-
Notifications
You must be signed in to change notification settings - Fork 11
/
dining_philosophers.html
1338 lines (1211 loc) · 42.3 KB
/
dining_philosophers.html
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
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
611
612
613
614
615
616
617
618
619
620
621
622
623
624
625
626
627
628
629
630
631
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
650
651
652
653
654
655
656
657
658
659
660
661
662
663
664
665
666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
701
702
703
704
705
706
707
708
709
710
711
712
713
714
715
716
717
718
719
720
721
722
723
724
725
726
727
728
729
730
731
732
733
734
735
736
737
738
739
740
741
742
743
744
745
746
747
748
749
750
751
752
753
754
755
756
757
758
759
760
761
762
763
764
765
766
767
768
769
770
771
772
773
774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
838
839
840
841
842
843
844
845
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898
899
900
901
902
903
904
905
906
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
922
923
924
925
926
927
928
929
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
966
967
968
969
970
971
972
973
974
975
976
977
978
979
980
981
982
983
984
985
986
987
988
989
990
991
992
993
994
995
996
997
998
999
1000
<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 4.01 Transitional//EN"
"http://www.w3.org/TR/html4/loose.dtd">
<html>
<head>
<title>Dining Philosophers Rebooted</title>
<style>
p {text-align:justify}
li {text-align:justify}
blockquote.note
{
background-color:#E0E0E0;
padding-left: 15px;
padding-right: 15px;
padding-top: 1px;
padding-bottom: 1px;
}
ins {color:#00A000}
del {color:#A00000}
</style>
</head>
<body>
<address align=right>
<br/>
<br/>
<a href="mailto:[email protected]">Howard E. Hinnant</a><br/>
2014-05-18<br/>
<a rel="license" href="http://creativecommons.org/licenses/by/4.0/">
<img alt="Creative Commons License" style="border-width:0" src="http://i.creativecommons.org/l/by/4.0/80x15.png" /></a><br />
This work is licensed under a <a rel="license" href="http://creativecommons.org/licenses/by/4.0/">Creative Commons Attribution 4.0 International License</a>.
</address>
<hr/>
<h1 align=center>Dining Philosophers Rebooted</h1>
<h2>Contents</h2>
<ul>
<li><a href="#Introduction">Introduction</a></li>
<li><a href="#Problem">Problem Description</a></li>
<li><a href="#Solutions">The Solutions</a>
<ul>
<li><a href="#Ordered">Ordered</a></li>
<li><a href="#Persistent">Persistent</a></li>
<li><a href="#Smart">Smart</a></li>
<li><a href="#Polite">Smart & Polite</a></li>
</ul>
</li>
<li><a href="#Results">The Results</a>
<ul>
<li><a href="#2dp4">Round Table on a 4 Core Machine</a></li>
<li><a href="#d2p8">Round Table on a 8 Core Machine</a></li>
<li><a href="#Explanation">Explanation</a></li>
<li><a href="#d3p4">A 3-D Table on a 4 Core Machine</a></li>
<li><a href="#d3p8">A 3-D Table on an 8 Core Machine</a></li>
</ul>
</li>
<li><a href="#Summary">Summary</a></li>
<li><a href="#codeA">Appendix A: Round Table Code</a></li>
<li><a href="#codeB">Appendix B: 3-D Table Code</a></li>
<li><a href="#Acknowledgments">Acknowledgments</a></li>
</ul>
<a name="Introduction"></a><h2>Introduction</h2>
<p>
The
<a href="http://en.wikipedia.org/wiki/Dining_philosophers_problem">dining
philosophers problem</a> has been a famous computer science problem for half
a century. When first presented, the challenge was simply to find a solution
that did not deadlock. I.e. a solution where none of the diners starved to
death in the process of waiting for a chance to eat.
</p>
<p>
This paper presents four solutions to the problem, and compares the
performance of each solution. Additionally the impact of the number of
diners, and the number of processors is explored to see how these factors
impact overall performance. And finally, an alternate topology, where each
diner requires 3 forks to eat, is explored with these same 4 algorithms. It
will be shown that there is a single algorithm that consistently performs as
well as, or better than, the other 3 algorithms, as all factors are varied
(number of processors, number of diners, topology).
</p>
<p>
The complete C++11 source code for this study is included in this paper so that
others may easily confirm or refute the results presented herein.
</p>
<p>
A practical application of the results of this study is the algorithm
underlying the <code>std::lock(L1, L2, ...)</code> function in section 30.4.3
[thread.lock.algorithm] of the C++11 and C++14 standards:
</p>
<blockquote>
<pre>
template <class L1, class L2, class... L3> void lock(L1&, L2&, L3&...);
</pre>
<blockquote>
<p>
<i>Requires:</i> Each template parameter type shall meet the
<code>Lockable</code> requirements, [<i>Note:</i> The
<code>unique_lock></code> class template meets these requirements when
suitably instantiated. — <i>end note</i>]
</p>
<p>
<i>Effects:</i> All arguments are locked via a sequence of calls to
<code>lock()</code>, <code>try_lock()</code>, or <code>unlock()</code> on
each argument. The sequence of calls shall not result in deadlock, but is
otherwise unspecified. [<i>Note:</i> A deadlock avoidance algorithm such as
try-and-back-off must be used, but the specific algorithm is not specified to
avoid over-constraining implementations. — <i>end note</i>] If a call
to <code>lock()</code> or <code>try_lock()</code> throws an exception,
<code>unlock()</code> shall be called for any argument that had been locked
by a call to <code>lock()</code> or <code>try_lock()</code>.
</p>
</blockquote>
</blockquote>
<p>
Indeed, all of the test software used by this paper will call
<code>::lock</code> to obtain "forks" (lock two or three
<code>std::mutex</code>es). One can safely assume that <code>::lock()</code>
in this paper represents nothing but example implementations of
<code>std::lock()</code>.
</p>
<a name="Problem"></a><h2>Problem Description</h2>
<p>
<a href="http://en.wikipedia.org/wiki/Dining_philosophers_problem">This
Wikipedia link</a> has a great description of the problem. If you haven't
read it yet, read it now. I'll wait...
</p>
<p>
Ok, now that we're all on the same page (and back on this one), I'll explain
the minor deviations that this paper takes, and why.
</p>
<p>
As it turns out, any algorithm that solves this problem without deadlock, will
perform wonderfully when the philosophers spend any appreciable amount of time
thinking, compared to eating. I.e. they can each think independently (that
is what makes them philosophers after all). When they do as much thinking as
they do eating, we call this a <i>low contention</i> scenario because the
philosophers spend relatively little time <i>contending</i> for the forks.
</p>
<p>
However when the philosophers are all <i>really</i> hungry, they tend to eat
more and think less (just like the rest of us). This means they spend more
time contending for the forks, and subsequently the nature of the algorithm
which arbitrates who gets what fork when, becomes more and more important.
In the limit, as thinking time goes to zero, the importance of the algorithm
which hands out the forks becomes paramount, and dominates the performance of
the entire meal (the application).
</p>
<p>
Therefore in the tests included herein:
</p>
<ol>
<li>The diners do not think at all. They only wish to eat.</li>
<li>The diners can only eat for at most 10 milliseconds at a time, before
they have to relinquish their forks while they chew. This is sometimes
as little as 1 millisecond. The exact duration is chosen randomly each
time a diner obtains the forks.</li>
<li>The diner randomly chooses what order to <i>request</i> the forks in.
I.e. what order the forks are given to the <code>::lock()</code> algorithm.
The actual order the forks are obtained is encapsulated within the
<code>::lock()</code> algorithm.</li>
<li>
The meal is considered complete when each diner has eaten for a cumulative
total of 30 seconds.
</li>
<li>
The efficiency of the algorithm is measured by measuring the wall clock time
elapsed from the beginning of the meal to the end of the meal (shorter is
better).
</li>
</ol>
<p>
These parameters have been chosen to highlight the performance differences
between the 4 algorithms presented herein, and to somewhat approximate a
real-world high-contention scenario. If the scenario is low-contention, the
algorithm does not matter, as long as it avoids deadlock.
</p>
<a name="Solutions"></a><h2>The Solutions</h2>
<p>
For each solution, the forks are represented as a
<code>vector<mutex></code>:
</p>
<blockquote><pre>
std::vector<std::mutex> table(nt);
</pre></blockquote>
<p>
There is a <code>class Philosopher</code> which will reference two (or three)
<code>mutex</code>es, and the table setting is represented as a
<code>vector<Philosopher></code>:
</p>
<blockquote><pre>
std::vector<Philosopher> diners;
</pre></blockquote>
<ol>
<li>
<a name="Ordered"></a><h3>Ordered</h3>
<p>
The ordered solution is the one originally proposed by Edsger Dijkstra in
1965. One assigns an order to the forks (we will use their address in the
<code>vector</code>), and each <code>Philosopher</code> will first lock the
lower-numbered <code>mutex</code>, and then lock the higher-numbered
<code>mutex</code>.
</p>
<p>
The two-<code>mutex</code> variant of <code>lock</code> can be coded like so
if we assume that the template parameter <code>L0</code> is always a
<code>std::unique_lock</code> (which is not a good assumption for
<code>std::lock</code> but we overlook that detail here).
</p>
<blockquote><pre>
template <class L0>
void
lock(L0& l0, L0& l1)
{
if (l0.mutex() < l1.mutex())
{
std::unique_lock<L0> u0(l0);
l1.lock();
u0.release();
}
else
{
std::unique_lock<L0> u1(l1);
l0.lock();
u1.release();
}
}
</pre></blockquote>
<p>
The purpose of the internal use of <code>std::unique_lock<L0></code> is
to make the code exception safe. If the second <code>lock()</code> throws,
the local <code>std::unique_lock<L0></code> ensures that the first lock
is unlocked while propagating the exception out.
</p>
<p>
Note that this algorithm has a very predictable code flow. There are only
two ways to get the job done, and there are no loops.
</p>
</li>
<li>
<a name="Persistent"></a><h3>Persistent</h3>
<p>
No one that I'm aware of has seriously proposed this algorithm as a good
solution. However it is included here as there is at least one shipping
implementation of <code>std::lock</code> that implements this exact algorithm.
Furthermore, a naive reading of the C++ specification for
<code>std::lock</code> has led more than one person to believe that this is
the only algorithm possible which will conform to the C++ specification.
Nothing could be further from the truth.
</p>
<p>
This algorithm is called "persistent" as the <code>Philosopher</code> simply
doggedly locks one <code>mutex</code>, and then <code>try_lock()</code> the
others. If the <code>try_lock()</code>s succeed, he is done, else he unlocks
everything, and immediately tries the exact same thing again, and again, and
again, until he succeeds.
</p>
<p>
This is simple to code for the two-<code>mutex</code> variant as:
</p>
<blockquote><pre>
template <class L0, class L1>
void
lock(L0& l0, L1& l1)
{
while (true)
{
std::unique_lock<L0> u0(l0);
if (l1.try_lock())
{
u0.release();
break;
}
}
}
</pre></blockquote>
<p>
Results will later show that this algorithm, while not ideal, actually
performs relatively well when there is plenty of spare processing power. Or
said differently, the algorithm works, but is power hungry.
</p>
</li>
<li>
<a name="Smart"></a><h3>Smart</h3>
<p>
A simple but important variation of the <a href="#Persistent">persistent</a>
algorithm is when a <code>try_lock()</code> fails, then block on <i>that</i>
<code>mutex</code>. This eliminates a lot of useless <i>spinning</i>, thus
consuming less power, and thus leaving more processing power available to
other diners. As it turns out, a diner needs not only forks to eat, he also
needs an available processor. If you don't have the forks, don't waste power.
</p>
<p>
This is simple to code for the two-<code>mutex</code> variant as:
</p>
<blockquote><pre>
template <class L0, class L1>
void
lock(L0& l0, L1& l1)
{
while (true)
{
{
std::unique_lock<L0> u0(l0);
if (l1.try_lock())
{
u0.release();
break;
}
}
{
std::unique_lock<L1> u1(l1);
if (l0.try_lock())
{
u1.release();
break;
}
}
}
}
</pre></blockquote>
<p>
This algorithm still contains a theoretical infinite loop. However it will
go through this loop rather slowly, as each <code>mutex</code> locked besides
the very first, is one for which the thread has just failed a call to
<code>try_lock()</code> (and so the subsequent <code>lock()</code> is likely
to block).
</p>
<p>
Some people have expressed a great deal of concern about <a
href="http://en.wikipedia.org/wiki/Deadlock#Livelock"><i>livelock</i></a>
with this algorithm. And indeed experiments have revealed a very small
amount of <i>temporary</i> livelock can occur under high-contention
conditions as emphasized by the tests herein. The 4th algorithm is designed
to reduce this small amount of experimentally observed livelock to zero.
</p>
</li>
<li>
<a name="Polite"></a><h3>Smart & Polite</h3>
<p>
This algorithm is a minor variant of the <a href="#Smart">smart</a>
algorithm. It has experimentally shown small performance advantages over the
<a href="#Smart">smart</a> algorithm on <a
href="http://www.apple.com/osx/">OS X</a>. After the thread has failed a
<code>try_lock()</code> on a <code>mutex</code>, but prior to blocking on
that <code>mutex</code>, yield the processor to anyone else who might need
it. Results may be different on other OS's. But on OS X, it is just the
polite thing to do. And the system as a whole (though not the individual
<code>Philosopher</code>) benefits under conditions where processing power is
already maxed out.
</p>
<blockquote><pre>
template <class L0, class L1>
void
lock(L0& l0, L1& l1)
{
while (true)
{
{
std::unique_lock<L0> u0(l0);
if (l1.try_lock())
{
u0.release();
break;
}
}
std::this_thread::yield();
{
std::unique_lock<L1> u1(l1);
if (l0.try_lock())
{
u1.release();
break;
}
}
std::this_thread::yield();
}
}
</pre></blockquote>
</li>
</ol>
<a name="Results"></a><h2>The Results</h2>
<a name="2dp4"></a><h3>Round Table on a 4 Core Machine</h3>
<img src="d2p4.jpg" align="right">
<p>
In the figure to the right I have set up 31 tests. Each test has a number of
philosophers seated at a round table. The number of philosophers varies from
2 to 32. There is one fork (<code>mutex</code>) between every two adjacent
philosophers. Each philosopher must obtain his two adjacent forks in order
to eat. This test shows timing results for a 4 processor Intel Core i5 running
Apple OS X 10.9.2.
</p>
<p>
The vertical axis represents the total number of seconds it takes for all
philosophers at the table to get a total of 30 seconds each of "quality fork
time."
</p>
<p>
When there are only two philosophers at the table, it seems clear that only
one of them can eat at a time, and thus it will take 60 seconds for each of
them to eat for 30 seconds. This is true whether that each eat for 30 seconds
at a time, or if they each eat for a few milliseconds at a time.
</p>
<p>
The chart shows in blue a theoretical minimum amount of time the meal must
take for everyone to get 30 seconds. When there is a even number of
philosophers at the table, it is easy to see that every other philosopher can
eat at one time (say the even numbered philosophers if you numbered them).
And then the odd-numbered philosophers can eat. Whether they all eat for a
few milliseconds or 30 seconds each, it should take no more than 60 seconds
for everyone to get a full meal, assuming one has a sufficient number of
processors to supply to each philosopher whenever he needs one (has obtained
two forks).
</p>
<p>
When the number of philosophers at the table is odd, it can be shown that the
theoretical minimum meal time is 30 * N /((N-1)/2) seconds. When N is 3, it
is easy to see that there is no room for concurrency. Just like the N == 2
case, only one philosopher can eat at a time. Thus the minimum meal time is
90 seconds. For higher odd numbers of philosophers at the table, the minimum
time actually drops, and approaches 60 seconds as N goes to infinity.
</p>
<p>
All 4 algorithms nail the N == 2, and N == 3 cases. However, with N >= 4,
the <a href="#Ordered">ordered</a> algorithm breaks away from the theoretical
minimum and climbs in a close to linear fashion with the number of dining
philosophers. This essentially represents the algorithm's lack of ability to
evenly distribute processing power equally to each philosopher. To the right
of the chart are CPU Load graphics, one for each algorithm at the N == 32
case. The second from the top is for the ordered algorithm. In this figure
one can see that the cpu load tapers off somewhat at the end of the test,
indicating that towards the end there are fewer and fewer philosophers that
are still hungry. This also indicates that those still-hungry philosophers
were experiencing mild starvation earlier in the test (else they would not
still be hungry).
</p>
<p>
The <a href="#Persistent">persistent</a> algorithm starts off outperforming
the <a href="#Ordered">ordered</a> algorithm. Up through N == 5, the results
are virtually indistinguishable from the theoretical minimum. And up through
N == 7, the results are only slightly worse than the theoretical minimum.
But by N == 8, the cost of this algorithm starts to sharply rise as more
philosophers come to the table. The rise is so sharp that the algorithm
begins to get outperformed by the <a href="#Ordered">ordered</a> algorithm by
N == 13. The top cpu load graphic indicates that a significant portion of
the cpu is spent in system calls (the red area), which is consistent with the
notion that this algorithm is needlessly locking and unlocking mutexes
without getting any real work (eating) done.
</p>
<p>
The <a href="#Smart">smart</a> and <a href="#Polite">smart & polite</a>
algorithms have very similar performance. They both perform identically to
the theoretical minimum up through N == 9. This is the point that even with a
perfectly fair distribution of processing power, the philosophers start
collectively asking for more than 4 cpus. As the number of philosophers
increases, the slope of the <a href="#Polite">smart & polite</a>
algorithm is slightly less than the <a href="#Smart">smart</a> algorithm, and
appears equal to the slope of the <a href="#Ordered">ordered</a> algorithm.
Note that in the CPU load factor graphics for these two algorithms, the meal
ends relatively abruptly, with all philosophers finishing at about the same
time. Indeed, the success of these algorithms resides in the fact that all
philosophers are treated equally during the meal, none getting starved any
more than the others.
</p>
<p>
The question naturally arises now:
</p>
<blockquote>
<p>
How do these results scale with the number of processors?
</p>
</blockquote>
<a name="d2p8"></a><h3>Round Table on a 8 Core Machine</h3>
<img src="d2p8.jpg" align="right">
<p>
As luck would have it, I have an 8 core Intel Core i7 running Apple OS X 10.9.2
available to run the exact same code.
</p>
<p>
The results are qualitatively the same.
</p>
<ul>
<li><p>
The <a href="#Ordered">ordered</a> algorithm again breaks from the minimum at
N == 4, and rises. The rise is not as rapid as on the 4 core machine, but
neither is the performance twice as fast.
</p></li>
<li><p>
The <a href="#Persistent">persistent</a> algorithm sticks to the theoretical
minimum up to about N == 13, and then sharply rises. The rise is sharp
enough such that the <a href="#Ordered">ordered</a> algorithm will eventually
outperform it, but that no longer happens below N == 32. The CPU load
graphic again shows excessive cpu devoted to system calls.
</p></li>
<li><p>
The <a href="#Smart">smart</a> and <a href="#Polite">smart & polite</a>
algorithms stay on the theoretical minimum out to 17 philosophers, and then
rise approximately linearly.
</p></li>
<li><p>
The <a href="#Polite">smart & polite</a> algorithm is consistently the
highest performing algorithm, or at the very least, never outperformed by any
of the other 3 algorithms. Concerns of any significant livelock are not
supported by these results. Though please feel free to run <a
href="#codeA">this test</a> on your own machine and publicly report your
results.
</p></li>
</ul>
<table style="border-spacing:20px">
<tr>
<td>
<a name="Explanation"></a><h3>Explanation</h3>
<p>
To help visualize the problem, lets concentrate on the case of five
philosophers. And to simplify the analysis, assume we have enough
cores to give each philosopher a dedicated processor.
</p>
<p>
Imagine that all five philosophers try to initiate grabbing their lower-numbered
fork at once. Philosophers 2, 3 and 4 will lock mutexes 1, 2 and 3 respectively.
Philosophers 0 and 1 will race to get mutex 0. One of them will succeed, and
the other will block.
</p>
<p>
Next, the non-blocked philosophers (say 0, 2, 3 and 4) will try to lock their
higher-numbered mutex. Philosophers 2 and 3 will block when they do this,
because their higher-numbered mutex is already owned by the philosopher to
their right. Philosophers 0 and 4 will race to obtain mutex 4. One of them
will get the mutex, and the other will block.
</p>
<p>
The end result is that out of the 5 philosophers, 4 of them will be blocked,
waiting for the 1 runnable philosopher to finish eating.
</p>
<p>
This doesn't <i>always</i> happen. Otherwise the graphs above would show this
case taking 150 seconds (5 x 30 seconds) instead of about 95 seconds. However
the 95 second result indicates that one philosopher is blocking the other four
from eating about half the time.
</p>
<p>
Ideally, two philosophers should be able to eat at once, 100% of the time.
</p>
</td>
<td>
<video width="480" height="360" controls>
<source src="dining_philosophers.m4v" type="video/mp4">
Your browser does not support the video tag.
</video>
</td>
</tr>
<tr>
<td>
<p>
Using the "smart" locking algorithm, assume we start out the same way as
the ordered algorithm, with philosophers 2, 3 and 4 obtaining mutexes 1, 2
and 3 respectively, and philosophers 0 and 1 racing to lock mutex 0. Note
that we don't have to start out this way. The philosophers can try to grab
either mutex with this algorithm. But for the moment, assume things start
out the same.
</p>
<p>
Next, the non-blocked philosophers (say 0, 2, 3 and 4) will try to lock their
other mutex, which in this example just happens to be their higher-numbered
mutex (just like in the ordered algorithm). But this is where things begin
to deviate from the ordered algorithm.
</p>
<p>
Assume that in the race between philosopher 0 and philosopher 4 for mutex 4,
philosopher 0 wins. If this were the ordered algorithm, philosopher 2, 3 and
4 would block on failing to get their second mutex. However in this algorithm
the result is a failed <code>try_lock</code>. The response of philosophers 2,
3 and 4 is to unlock their first mutex and <code>lock</code> their second.
When this happens, only philosopher 4 blocks as mutex 4 is already owned by
philosopher 0. Philosophers 2 and 3 succeed in locking mutexes 2 and 3
respectively.
</p>
<p>
Now philosophers 2 and 3 attempt to lock mutexes 1 and 2 respectively.
Philosopher 2 succeeds and philosopher 3 fails, and in response philosopher 3
unlocks mutex 3. Philosopher 3 then blocks on attempting to lock mutex 2.
</p>
<p>
At this point philosophers 0 and 2 are eating, and philosophers 1, 3 and 4
are blocked. For this topology, 2 philosophers eating while the other 3 are
blocked is an optimum. The smart locking algorithm will quickly find this
optimum in every situation. This is evidenced by the experimental result of
75 seconds: exactly half of the purely sequential result of 150 seconds.
</p>
</td>
<td>
<video width="480" height="360" controls>
<source src="dining_philosophers2.m4v" type="video/mp4">
Your browser does not support the video tag.
</video>
</td>
</tr>
</table>
<p>
The next question to naturally arise is:
</p>
<blockquote>
<p>
How do these results scale with the number of mutexes one needs to lock?
</p>
</blockquote>
<a name="d3p4"></a><h3>A 3-D Table on a 4 Core Machine</h3>
<img src="d3p4.jpg" align="right">
<p>
Though not a complete answer, I have created a partial answer to the above
question which should shed some light.
</p>
<p>
Instead of the philosophers sitting at a round table, imagine they are each
seated at a vertex of a
<a href="http://en.wikipedia.org/wiki/Platonic_solid">Platonic solid</a>. And
further imagine that we restrict ourselves to those solids for which each
vertex is the intersection of exactly 3 faces (and thus 3 edges). And finally
imagine that there is a fork at the middle of each edge.
</p>
<p>
Due to the limits of both Euclidean geometry, and my visualization abilities,
this experiment will take on only 3 forms:
</p>
<ol>
<li><a href="http://en.wikipedia.org/wiki/Tetrahedron">A tetrahedron</a>,
representing 4 philosophers sharing 6 forks.</li>
<li><a href="http://en.wikipedia.org/wiki/Cube">A cube</a>,
representing 8 philosophers sharing 12 forks.</li>
<li><a href="http://en.wikipedia.org/wiki/Dodecahedron">A dodecahedron</a>,
representing 20 philosophers sharing 30 forks.</li>
</ol>
<p>
In order to eat, each philosopher must obtain all 3 of his adjacent forks.
</p>
<p>
The tetrahedron case is like the 2 and 3 philosopher round table case. It is
impossible for two or more philosophers to eat at once, and so the best that
can be done is for the 4 philosophers to each eat by themselves (30 seconds
each) for a total of 120 seconds. All 4 algorithms nail this degenerate case.
</p>
<p>
The cube case is easy to analyze. Four of the eight philosophers can eat at
any one time. Thus in two 30 second time slots, everyone can get a full
tummy. However only the <a href="#Smart">smart</a>, and <a
href="#Polite">smart & polite</a> algorithms are able to achieve this
minimum (with 4 cores). The <a href="#Persistent">persistent</a> and <a
href="#Ordered">ordered</a> algorithms are both significantly slower than
this. As we saw in the 2-D tests, the <a href="#Ordered">ordered</a>
algorithm is never faster than the degenerate sequential case.
</p>
<p>
As we move to the dodecahedron, 4 cores are not enough for even the <a
href="#Smart">smart</a> and <a href="#Polite">smart & polite</a>
algorithms to stay at the theoretical minimum. But the <a
href="#Polite">smart & polite</a> shows a small advantage over the <a
href="#Smart">smart</a> algorithm. A small amount of livelock is visible on
the <a href="#Smart">smart</a> algorithm's CPU load graphic (3rd from the
top), visualized by the bits of red.
</p>
<p>
The <a href="#Ordered">ordered</a> algorithm running on the dodecahedron
shows a relatively gradual "trailing off" slope in the CPU load graphic,
indicating mild starvation, and thus penalizing the performance of the
algorithm.
</p>
<p>
The <a href="#Persistent">persistent</a> algorithm running on the
dodecahedron performs the worst. In the CPU load graphic a significant
amount of cpu wasted on system calls is quite evident.
</p>
<a name="d3p8"></a><h3>A 3-D Table on a 8 Core Machine</h3>
<img src="d3p8.jpg" align="right">
<p>
Running the
<a href="#codeB">same test</a> on an 8 core machine is qualitatively the same
but with a few differences worth pointing out:
</p>
<ul>
<li><p>
The persistent algorithm now has enough processing power to nail the theoretical
minimum on the cube.
</p></li>
<li><p>
The slope of the expense of the <a href="#Persistent">persistent</a>
algorithm from the cube to the dodecahedron appears greater than that of the
<a href="#Ordered">ordered</a> algorithm, and thus would likely eventually
become more expensive than the <a href="#Ordered">ordered</a> algorithm as
more philosophers are added.
</p></li>
<li><p>
The <a href="#Smart">smart</a> and <a href="#Polite">smart & polite</a>
algorithms now have enough processing power to very nearly nail the
theoretical minimum on the dodecahedron. This theoretical minimum requires 8
processors, so this machine is just on the edge of delivering that minimum.
</p></li>
</ul>
<p>
Concerns of any significant livelock appear to be 100% addressed by the smart
& polite algorithm. Please feel free to run <a href="#codeB">this
test</a> on your own machine and publicly report your results.
</p>
<a name="Summary"></a><h2>Summary</h2>
<p>
Four algorithms have been presented and performance tested on 4 and 8 core
machines, and under a variety of tests. Each of these four algorithms is a
different implementation for <code>std::lock()</code> for the two and three
mutex locking case. An algorithm termed herein as <a href="#Polite">smart
& polite</a> has been shown to never be worse than any other algorithm,
and often significantly superior.
</p>
<p>
The <a href="#Polite">smart & polite</a> algorithm attempts to lock the
first mutex in the group and then try-lock the rest. If any mutex fails the
try-lock, everything is unlocked, a call to yield is made, and then the
algorithm repeats except that the mutex that previously failed the try-lock
is the first one locked. Code is given for the 2 and 3 mutex cases.
Expanding this algorithm to N variadic mutexes is left as an exercise for the
reader, but has been implemented in <a
href="http://libcxx.llvm.org">libc++</a> (i.e. it is not unreasonably
difficult).
</p>
<a name="codeA"></a><h2>Appendix A: Round Table Code</h2>
<blockquote><pre>
#include <chrono>
#include <mutex>
#include <random>
#include <array>
#include <vector>
#include <thread>
#include <iostream>
#ifdef SMART_POLITE
template <class L0, class L1>
void
lock(L0& l0, L1& l1)
{
while (true)
{
{
std::unique_lock<L0> u0(l0);
if (l1.try_lock())
{
u0.release();
break;
}
}
std::this_thread::yield();
{
std::unique_lock<L1> u1(l1);
if (l0.try_lock())
{
u1.release();
break;
}
}
std::this_thread::yield();
}
}
#elif defined(SMART)
template <class L0, class L1>
void
lock(L0& l0, L1& l1)
{
while (true)
{
{
std::unique_lock<L0> u0(l0);
if (l1.try_lock())
{
u0.release();
break;
}
}
{
std::unique_lock<L1> u1(l1);
if (l0.try_lock())
{
u1.release();
break;
}
}
}
}
#elif defined(PERSISTENT)
template <class L0, class L1>
void
lock(L0& l0, L1& l1)
{
while (true)
{
std::unique_lock<L0> u0(l0);
if (l1.try_lock())
{
u0.release();
break;
}
}
}
#elif defined(ORDERED)
template <class L0>
void
lock(L0& l0, L0& l1)
{
if (l0.mutex() < l1.mutex())
{
std::unique_lock<L0> u0(l0);
l1.lock();
u0.release();
}
else
{
std::unique_lock<L0> u1(l1);
l0.lock();
u1.release();
}
}
#endif
class Philosopher
{
std::mt19937_64 eng_{std::random_device{}()};
std::mutex& left_fork_;
std::mutex& right_fork_;
std::chrono::milliseconds eat_time_{0};
static constexpr std::chrono::seconds full_{30};
public:
Philosopher(std::mutex& left, std::mutex& right);
void dine();
private:
void eat();
bool flip_coin();
std::chrono::milliseconds get_eat_duration();
};
constexpr std::chrono::seconds Philosopher::full_;
Philosopher::Philosopher(std::mutex& left, std::mutex& right)
: left_fork_(left)
, right_fork_(right)
{}
void
Philosopher::dine()
{
while (eat_time_ < full_)
eat();
}
void
Philosopher::eat()
{
using Lock = std::unique_lock<std::mutex>;
Lock first;
Lock second;
if (flip_coin())
{
first = Lock(left_fork_, std::defer_lock);
second = Lock(right_fork_, std::defer_lock);
}
else
{
first = Lock(right_fork_, std::defer_lock);
second = Lock(left_fork_, std::defer_lock);
}
auto d = get_eat_duration();
::lock(first, second);
auto end = std::chrono::steady_clock::now() + d;
while (std::chrono::steady_clock::now() < end)
;
eat_time_ += d;
}
bool
Philosopher::flip_coin()
{
std::bernoulli_distribution d;
return d(eng_);
}
std::chrono::milliseconds
Philosopher::get_eat_duration()
{
std::uniform_int_distribution<> ms(1, 10);
return std::min(std::chrono::milliseconds(ms(eng_)), full_ - eat_time_);
}
int
main()
{
#ifdef SMART_POLITE
std::cout << "SMART_POLITE\n";
#elif defined(SMART)
std::cout << "SMART\n";
#elif defined(PERSISTENT)
std::cout << "PERSISTENT\n";
#elif defined(ORDERED)
std::cout << "ORDERED\n";
#endif
for (unsigned nt = 2; nt <= 32; ++nt)
{
std::vector<std::mutex> table(nt);
std::vector<Philosopher> diners;
for (unsigned i = 0; i < table.size(); ++i)
{
int j = i;
int k = j < table.size() -1 ? j+1 : 0;
diners.push_back(Philosopher(table[j], table[k]));
}
std::vector<std::thread> threads(diners.size());
unsigned i = 0;