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root/jsr166/jsr166/src/main/java/util/concurrent/Exchanger.java
Revision: 1.62
Committed: Sun Nov 25 21:48:00 2012 UTC (11 years, 6 months ago) by jsr166
Branch: MAIN
Changes since 1.61: +2 -2 lines
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File Contents

# Content
1 /*
2 * Written by Doug Lea, Bill Scherer, and Michael Scott with
3 * assistance from members of JCP JSR-166 Expert Group and released to
4 * the public domain, as explained at
5 * http://creativecommons.org/publicdomain/zero/1.0/
6 */
7
8 package java.util.concurrent;
9 import java.util.concurrent.atomic.AtomicInteger;
10 import java.util.concurrent.atomic.AtomicReference;
11 import java.util.concurrent.locks.LockSupport;
12
13 /**
14 * A synchronization point at which threads can pair and swap elements
15 * within pairs. Each thread presents some object on entry to the
16 * {@link #exchange exchange} method, matches with a partner thread,
17 * and receives its partner's object on return. An Exchanger may be
18 * viewed as a bidirectional form of a {@link SynchronousQueue}.
19 * Exchangers may be useful in applications such as genetic algorithms
20 * and pipeline designs.
21 *
22 * <p><b>Sample Usage:</b>
23 * Here are the highlights of a class that uses an {@code Exchanger}
24 * to swap buffers between threads so that the thread filling the
25 * buffer gets a freshly emptied one when it needs it, handing off the
26 * filled one to the thread emptying the buffer.
27 * <pre> {@code
28 * class FillAndEmpty {
29 * Exchanger<DataBuffer> exchanger = new Exchanger<DataBuffer>();
30 * DataBuffer initialEmptyBuffer = ... a made-up type
31 * DataBuffer initialFullBuffer = ...
32 *
33 * class FillingLoop implements Runnable {
34 * public void run() {
35 * DataBuffer currentBuffer = initialEmptyBuffer;
36 * try {
37 * while (currentBuffer != null) {
38 * addToBuffer(currentBuffer);
39 * if (currentBuffer.isFull())
40 * currentBuffer = exchanger.exchange(currentBuffer);
41 * }
42 * } catch (InterruptedException ex) { ... handle ... }
43 * }
44 * }
45 *
46 * class EmptyingLoop implements Runnable {
47 * public void run() {
48 * DataBuffer currentBuffer = initialFullBuffer;
49 * try {
50 * while (currentBuffer != null) {
51 * takeFromBuffer(currentBuffer);
52 * if (currentBuffer.isEmpty())
53 * currentBuffer = exchanger.exchange(currentBuffer);
54 * }
55 * } catch (InterruptedException ex) { ... handle ...}
56 * }
57 * }
58 *
59 * void start() {
60 * new Thread(new FillingLoop()).start();
61 * new Thread(new EmptyingLoop()).start();
62 * }
63 * }}</pre>
64 *
65 * <p>Memory consistency effects: For each pair of threads that
66 * successfully exchange objects via an {@code Exchanger}, actions
67 * prior to the {@code exchange()} in each thread
68 * <a href="package-summary.html#MemoryVisibility"><i>happen-before</i></a>
69 * those subsequent to a return from the corresponding {@code exchange()}
70 * in the other thread.
71 *
72 * @since 1.5
73 * @author Doug Lea and Bill Scherer and Michael Scott
74 * @param <V> The type of objects that may be exchanged
75 */
76 public class Exchanger<V> {
77
78 /*
79 * Overview: The core algorithm is, for an exchange "slot",
80 * and a participant (caller) with an item:
81 *
82 * for (;;) {
83 * if (slot is empty) { // offer
84 * place item in a Node;
85 * if (can CAS slot from empty to node) {
86 * wait for release;
87 * return matching item in node;
88 * }
89 * }
90 * else if (can CAS slot from node to empty) { // release
91 * get the item in node;
92 * set matching item in node;
93 * release waiting thread;
94 * }
95 * // else retry on CAS failure
96 * }
97 *
98 * This is among the simplest forms of a "dual data structure" --
99 * see Scott and Scherer's DISC 04 paper and
100 * http://www.cs.rochester.edu/research/synchronization/pseudocode/duals.html
101 *
102 * This works great in principle. But in practice, like many
103 * algorithms centered on atomic updates to a single location, it
104 * scales horribly when there are more than a few participants
105 * using the same Exchanger. So the implementation instead uses a
106 * form of elimination arena, that spreads out this contention by
107 * arranging that some threads typically use different slots,
108 * while still ensuring that eventually, any two parties will be
109 * able to exchange items. That is, we cannot completely partition
110 * across threads, but instead give threads arena indices that
111 * will on average grow under contention and shrink under lack of
112 * contention. We approach this by defining the Nodes that we need
113 * anyway as ThreadLocals, and include in them per-thread index
114 * and related bookkeeping state. (We can safely reuse per-thread
115 * nodes rather than creating them fresh each time because slots
116 * alternate between pointing to a node vs null, so cannot
117 * encounter ABA problems. However, we do need some care in
118 * resetting them between uses.)
119 *
120 * Implementing an effective arena requires allocating a bunch of
121 * space, so we only do so upon detecting contention (except on
122 * uniprocessors, where they wouldn't help, so aren't used).
123 * Otherwise, exchanges use the single-slot slotExchange method.
124 * On contention, not only must the slots be in different
125 * locations, but the locations must not encounter memory
126 * contention due to being on the same cache line (or more
127 * generally, the same coherence unit). Because, as of this
128 * writing, there is no way to determine cacheline size, we define
129 * a value that is enough for common platforms. Additionally,
130 * extra care elsewhere is taken to avoid other false/unintended
131 * sharing and to enhance locality, including adding padding to
132 * Nodes, embedding "bound" as an Exchanger field, and reworking
133 * some park/unpark mechanics compared to LockSupport versions.
134 *
135 * The arena starts out with only one used slot. We expand the
136 * effective arena size by tracking collisions; i.e., failed CASes
137 * while trying to exchange. By nature of the above algorithm, the
138 * only kinds of collision that reliably indicate contention are
139 * when two attempted releases collide -- one of two attempted
140 * offers can legitimately fail to CAS without indicating
141 * contention by more than one other thread. (Note: it is possible
142 * but not worthwhile to more precisely detect contention by
143 * reading slot values after CAS failures.) When a thread has
144 * collided at each slot within the current arena bound, it tries
145 * to expand the arena size by one. We track collisions within
146 * bounds by using a version (sequence) number on the "bound"
147 * field, and conservatively reset collision counts when a
148 * participant notices that bound has been updated (in either
149 * direction).
150 *
151 * The effective arena size is reduced (when there is more than
152 * one slot) by giving up on waiting after a while and trying to
153 * decrement the arena size on expiration. The value of "a while"
154 * is an empirical matter. We implement by piggybacking on the
155 * use of spin->yield->block that is essential for reasonable
156 * waiting performance anyway -- in a busy exchanger, offers are
157 * usually almost immediately released, in which case context
158 * switching on multiprocessors is extremely slow/wasteful. Arena
159 * waits just omit the blocking part, and instead cancel. The spin
160 * count is empirically chosen to be a value that avoids blocking
161 * 99% of the time under maximum sustained exchange rates on a
162 * range of test machines. Spins and yields entail some limited
163 * randomness (using a cheap xorshift) to avoid regular patterns
164 * that can induce unproductive grow/shrink cycles. (Using a
165 * pseudorandom also helps regularize spin cycle duration by
166 * making branches unpredictable.) Also, during an offer, a
167 * waiter can "know" that it will be released when its slot has
168 * changed, but cannot yet proceed until match is set. In the
169 * mean time it cannot cancel the offer, so instead spins/yields.
170 * Note: It is possible to avoid this secondary check by changing
171 * the linearization point to be a CAS of the match field (as done
172 * in one case in the Scott & Scherer DISC paper), which also
173 * increases asynchrony a bit, at the expense of poorer collision
174 * detection and inability to always reuse per-thread nodes. So
175 * the current scheme is typically a better tradeoff.
176 *
177 * On collisions, indices traverse the arena cyclically in reverse
178 * order, restarting at the maximum index (which will tend to be
179 * sparsest) when bounds change. (On expirations, indices instead
180 * are halved until reaching 0.) It is possible (and has been
181 * tried) to use randomized, prime-value-stepped, or double-hash
182 * style traversal instead of simple cyclic traversal to reduce
183 * bunching. But empirically, whatever benefits these may have
184 * don't overcome their added overhead: We are managing operations
185 * that occur very quickly unless there is sustained contention,
186 * so simpler/faster control policies work better than more
187 * accurate but slower ones.
188 *
189 * Because we use expiration for arena size control, we cannot
190 * throw TimeoutExceptions in the timed version of the public
191 * exchange method until the arena size has shrunken to zero (or
192 * the arena isn't enabled). This may delay response to timeout
193 * but is still within spec.
194 *
195 * Essentially all of the implementation is in methods
196 * slotExchange and arenaExchange. These have similar overall
197 * structure, but differ in too many details to combine. The
198 * slotExchange method uses the single Exchanger field "slot"
199 * rather than arena array elements. However, it still needs
200 * minimal collision detection to trigger arena construction.
201 * (The messiest part is making sure interrupt status and
202 * InterruptedExceptions come out right during transitions when
203 * both methods may be called. This is done by using null return
204 * as a sentinel to recheck interrupt status.)
205 *
206 * As is too common in this sort of code, methods are monolithic
207 * because most of the logic relies on reads of fields that are
208 * maintained as local variables so can't be nicely factored --
209 * mainly, here, bulky spin->yield->block/cancel code), and
210 * heavily dependent on intrinsics (Unsafe) to use inlined
211 * embedded CAS and related memory access operations (that tend
212 * not to be as readily inlined by dynamic compilers when they are
213 * hidden behind other methods that would more nicely name and
214 * encapsulate the intended effects). This includes the use of
215 * putOrderedX to clear fields of the per-thread Nodes between
216 * uses. Note that field Node.item is not declared as volatile
217 * even though it is read by releasing threads, because they only
218 * do so after CAS operations that must precede access, and all
219 * uses by the owning thread are otherwise acceptably ordered by
220 * other operations. (Because the actual points of atomicity are
221 * slot CASes, it would also be legal for the write to Node.match
222 * in a release to be weaker than a full volatile write. However,
223 * this is not done because it could allow further postponement of
224 * the write, delaying progress.)
225 */
226
227 /**
228 * The byte distance (as a shift value) between any two used slots
229 * in the arena. 1 << ASHIFT should be at least cacheline size.
230 */
231 private static final int ASHIFT = 7;
232
233 /**
234 * The maximum supported arena index. The maximum allocatable
235 * arena size is MMASK + 1. Must be a power of two minus one, less
236 * than (1<<(31-ASHIFT)). The cap of 255 (0xff) more than suffices
237 * for the expected scaling limits of the main algorithms.
238 */
239 private static final int MMASK = 0xff;
240
241 /**
242 * Unit for sequence/version bits of bound field. Each successful
243 * change to the bound also adds SEQ.
244 */
245 private static final int SEQ = MMASK + 1;
246
247 /** The number of CPUs, for sizing and spin control */
248 private static final int NCPU = Runtime.getRuntime().availableProcessors();
249
250 /**
251 * The maximum slot index of the arena: The number of slots that
252 * can in principle hold all threads without contention, or at
253 * most the maximum indexable value.
254 */
255 static final int FULL = (NCPU >= (MMASK << 1)) ? MMASK : NCPU >>> 1;
256
257 /**
258 * The bound for spins while waiting for a match. The actual
259 * number of iterations will on average be about twice this value
260 * due to randomization. Note: Spinning is disabled when NCPU==1.
261 */
262 private static final int SPINS = 1 << 10;
263
264 /**
265 * Value representing null arguments/returns from public
266 * methods. Needed because the API originally didn't disallow null
267 * arguments, which it should have.
268 */
269 private static final Object NULL_ITEM = new Object();
270
271 /**
272 * Sentinel value returned by internal exchange methods upon
273 * timeout, to avoid need for separate timed versions of these
274 * methods.
275 */
276 private static final Object TIMED_OUT = new Object();
277
278 /**
279 * Nodes hold partially exchanged data, plus other per-thread
280 * bookkeeping.
281 */
282 static final class Node {
283 int index; // Arena index
284 int bound; // Last recorded value of Exchanger.bound
285 int collides; // Number of CAS failures at current bound
286 int hash; // Pseudo-random for spins
287 Object item; // This thread's current item
288 volatile Object match; // Item provided by releasing thread
289 volatile Thread parked; // Set to this thread when parked, else null
290
291 // Padding to ameliorate unfortunate memory placements
292 Object p0, p1, p2, p3, p4, p5, p6, p7, p8, p9, pa, pb, pc, pd, pe, pf;
293 Object q0, q1, q2, q3, q4, q5, q6, q7, q8, q9, qa, qb, qc, qd, qe, qf;
294 }
295
296 /** The corresponding thread local class */
297 static final class Participant extends ThreadLocal<Node> {
298 public Node initialValue() { return new Node(); }
299 }
300
301 /**
302 * Per-thread state
303 */
304 private final Participant participant;
305
306 /**
307 * Elimination array; null until enabled (within slotExchange).
308 * Element accesses use emulation of volatile gets and CAS.
309 */
310 private volatile Node[] arena;
311
312 /**
313 * Slot used until contention detected.
314 */
315 private volatile Node slot;
316
317 /**
318 * The index of the largest valid arena position, OR'ed with SEQ
319 * number in high bits, incremented on each update. The initial
320 * update from 0 to SEQ is used to ensure that the arena array is
321 * constructed only once.
322 */
323 private volatile int bound;
324
325 /**
326 * Exchange function when arenas enabled. See above for explanation.
327 *
328 * @param item the (non-null) item to exchange
329 * @param timed true if the wait is timed
330 * @param ns if timed, the maximum wait time, else 0L
331 * @return the other thread's item; or null if interrupted; or
332 * TIMED_OUT if timed and timed out
333 */
334 private final Object arenaExchange(Object item, boolean timed, long ns) {
335 Node[] a = arena;
336 Node p = participant.get();
337 for (int i = p.index;;) { // access slot at i
338 int b, m, c; long j; // j is raw array offset
339 Node q = (Node)U.getObjectVolatile(a, j = (i << ASHIFT) + ABASE);
340 if (q != null && U.compareAndSwapObject(a, j, q, null)) {
341 Object v = q.item; // release
342 q.match = item;
343 Thread w = q.parked;
344 if (w != null)
345 U.unpark(w);
346 return v;
347 }
348 else if (i <= (m = (b = bound) & MMASK) && q == null) {
349 p.item = item; // offer
350 if (U.compareAndSwapObject(a, j, null, p)) {
351 long end = (timed && m == 0) ? System.nanoTime() + ns : 0L;
352 Thread t = Thread.currentThread(); // wait
353 for (int h = p.hash, spins = SPINS;;) {
354 Object v = p.match;
355 if (v != null) {
356 U.putOrderedObject(p, MATCH, null);
357 p.item = null; // clear for next use
358 p.hash = h;
359 return v;
360 }
361 else if (spins > 0) {
362 h ^= h << 1; h ^= h >>> 3; h ^= h << 10; // xorshift
363 if (h == 0) // initialize hash
364 h = SPINS | (int)t.getId();
365 else if (h < 0 && // approx 50% true
366 (--spins & ((SPINS >>> 1) - 1)) == 0)
367 Thread.yield(); // two yields per wait
368 }
369 else if (U.getObjectVolatile(a, j) != p)
370 spins = SPINS; // releaser hasn't set match yet
371 else if (!t.isInterrupted() && m == 0 &&
372 (!timed ||
373 (ns = end - System.nanoTime()) > 0L)) {
374 U.putObject(t, BLOCKER, this); // emulate LockSupport
375 p.parked = t; // minimize window
376 if (U.getObjectVolatile(a, j) == p)
377 U.park(false, ns);
378 p.parked = null;
379 U.putObject(t, BLOCKER, null);
380 }
381 else if (U.getObjectVolatile(a, j) == p &&
382 U.compareAndSwapObject(a, j, p, null)) {
383 if (m != 0) // try to shrink
384 U.compareAndSwapInt(this, BOUND, b, b + SEQ - 1);
385 p.item = null;
386 p.hash = h;
387 i = p.index >>>= 1; // descend
388 if (Thread.interrupted())
389 return null;
390 if (timed && m == 0 && ns <= 0L)
391 return TIMED_OUT;
392 break; // expired; restart
393 }
394 }
395 }
396 else
397 p.item = null; // clear offer
398 }
399 else {
400 if (p.bound != b) { // stale; reset
401 p.bound = b;
402 p.collides = 0;
403 i = (i != m || m == 0) ? m : m - 1;
404 }
405 else if ((c = p.collides) < m || m == FULL ||
406 !U.compareAndSwapInt(this, BOUND, b, b + SEQ + 1)) {
407 p.collides = c + 1;
408 i = (i == 0) ? m : i - 1; // cyclically traverse
409 }
410 else
411 i = m + 1; // grow
412 p.index = i;
413 }
414 }
415 }
416
417 /**
418 * Exchange function used until arenas enabled. See above for explanation.
419 *
420 * @param item the item to exchange
421 * @param timed true if the wait is timed
422 * @param ns if timed, the maximum wait time, else 0L
423 * @return the other thread's item; or null if either the arena
424 * was enabled or the thread was interrupted before completion; or
425 * TIMED_OUT if timed and timed out
426 */
427 private final Object slotExchange(Object item, boolean timed, long ns) {
428 Node p = participant.get();
429 Thread t = Thread.currentThread();
430 if (t.isInterrupted()) // preserve interrupt status so caller can recheck
431 return null;
432
433 for (Node q;;) {
434 if ((q = slot) != null) {
435 if (U.compareAndSwapObject(this, SLOT, q, null)) {
436 Object v = q.item;
437 q.match = item;
438 Thread w = q.parked;
439 if (w != null)
440 U.unpark(w);
441 return v;
442 }
443 // create arena on contention, but continue until slot null
444 if (NCPU > 1 && bound == 0 &&
445 U.compareAndSwapInt(this, BOUND, 0, SEQ))
446 arena = new Node[(FULL + 2) << ASHIFT];
447 }
448 else if (arena != null)
449 return null; // caller must reroute to arenaExchange
450 else {
451 p.item = item;
452 if (U.compareAndSwapObject(this, SLOT, null, p))
453 break;
454 p.item = null;
455 }
456 }
457
458 // await release
459 int h = p.hash;
460 long end = timed ? System.nanoTime() + ns : 0L;
461 int spins = (NCPU > 1) ? SPINS : 1;
462 Object v;
463 while ((v = p.match) == null) {
464 if (spins > 0) {
465 h ^= h << 1; h ^= h >>> 3; h ^= h << 10;
466 if (h == 0)
467 h = SPINS | (int)t.getId();
468 else if (h < 0 && (--spins & ((SPINS >>> 1) - 1)) == 0)
469 Thread.yield();
470 }
471 else if (slot != p)
472 spins = SPINS;
473 else if (!t.isInterrupted() && arena == null &&
474 (!timed || (ns = end - System.nanoTime()) > 0L)) {
475 U.putObject(t, BLOCKER, this);
476 p.parked = t;
477 if (slot == p)
478 U.park(false, ns);
479 p.parked = null;
480 U.putObject(t, BLOCKER, null);
481 }
482 else if (U.compareAndSwapObject(this, SLOT, p, null)) {
483 v = timed && ns <= 0L && !t.isInterrupted() ? TIMED_OUT : null;
484 break;
485 }
486 }
487 U.putOrderedObject(p, MATCH, null);
488 p.item = null;
489 p.hash = h;
490 return v;
491 }
492
493 /**
494 * Creates a new Exchanger.
495 */
496 public Exchanger() {
497 participant = new Participant();
498 }
499
500 /**
501 * Waits for another thread to arrive at this exchange point (unless
502 * the current thread is {@linkplain Thread#interrupt interrupted}),
503 * and then transfers the given object to it, receiving its object
504 * in return.
505 *
506 * <p>If another thread is already waiting at the exchange point then
507 * it is resumed for thread scheduling purposes and receives the object
508 * passed in by the current thread. The current thread returns immediately,
509 * receiving the object passed to the exchange by that other thread.
510 *
511 * <p>If no other thread is already waiting at the exchange then the
512 * current thread is disabled for thread scheduling purposes and lies
513 * dormant until one of two things happens:
514 * <ul>
515 * <li>Some other thread enters the exchange; or
516 * <li>Some other thread {@linkplain Thread#interrupt interrupts}
517 * the current thread.
518 * </ul>
519 * <p>If the current thread:
520 * <ul>
521 * <li>has its interrupted status set on entry to this method; or
522 * <li>is {@linkplain Thread#interrupt interrupted} while waiting
523 * for the exchange,
524 * </ul>
525 * then {@link InterruptedException} is thrown and the current thread's
526 * interrupted status is cleared.
527 *
528 * @param x the object to exchange
529 * @return the object provided by the other thread
530 * @throws InterruptedException if the current thread was
531 * interrupted while waiting
532 */
533 @SuppressWarnings("unchecked")
534 public V exchange(V x) throws InterruptedException {
535 Object v;
536 Object item = (x == null) ? NULL_ITEM : x; // translate null args
537 if ((arena != null ||
538 (v = slotExchange(item, false, 0L)) == null) &&
539 ((Thread.interrupted() || // disambiguates null return
540 (v = arenaExchange(item, false, 0L)) == null)))
541 throw new InterruptedException();
542 return (v == NULL_ITEM) ? null : (V)v;
543 }
544
545 /**
546 * Waits for another thread to arrive at this exchange point (unless
547 * the current thread is {@linkplain Thread#interrupt interrupted} or
548 * the specified waiting time elapses), and then transfers the given
549 * object to it, receiving its object in return.
550 *
551 * <p>If another thread is already waiting at the exchange point then
552 * it is resumed for thread scheduling purposes and receives the object
553 * passed in by the current thread. The current thread returns immediately,
554 * receiving the object passed to the exchange by that other thread.
555 *
556 * <p>If no other thread is already waiting at the exchange then the
557 * current thread is disabled for thread scheduling purposes and lies
558 * dormant until one of three things happens:
559 * <ul>
560 * <li>Some other thread enters the exchange; or
561 * <li>Some other thread {@linkplain Thread#interrupt interrupts}
562 * the current thread; or
563 * <li>The specified waiting time elapses.
564 * </ul>
565 * <p>If the current thread:
566 * <ul>
567 * <li>has its interrupted status set on entry to this method; or
568 * <li>is {@linkplain Thread#interrupt interrupted} while waiting
569 * for the exchange,
570 * </ul>
571 * then {@link InterruptedException} is thrown and the current thread's
572 * interrupted status is cleared.
573 *
574 * <p>If the specified waiting time elapses then {@link
575 * TimeoutException} is thrown. If the time is less than or equal
576 * to zero, the method will not wait at all.
577 *
578 * @param x the object to exchange
579 * @param timeout the maximum time to wait
580 * @param unit the time unit of the <tt>timeout</tt> argument
581 * @return the object provided by the other thread
582 * @throws InterruptedException if the current thread was
583 * interrupted while waiting
584 * @throws TimeoutException if the specified waiting time elapses
585 * before another thread enters the exchange
586 */
587 @SuppressWarnings("unchecked")
588 public V exchange(V x, long timeout, TimeUnit unit)
589 throws InterruptedException, TimeoutException {
590 Object v;
591 Object item = (x == null) ? NULL_ITEM : x;
592 long ns = unit.toNanos(timeout);
593 if ((arena != null ||
594 (v = slotExchange(item, true, ns)) == null) &&
595 ((Thread.interrupted() ||
596 (v = arenaExchange(item, true, ns)) == null)))
597 throw new InterruptedException();
598 if (v == TIMED_OUT)
599 throw new TimeoutException();
600 return (v == NULL_ITEM) ? null : (V)v;
601 }
602
603 // Unsafe mechanics
604 private static final sun.misc.Unsafe U;
605 private static final long BOUND;
606 private static final long SLOT;
607 private static final long MATCH;
608 private static final long BLOCKER;
609 private static final int ABASE;
610 static {
611 int s;
612 try {
613 U = sun.misc.Unsafe.getUnsafe();
614 Class<?> ek = Exchanger.class;
615 Class<?> nk = Node.class;
616 Class<?> ak = Node[].class;
617 Class<?> tk = Thread.class;
618 BOUND = U.objectFieldOffset
619 (ek.getDeclaredField("bound"));
620 SLOT = U.objectFieldOffset
621 (ek.getDeclaredField("slot"));
622 MATCH = U.objectFieldOffset
623 (nk.getDeclaredField("match"));
624 BLOCKER = U.objectFieldOffset
625 (tk.getDeclaredField("parkBlocker"));
626 s = U.arrayIndexScale(ak);
627 // ABASE absorbs padding in front of element 0
628 ABASE = U.arrayBaseOffset(ak) + (1 << ASHIFT);
629
630 } catch (Exception e) {
631 throw new Error(e);
632 }
633 if ((s & (s-1)) != 0 || s > (1 << ASHIFT))
634 throw new Error("Unsupported array scale");
635 }
636
637 }