookup was
	 * unsuccessful or non-tagged then nobody cares about ->tags.
	 *
	 * Set index to zero to bypass next_index overflow protection.
	 * See the comment in radix_tree_next_chunk() for details.
	 */
	iter->index = 0;
	iter->next_index = start;
	return NULL;
}

/**
 * radix_tree_next_chunk - find next chunk of slots for iteration
 *
 * @root:	radix tree root
 * @iter:	iterator state
 * @flags:	RADIX_TREE_ITER_* flags and tag index
 * Returns:	pointer to chunk first slot, or NULL if there no more left
 *
 * This function looks up the next chunk in the radix tree starting from
 * @iter->next_index.  It returns a pointer to the chunk's first slot.
 * Also it fills @iter with data about chunk: position in the tree (index),
 * its end (next_index), and constructs a bit mask for tagged iterating (tags).
 */
void **radix_tree_next_chunk(struct radix_tree_root *root,
			     struct radix_tree_iter *iter, unsigned flags);

/**
 * radix_tree_iter_retry - retry this chunk of the iteration
 * @iter:	iterator state
 *
 * If we iterate over a tree protected only by the RCU lock, a race
 * against deletion or creation may result in seeing a slot for which
 * radix_tree_deref_retry() returns true.  If so, call this function
 * and continue the iteration.
 */
static inline __must_check
void **radix_tree_iter_retry(struct radix_tree_iter *iter)
{
	iter->next_index = iter->index;
	return NULL;
}

static inline unsigned long
__radix_tree_iter_add(struct radix_tree_iter *iter, unsigned long slots)
{
	return iter->index + (slots << iter_shift(iter));
}

/**
 * radix_tree_iter_next - resume iterating when the chunk may be invalid
 * @iter:	iterator state
 *
 * If the iterator needs to release then reacquire a lock, the chunk may
 * have been invalidated by an insertion or deletion.  Call this function
 * to continue the iteration from the next index.
 */
static inline __must_check
void **radix_tree_iter_next(struct radix_tree_iter *iter)
{
	iter->next_index = __radix_tree_iter_add(iter, 1);
	iter->tags = 0;
	return NULL;
}

/**
 * radix_tree_chunk_size - get current chunk size
 *
 * @iter:	pointer to radix tree iterator
 * Returns:	current chunk size
 */
static __always_inline long
radix_tree_chunk_size(struct radix_tree_iter *iter)
{
	return (iter->next_index - iter->index) >> iter_shift(iter);
}

static inline struct radix_tree_node *entry_to_node(void *ptr)
{
	return (void *)((unsigned long)ptr & ~RADIX_TREE_INTERNAL_NODE);
}

/**
 * radix_tree_next_slot - find next slot in chunk
 *
 * @slot:	pointer to current slot
 * @iter:	pointer to interator state
 * @flags:	RADIX_TREE_ITER_*, should be constant
 * Returns:	pointer to next slot, or NULL if there no more left
 *
 * This function updates @iter->index in the case of a successful lookup.
 * For tagged lookup it also eats @iter->tags.
 */
static __always_inline void **
radix_tree_next_slot(void **slot, struct radix_tree_iter *iter, unsigned flags)
{
	if (flags & RADIX_TREE_ITER_TAGGED) {
		void *canon = slot;

		iter->tags >>= 1;
		if (unlikely(!iter->tags))
			return NULL;
		while (IS_ENABLED(CONFIG_RADIX_TREE_MULTIORDER) &&
					radix_tree_is_internal_node(slot[1])) {
			if (entry_to_node(slot[1]) == canon) {
				iter->tags >>= 1;
				iter->index = __radix_tree_iter_add(iter, 1);
				slot++;
				continue;
			}
			iter->next_index = __radix_tree_iter_add(iter, 1);
			return NULL;
		}
		if (likely(iter->tags & 1ul)) {
			iter->index = __radix_tree_iter_add(iter, 1);
			return slot + 1;
		}
		if (!(flags & RADIX_TREE_ITER_CONTIG)) {
			unsigned offset = __ffs(iter->tags);

			iter->tags >>= offset;
			iter->index = __radix_tree_iter_add(iter, offset + 1);
			return slot + offset + 1;
		}
	} else {
		long count = radix_tree_chunk_size(iter);
		void *canon = slot;

		while (--count > 0) {
			slot++;
			iter->index = __radix_tree_iter_add(iter, 1);

			if (IS_ENABLED(CONFIG_RADIX_TREE_MULTIORDER) &&
			    radix_tree_is_internal_node(*slot)) {
				if (entry_to_node(*slot) == canon)
					continue;
				iter->next_index = iter->index;
				break;
			}

			if (likely(*slot))
				return slot;
			if (flags & RADIX_TREE_ITER_CONTIG) {
				/* forbid switching to the next chunk */
				iter->next_index = 0;
				break;
			}
		}
	}
	return NULL;
}

/**
 * radix_tree_for_each_slot - iterate over non-empty slots
 *
 * @slot:	the void** variable for pointer to slot
 * @root:	the struct radix_tree_root pointer
 * @iter:	the struct radix_tree_iter pointer
 * @start:	iteration starting index
 *
 * @slot points to radix tree slot, @iter->index contains its index.
 */
#define radix_tree_for_each_slot(slot, root, iter, start)		\
	for (slot = radix_tree_iter_init(iter, start) ;			\
	     slot || (slot = radix_tree_next_chunk(root, iter, 0)) ;	\
	     slot = radix_tree_next_slot(slot, iter, 0))

/**
 * radix_tree_for_each_contig - iterate over contiguous slots
 *
 * @slot:	the void** variable for pointer to slot
 * @root:	the struct radix_tree_root pointer
 * @iter:	the struct radix_tree_iter pointer
 * @start:	iteration starting index
 *
 * @slot points to radix tree slot, @iter->index contains its index.
 */
#define radix_tree_for_each_contig(slot, root, iter, start)		\
	for (slot = radix_tree_iter_init(iter, start) ;			\
	     slot || (slot = radix_tree_next_chunk(root, iter,		\
				RADIX_TREE_ITER_CONTIG)) ;		\
	     slot = radix_tree_next_slot(slot, iter,			\
				RADIX_TREE_ITER_CONTIG))

/**
 * radix_tree_for_each_tagged - iterate over tagged slots
 *
 * @slot:	the void** variable for pointer to slot
 * @root:	the struct radix_tree_root pointer
 * @iter:	the struct radix_tree_iter pointer
 * @start:	iteration starting index
 * @tag:	tag index
 *
 * @slot points to radix tree slot, @iter->index contains its index.
 */
#define radix_tree_for_each_tagged(slot, root, iter, start, tag)	\
	for (slot = radix_tree_iter_init(iter, start) ;			\
	     slot || (slot = radix_tree_next_chunk(root, iter,		\
			      RADIX_TREE_ITER_TAGGED | tag)) ;		\
	     slot = radix_tree_next_slot(slot, iter,			\
				RADIX_TREE_ITER_TAGGED))

#endif /* _LINUX_RADIX_TREE_H */