1 /* This file is part of the Linux Trace Toolkit viewer
2 * Copyright (C) 2009, 2010 Benjamin Poirier <benjamin.poirier@polymtl.ca>
4 * This program is free software: you can redistribute it and/or modify it
5 * under the terms of the GNU Lesser General Public License as published by
6 * the Free Software Foundation, either version 2.1 of the License, or (at
7 * your option) any later version.
9 * This program is distributed in the hope that it will be useful, but WITHOUT
10 * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
11 * FITNESS FOR A PARTICULAR PURPOSE. See the GNU Lesser General Public
12 * License for more details.
14 * You should have received a copy of the GNU Lesser General Public License
15 * along with this program. If not, see <http://www.gnu.org/licenses/>.
17 #define _ISOC99_SOURCE
32 #include "sync_chain.h"
34 #include "event_analysis_chull.h"
51 // Functions common to all analysis modules
52 static void initAnalysisCHull(SyncState
* const syncState
);
53 static void destroyAnalysisCHull(SyncState
* const syncState
);
55 static void analyzeMessageCHull(SyncState
* const syncState
, Message
* const
57 static GArray
* finalizeAnalysisCHull(SyncState
* const syncState
);
58 static void printAnalysisStatsCHull(SyncState
* const syncState
);
59 static void writeAnalysisGraphsPlotsCHull(SyncState
* const syncState
, const
60 unsigned int i
, const unsigned int j
);
62 // Functions specific to this module
63 static void openGraphFiles(SyncState
* const syncState
);
64 static void closeGraphFiles(SyncState
* const syncState
);
65 static void writeGraphFiles(SyncState
* const syncState
);
66 static void gfDumpHullToFile(gpointer data
, gpointer userData
);
68 static void grahamScan(GQueue
* const hull
, Point
* const newPoint
, const
70 static int jointCmp(const Point
* const p1
, const Point
* const p2
, const Point
*
71 const p3
) __attribute__((pure
));
72 static double crossProductK(const Point
const* p1
, const Point
const* p2
,
73 const Point
const* p3
, const Point
const* p4
) __attribute__((pure
));
74 static Factors
* calculateFactorsExact(GQueue
* const cu
, GQueue
* const cl
, const
75 LineType lineType
) __attribute__((pure
));
76 static void calculateFactorsFallback(GQueue
* const cr
, GQueue
* const cs
,
77 FactorsCHull
* const result
);
78 static double slope(const Point
* const p1
, const Point
* const p2
)
79 __attribute__((pure
));
80 static double intercept(const Point
* const p1
, const Point
* const p2
)
81 __attribute__((pure
));
82 static GArray
* reduceFactors(SyncState
* const syncState
, FactorsCHull
**
84 static double verticalDistance(Point
* p1
, Point
* p2
, Point
* const point
)
85 __attribute__((pure
));
86 static void floydWarshall(SyncState
* const syncState
, FactorsCHull
** const
87 allFactors
, double*** const distances
, unsigned int*** const
89 static void getFactors(FactorsCHull
** const allFactors
, unsigned int** const
90 predecessors
, unsigned int* const references
, const unsigned int traceNum
,
91 Factors
* const factors
);
93 static void gfPointDestroy(gpointer data
, gpointer userData
);
96 static AnalysisModule analysisModuleCHull
= {
98 .initAnalysis
= &initAnalysisCHull
,
99 .destroyAnalysis
= &destroyAnalysisCHull
,
100 .analyzeMessage
= &analyzeMessageCHull
,
101 .finalizeAnalysis
= &finalizeAnalysisCHull
,
102 .printAnalysisStats
= &printAnalysisStatsCHull
,
104 .writeTraceTraceForePlots
= &writeAnalysisGraphsPlotsCHull
,
108 const char* const approxNames
[]= {
111 [FALLBACK
]= "Fallback",
112 [INCOMPLETE
]= "Incomplete",
114 [SCREWED
]= "Screwed",
119 * Analysis module registering function
121 void registerAnalysisCHull()
123 g_queue_push_tail(&analysisModules
, &analysisModuleCHull
);
128 * Analysis init function
130 * This function is called at the beginning of a synchronization run for a set
133 * Allocate some of the analysis specific data structures
136 * syncState container for synchronization data.
137 * This function allocates or initializes these analysisData
142 static void initAnalysisCHull(SyncState
* const syncState
)
145 AnalysisDataCHull
* analysisData
;
147 analysisData
= malloc(sizeof(AnalysisDataCHull
));
148 syncState
->analysisData
= analysisData
;
150 analysisData
->hullArray
= malloc(syncState
->traceNb
* sizeof(GQueue
**));
151 for (i
= 0; i
< syncState
->traceNb
; i
++)
153 analysisData
->hullArray
[i
]= malloc(syncState
->traceNb
* sizeof(GQueue
*));
155 for (j
= 0; j
< syncState
->traceNb
; j
++)
157 analysisData
->hullArray
[i
][j
]= g_queue_new();
161 if (syncState
->stats
)
163 analysisData
->stats
= malloc(sizeof(AnalysisStatsCHull
));
164 analysisData
->stats
->dropped
= 0;
165 analysisData
->stats
->allFactors
= NULL
;
168 if (syncState
->graphsStream
)
170 analysisData
->graphsData
= malloc(sizeof(AnalysisGraphsDataCHull
));
171 openGraphFiles(syncState
);
172 analysisData
->graphsData
->allFactors
= NULL
;
178 * Create and open files used to store convex hull points to genereate
179 * graphs. Allocate and populate array to store file pointers.
182 * syncState: container for synchronization data
184 static void openGraphFiles(SyncState
* const syncState
)
190 AnalysisDataCHull
* analysisData
;
192 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
194 cwd
= changeToGraphsDir(syncState
->graphsDir
);
196 analysisData
->graphsData
->hullPoints
= malloc(syncState
->traceNb
*
198 for (i
= 0; i
< syncState
->traceNb
; i
++)
200 analysisData
->graphsData
->hullPoints
[i
]= malloc(syncState
->traceNb
*
202 for (j
= 0; j
< syncState
->traceNb
; j
++)
206 retval
= snprintf(name
, sizeof(name
),
207 "analysis_chull-%03u_to_%03u.data", j
, i
);
208 if (retval
> sizeof(name
) - 1)
210 name
[sizeof(name
) - 1]= '\0';
212 if ((analysisData
->graphsData
->hullPoints
[i
][j
]= fopen(name
, "w")) ==
215 g_error(strerror(errno
));
224 g_error(strerror(errno
));
231 * Write hull points to files to generate graphs.
234 * syncState: container for synchronization data
236 static void writeGraphFiles(SyncState
* const syncState
)
239 AnalysisDataCHull
* analysisData
;
241 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
243 for (i
= 0; i
< syncState
->traceNb
; i
++)
245 for (j
= 0; j
< syncState
->traceNb
; j
++)
249 g_queue_foreach(analysisData
->hullArray
[i
][j
],
251 analysisData
->graphsData
->hullPoints
[i
][j
]);
259 * A GFunc for g_queue_foreach. Write a hull point to a file used to generate
263 * data: Point*, point to write to the file
264 * userData: FILE*, file pointer where to write the point
266 static void gfDumpHullToFile(gpointer data
, gpointer userData
)
270 point
= (Point
*) data
;
271 fprintf((FILE*) userData
, "%20" PRIu64
" %20" PRIu64
"\n", point
->x
, point
->y
);
276 * Close files used to store convex hull points to generate graphs.
277 * Deallocate array to store file pointers.
280 * syncState: container for synchronization data
282 static void closeGraphFiles(SyncState
* const syncState
)
285 AnalysisDataCHull
* analysisData
;
288 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
290 if (analysisData
->graphsData
->hullPoints
== NULL
)
295 for (i
= 0; i
< syncState
->traceNb
; i
++)
297 for (j
= 0; j
< syncState
->traceNb
; j
++)
301 retval
= fclose(analysisData
->graphsData
->hullPoints
[i
][j
]);
304 g_error(strerror(errno
));
308 free(analysisData
->graphsData
->hullPoints
[i
]);
310 free(analysisData
->graphsData
->hullPoints
);
311 analysisData
->graphsData
->hullPoints
= NULL
;
316 * Analysis destroy function
318 * Free the analysis specific data structures
321 * syncState container for synchronization data.
322 * This function deallocates these analysisData members:
326 static void destroyAnalysisCHull(SyncState
* const syncState
)
329 AnalysisDataCHull
* analysisData
;
331 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
333 if (analysisData
== NULL
)
338 for (i
= 0; i
< syncState
->traceNb
; i
++)
340 for (j
= 0; j
< syncState
->traceNb
; j
++)
342 g_queue_foreach(analysisData
->hullArray
[i
][j
], gfPointDestroy
, NULL
);
343 g_queue_free(analysisData
->hullArray
[i
][j
]);
345 free(analysisData
->hullArray
[i
]);
347 free(analysisData
->hullArray
);
349 if (syncState
->stats
)
351 if (analysisData
->stats
->allFactors
!= NULL
)
353 freeAllFactors(syncState
->traceNb
, analysisData
->stats
->allFactors
);
356 free(analysisData
->stats
);
359 if (syncState
->graphsStream
)
361 if (analysisData
->graphsData
->hullPoints
!= NULL
)
363 closeGraphFiles(syncState
);
366 if (!syncState
->stats
&& analysisData
->graphsData
->allFactors
!= NULL
)
368 freeAllFactors(syncState
->traceNb
, analysisData
->graphsData
->allFactors
);
371 free(analysisData
->graphsData
);
374 free(syncState
->analysisData
);
375 syncState
->analysisData
= NULL
;
380 * Perform analysis on an event pair.
383 * syncState container for synchronization data
384 * message structure containing the events
386 static void analyzeMessageCHull(SyncState
* const syncState
, Message
* const message
)
388 AnalysisDataCHull
* analysisData
;
393 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
395 newPoint
= malloc(sizeof(Point
));
396 if (message
->inE
->traceNum
< message
->outE
->traceNum
)
398 // CA is inE->traceNum
399 newPoint
->x
= message
->inE
->cpuTime
;
400 newPoint
->y
= message
->outE
->cpuTime
;
402 g_debug("Reception point hullArray[%lu][%lu] "
403 "x= inE->time= %" PRIu64
" y= outE->time= %" PRIu64
,
404 message
->inE
->traceNum
, message
->outE
->traceNum
, newPoint
->x
,
409 // CA is outE->traceNum
410 newPoint
->x
= message
->outE
->cpuTime
;
411 newPoint
->y
= message
->inE
->cpuTime
;
413 g_debug("Send point hullArray[%lu][%lu] "
414 "x= inE->time= %" PRIu64
" y= outE->time= %" PRIu64
,
415 message
->inE
->traceNum
, message
->outE
->traceNum
, newPoint
->x
,
420 analysisData
->hullArray
[message
->inE
->traceNum
][message
->outE
->traceNum
];
422 if (hull
->length
>= 1 && newPoint
->x
< ((Point
*)
423 g_queue_peek_tail(hull
))->x
)
425 if (syncState
->stats
)
427 analysisData
->stats
->dropped
++;
434 grahamScan(hull
, newPoint
, hullType
);
440 * Construct one half of a convex hull from abscissa-sorted points
443 * hull: the points already in the hull
444 * newPoint: a new point to consider
445 * type: which half of the hull to construct
447 static void grahamScan(GQueue
* const hull
, Point
* const newPoint
, const
452 g_debug("grahamScan(hull (length: %u), newPoint, %s)", hull
->length
, type
453 == LOWER
? "LOWER" : "UPPER");
464 if (hull
->length
>= 2)
466 g_debug("jointCmp(hull[%u], hull[%u], newPoint) * inversionFactor = %d * %d = %d",
469 jointCmp(g_queue_peek_nth(hull
, hull
->length
- 2),
470 g_queue_peek_tail(hull
), newPoint
),
472 jointCmp(g_queue_peek_nth(hull
, hull
->length
- 2),
473 g_queue_peek_tail(hull
), newPoint
) * inversionFactor
);
475 while (hull
->length
>= 2 && jointCmp(g_queue_peek_nth(hull
, hull
->length
-
476 2), g_queue_peek_tail(hull
), newPoint
) * inversionFactor
<= 0)
478 g_debug("Removing hull[%u]", hull
->length
);
479 free((Point
*) g_queue_pop_tail(hull
));
481 if (hull
->length
>= 2)
483 g_debug("jointCmp(hull[%u], hull[%u], newPoint) * inversionFactor = %d * %d = %d",
486 jointCmp(g_queue_peek_nth(hull
, hull
->length
- 2),
487 g_queue_peek_tail(hull
), newPoint
),
489 jointCmp(g_queue_peek_nth(hull
, hull
->length
- 2),
490 g_queue_peek_tail(hull
), newPoint
) * inversionFactor
);
493 g_queue_push_tail(hull
, newPoint
);
498 * Finalize the factor calculations
501 * syncState container for synchronization data.
504 * Factors[traceNb] synchronization factors for each trace
506 static GArray
* finalizeAnalysisCHull(SyncState
* const syncState
)
508 AnalysisDataCHull
* analysisData
;
510 FactorsCHull
** allFactors
;
512 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
514 if (syncState
->graphsStream
&& analysisData
->graphsData
->hullPoints
!= NULL
)
516 writeGraphFiles(syncState
);
517 closeGraphFiles(syncState
);
520 allFactors
= calculateAllFactors(syncState
);
522 factors
= reduceFactors(syncState
, allFactors
);
524 if (syncState
->stats
|| syncState
->graphsStream
)
526 if (syncState
->stats
)
528 analysisData
->stats
->allFactors
= allFactors
;
531 if (syncState
->graphsStream
)
533 analysisData
->graphsData
->allFactors
= allFactors
;
538 freeAllFactors(syncState
->traceNb
, allFactors
);
546 * Print statistics related to analysis. Must be called after
550 * syncState container for synchronization data.
552 static void printAnalysisStatsCHull(SyncState
* const syncState
)
554 AnalysisDataCHull
* analysisData
;
557 if (!syncState
->stats
)
562 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
564 printf("Convex hull analysis stats:\n");
565 printf("\tout of order packets dropped from analysis: %u\n",
566 analysisData
->stats
->dropped
);
568 printf("\tNumber of points in convex hulls:\n");
570 for (i
= 0; i
< syncState
->traceNb
; i
++)
572 for (j
= i
+ 1; j
< syncState
->traceNb
; j
++)
574 printf("\t\t%3d - %-3d: lower half-hull %-5u upper half-hull %-5u\n",
575 i
, j
, analysisData
->hullArray
[j
][i
]->length
,
576 analysisData
->hullArray
[i
][j
]->length
);
580 printf("\tIndividual synchronization factors:\n");
582 for (i
= 0; i
< syncState
->traceNb
; i
++)
584 for (j
= i
+ 1; j
< syncState
->traceNb
; j
++)
586 FactorsCHull
* factorsCHull
;
588 factorsCHull
= &analysisData
->stats
->allFactors
[j
][i
];
589 printf("\t\t%3d - %-3d: %s", i
, j
,
590 approxNames
[factorsCHull
->type
]);
592 if (factorsCHull
->type
== EXACT
)
594 printf(" a0= % 7g a1= 1 %c %7g\n",
595 factorsCHull
->approx
->offset
,
596 factorsCHull
->approx
->drift
< 0. ? '-' : '+',
597 fabs(factorsCHull
->approx
->drift
));
599 else if (factorsCHull
->type
== MIDDLE
)
601 printf(" a0= % 7g a1= 1 %c %7g accuracy %7g\n",
602 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
603 - 1. < 0. ? '-' : '+', fabs(factorsCHull
->approx
->drift
-
604 1.), factorsCHull
->accuracy
);
605 printf("\t\t a0: % 7g to % 7g (delta= %7g)\n",
606 factorsCHull
->max
->offset
, factorsCHull
->min
->offset
,
607 factorsCHull
->min
->offset
- factorsCHull
->max
->offset
);
608 printf("\t\t a1: 1 %+7g to %+7g (delta= %7g)\n",
609 factorsCHull
->min
->drift
- 1., factorsCHull
->max
->drift
-
610 1., factorsCHull
->max
->drift
- factorsCHull
->min
->drift
);
612 else if (factorsCHull
->type
== FALLBACK
)
614 printf(" a0= % 7g a1= 1 %c %7g error= %7g\n",
615 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
616 - 1. < 0. ? '-' : '+', fabs(factorsCHull
->approx
->drift
-
617 1.), factorsCHull
->accuracy
);
619 else if (factorsCHull
->type
== INCOMPLETE
)
623 if (factorsCHull
->min
->drift
!= -INFINITY
)
625 printf("\t\t min: a0: % 7g a1: 1 %c %7g\n",
626 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
-
627 1. < 0 ? '-' : '+', fabs(factorsCHull
->min
->drift
-
630 if (factorsCHull
->max
->drift
!= INFINITY
)
632 printf("\t\t max: a0: % 7g a1: 1 %c %7g\n",
633 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
-
634 1. < 0 ? '-' : '+', fabs(factorsCHull
->max
->drift
-
638 else if (factorsCHull
->type
== SCREWED
)
642 if (factorsCHull
->min
!= NULL
&& factorsCHull
->min
->drift
!= -INFINITY
)
644 printf("\t\t min: a0: % 7g a1: 1 %c %7g\n",
645 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
-
646 1. < 0 ? '-' : '+', fabs(factorsCHull
->min
->drift
-
649 if (factorsCHull
->max
!= NULL
&& factorsCHull
->max
->drift
!= INFINITY
)
651 printf("\t\t max: a0: % 7g a1: 1 %c %7g\n",
652 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
-
653 1. < 0 ? '-' : '+', fabs(factorsCHull
->max
->drift
-
657 else if (factorsCHull
->type
== ABSENT
)
663 g_assert_not_reached();
671 * A GFunc for g_queue_foreach()
674 * data Point*, point to destroy
677 static void gfPointDestroy(gpointer data
, gpointer userData
)
681 point
= (Point
*) data
;
687 * Find out if a sequence of three points constitutes a "left turn" or a
691 * p1, p2, p3: The three points.
695 * 0 colinear (unlikely result since this uses floating point
699 static int jointCmp(const Point
const* p1
, const Point
const* p2
, const
703 const double fuzzFactor
= 0.;
705 result
= crossProductK(p1
, p2
, p1
, p3
);
706 g_debug("crossProductK(p1= (%" PRIu64
", %" PRIu64
"), "
707 "p2= (%" PRIu64
", %" PRIu64
"), p1= (%" PRIu64
", %" PRIu64
"), "
708 "p3= (%" PRIu64
", %" PRIu64
"))= %g",
709 p1
->x
, p1
->y
, p2
->x
, p2
->y
, p1
->x
, p1
->y
, p3
->x
, p3
->y
, result
);
710 if (result
< fuzzFactor
)
714 else if (result
> fuzzFactor
)
726 * Calculate the k component of the cross product of two vectors.
729 * p1, p2: start and end points of the first vector
730 * p3, p4: start and end points of the second vector
733 * the k component of the cross product when considering the two vectors to
734 * be in the i-j plane. The direction (sign) of the result can be useful to
735 * determine the relative orientation of the two vectors.
737 static double crossProductK(const Point
const* p1
, const Point
const* p2
,
738 const Point
const* p3
, const Point
const* p4
)
740 return ((double) p2
->x
- p1
->x
) * ((double) p4
->y
- p3
->y
) - ((double)
741 p2
->y
- p1
->y
) * ((double) p4
->x
- p3
->x
);
746 * Free a container of FactorsCHull
749 * traceNb: number of traces
750 * allFactors: container of FactorsCHull
752 void freeAllFactors(const unsigned int traceNb
, FactorsCHull
** const
757 for (i
= 0; i
< traceNb
; i
++)
759 for (j
= 0; j
<= i
; j
++)
761 destroyFactorsCHull(&allFactors
[i
][j
]);
770 * Free a FactorsCHull
773 * factorsCHull: container of Factors
775 void destroyFactorsCHull(FactorsCHull
* factorsCHull
)
777 if (factorsCHull
->type
== MIDDLE
|| factorsCHull
->type
==
778 INCOMPLETE
|| factorsCHull
->type
== ABSENT
)
780 free(factorsCHull
->min
);
781 free(factorsCHull
->max
);
783 else if (factorsCHull
->type
== SCREWED
)
785 if (factorsCHull
->min
!= NULL
)
787 free(factorsCHull
->min
);
789 if (factorsCHull
->max
!= NULL
)
791 free(factorsCHull
->max
);
795 if (factorsCHull
->type
== EXACT
|| factorsCHull
->type
== MIDDLE
||
796 factorsCHull
->type
== FALLBACK
)
798 free(factorsCHull
->approx
);
804 * Analyze the convex hulls to determine the synchronization factors between
805 * each pair of trace.
808 * syncState container for synchronization data.
811 * FactorsCHull*[TraceNum][TraceNum] array. See the documentation for the
812 * member allFactors of AnalysisStatsCHull.
814 FactorsCHull
** calculateAllFactors(SyncState
* const syncState
)
816 unsigned int traceNumA
, traceNumB
;
817 FactorsCHull
** allFactors
;
818 AnalysisDataCHull
* analysisData
;
820 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
822 // Allocate allFactors and calculate min and max
823 allFactors
= malloc(syncState
->traceNb
* sizeof(FactorsCHull
*));
824 for (traceNumA
= 0; traceNumA
< syncState
->traceNb
; traceNumA
++)
826 allFactors
[traceNumA
]= malloc((traceNumA
+ 1) * sizeof(FactorsCHull
));
828 allFactors
[traceNumA
][traceNumA
].type
= EXACT
;
829 allFactors
[traceNumA
][traceNumA
].approx
= malloc(sizeof(Factors
));
830 allFactors
[traceNumA
][traceNumA
].approx
->drift
= 1.;
831 allFactors
[traceNumA
][traceNumA
].approx
->offset
= 0.;
833 for (traceNumB
= 0; traceNumB
< traceNumA
; traceNumB
++)
840 size_t factorsOffset
;
842 {MINIMUM
, offsetof(FactorsCHull
, min
)},
843 {MAXIMUM
, offsetof(FactorsCHull
, max
)}
846 cr
= analysisData
->hullArray
[traceNumB
][traceNumA
];
847 cs
= analysisData
->hullArray
[traceNumA
][traceNumB
];
849 for (i
= 0; i
< sizeof(loopValues
) / sizeof(*loopValues
); i
++)
851 g_debug("allFactors[%u][%u].%s = calculateFactorsExact(cr= hullArray[%u][%u], cs= hullArray[%u][%u], %s)",
852 traceNumA
, traceNumB
, loopValues
[i
].factorsOffset
==
853 offsetof(FactorsCHull
, min
) ? "min" : "max", traceNumB
,
854 traceNumA
, traceNumA
, traceNumB
, loopValues
[i
].lineType
==
855 MINIMUM
? "MINIMUM" : "MAXIMUM");
856 *((Factors
**) ((void*) &allFactors
[traceNumA
][traceNumB
] +
857 loopValues
[i
].factorsOffset
))=
858 calculateFactorsExact(cr
, cs
, loopValues
[i
].lineType
);
863 // Calculate approx when possible
864 for (traceNumA
= 0; traceNumA
< syncState
->traceNb
; traceNumA
++)
866 for (traceNumB
= 0; traceNumB
< traceNumA
; traceNumB
++)
868 FactorsCHull
* factorsCHull
;
870 factorsCHull
= &allFactors
[traceNumA
][traceNumB
];
871 if (factorsCHull
->min
== NULL
&& factorsCHull
->max
== NULL
)
873 factorsCHull
->type
= FALLBACK
;
874 calculateFactorsFallback(analysisData
->hullArray
[traceNumB
][traceNumA
],
875 analysisData
->hullArray
[traceNumA
][traceNumB
],
876 &allFactors
[traceNumA
][traceNumB
]);
878 else if (factorsCHull
->min
!= NULL
&& factorsCHull
->max
!= NULL
)
880 if (factorsCHull
->min
->drift
!= -INFINITY
&&
881 factorsCHull
->max
->drift
!= INFINITY
)
883 factorsCHull
->type
= MIDDLE
;
884 calculateFactorsMiddle(factorsCHull
);
886 else if (factorsCHull
->min
->drift
!= -INFINITY
||
887 factorsCHull
->max
->drift
!= INFINITY
)
889 factorsCHull
->type
= INCOMPLETE
;
893 factorsCHull
->type
= ABSENT
;
898 //g_assert_not_reached();
899 factorsCHull
->type
= SCREWED
;
908 /* Calculate approximative factors based on minimum and maximum limits. The
909 * best approximation to make is the interior bissector of the angle formed by
910 * the minimum and maximum lines.
912 * The formulae used come from [Haddad, Yoram: Performance dans les systèmes
913 * répartis: des outils pour les mesures, Université de Paris-Sud, Centre
914 * d'Orsay, September 1988] Section 6.1 p.44
916 * The reasoning for choosing this estimator comes from [Duda, A., Harrus, G.,
917 * Haddad, Y., and Bernard, G.: Estimating global time in distributed systems,
918 * Proc. 7th Int. Conf. on Distributed Computing Systems, Berlin, volume 18,
922 * factors: contains the min and max limits, used to store the result
924 void calculateFactorsMiddle(FactorsCHull
* const factors
)
926 double amin
, amax
, bmin
, bmax
, bhat
;
928 amin
= factors
->max
->offset
;
929 amax
= factors
->min
->offset
;
930 bmin
= factors
->min
->drift
;
931 bmax
= factors
->max
->drift
;
933 g_assert_cmpfloat(bmax
, >=, bmin
);
935 factors
->approx
= malloc(sizeof(Factors
));
936 bhat
= (bmax
* bmin
- 1. + sqrt(1. + pow(bmax
, 2.) * pow(bmin
, 2.) +
937 pow(bmax
, 2.) + pow(bmin
, 2.))) / (bmax
+ bmin
);
938 factors
->approx
->offset
= amax
- (amax
- amin
) / 2. * (pow(bhat
, 2.) + 1.)
939 / (1. + bhat
* bmax
);
940 factors
->approx
->drift
= bhat
;
941 factors
->accuracy
= bmax
- bmin
;
946 * Analyze the convex hulls to determine the minimum or maximum
947 * synchronization factors between one pair of trace.
949 * This implements and improves upon the algorithm in [Haddad, Yoram:
950 * Performance dans les systèmes répartis: des outils pour les mesures,
951 * Université de Paris-Sud, Centre d'Orsay, September 1988] Section 6.2 p.47
953 * Some degenerate cases are possible:
954 * 1) the result is unbounded. In that case, when searching for the maximum
955 * factors, result->drift= INFINITY; result->offset= -INFINITY. When
956 * searching for the minimum factors, it is the opposite. It is not
957 * possible to improve the situation with this data.
958 * 2) no line can be above the upper hull and below the lower hull. This is
959 * because the hulls intersect each other or are reversed. This means that
960 * an assertion was false. Most probably, the clocks are not linear. It is
961 * possible to repeat the search with another algorithm that will find a
962 * "best effort" approximation. See calculateFactorsApprox().
965 * cu: the upper half-convex hull, the line must pass above this
966 * and touch it in one point
967 * cl: the lower half-convex hull, the line must pass below this
968 * and touch it in one point
969 * lineType: search for minimum or maximum factors
972 * If a result is found, a struct Factors is allocated, filed with the
973 * result and returned
974 * NULL otherwise, degenerate case 2 is in effect
976 static Factors
* calculateFactorsExact(GQueue
* const cu
, GQueue
* const cl
, const
982 double inversionFactor
;
985 g_debug("calculateFactorsExact(cu= %p, cl= %p, %s)", cu
, cl
, lineType
==
986 MINIMUM
? "MINIMUM" : "MAXIMUM");
988 if (lineType
== MINIMUM
)
992 inversionFactor
= -1.;
1004 // Check for degenerate case 1
1005 if (c1
->length
== 0 || c2
->length
== 0 || ((Point
*) g_queue_peek_nth(c1
,
1006 i1
))->x
>= ((Point
*) g_queue_peek_nth(c2
, i2
))->x
)
1008 result
= malloc(sizeof(Factors
));
1009 if (lineType
== MINIMUM
)
1011 result
->drift
= -INFINITY
;
1012 result
->offset
= INFINITY
;
1016 result
->drift
= INFINITY
;
1017 result
->offset
= -INFINITY
;
1029 g_queue_peek_nth(c1
, i1
),
1030 g_queue_peek_nth(c2
, i2
),
1031 g_queue_peek_nth(c1
, i1
),
1032 g_queue_peek_nth(c2
, i2
- 1)) * inversionFactor
< 0.
1035 if (((Point
*) g_queue_peek_nth(c1
, i1
))->x
1036 < ((Point
*) g_queue_peek_nth(c2
, i2
- 1))->x
)
1042 // Degenerate case 2
1048 i1
+ 1 < c1
->length
- 1
1050 g_queue_peek_nth(c1
, i1
),
1051 g_queue_peek_nth(c2
, i2
),
1052 g_queue_peek_nth(c1
, i1
+ 1),
1053 g_queue_peek_nth(c2
, i2
)) * inversionFactor
< 0.
1056 if (((Point
*) g_queue_peek_nth(c1
, i1
+ 1))->x
1057 < ((Point
*) g_queue_peek_nth(c2
, i2
))->x
)
1063 // Degenerate case 2
1071 g_queue_peek_nth(c1
, i1
),
1072 g_queue_peek_nth(c2
, i2
),
1073 g_queue_peek_nth(c1
, i1
),
1074 g_queue_peek_nth(c2
, i2
- 1)) * inversionFactor
< 0.
1077 p1
= g_queue_peek_nth(c1
, i1
);
1078 p2
= g_queue_peek_nth(c2
, i2
);
1080 g_debug("Resulting points are: c1[i1]: x= %" PRIu64
" y= %" PRIu64
1081 " c2[i2]: x= %" PRIu64
" y= %" PRIu64
"", p1
->x
, p1
->y
, p2
->x
, p2
->y
);
1083 result
= malloc(sizeof(Factors
));
1084 result
->drift
= slope(p1
, p2
);
1085 result
->offset
= intercept(p1
, p2
);
1087 g_debug("Resulting factors are: drift= %g offset= %g", result
->drift
,
1095 * Analyze the convex hulls to determine approximate synchronization factors
1096 * between one pair of trace when there is no line that can fit in the
1097 * corridor separating them.
1099 * This implements the algorithm in [Ashton, P.: Algorithms for Off-line Clock
1100 * Synchronisation, University of Canterbury, December 1995, 26] Section 4.2.2
1103 * For each point p1 in cr
1104 * For each point p2 in cs
1106 * Calculate the line paramaters
1107 * For each point p3 in each convex hull
1108 * If p3 is on the wrong side of the line
1110 * If error < errorMin
1114 * cr: the upper half-convex hull
1115 * cs: the lower half-convex hull
1116 * result: a pointer to the pre-allocated struct where the results
1119 static void calculateFactorsFallback(GQueue
* const cr
, GQueue
* const cs
,
1120 FactorsCHull
* const result
)
1122 unsigned int i
, j
, k
;
1127 approx
= malloc(sizeof(Factors
));
1129 for (i
= 0; i
< cs
->length
; i
++)
1131 for (j
= 0; j
< cr
->length
; j
++)
1138 if (((Point
*) g_queue_peek_nth(cs
, i
))->x
< ((Point
*)g_queue_peek_nth(cr
, j
))->x
)
1140 p1
= *(Point
*)g_queue_peek_nth(cs
, i
);
1141 p2
= *(Point
*)g_queue_peek_nth(cr
, j
);
1145 p1
= *(Point
*)g_queue_peek_nth(cr
, j
);
1146 p2
= *(Point
*)g_queue_peek_nth(cs
, i
);
1149 // The lower hull should be above the point
1150 for (k
= 0; k
< cs
->length
; k
++)
1152 if (jointCmp(&p1
, &p2
, g_queue_peek_nth(cs
, k
)) < 0.)
1154 error
+= verticalDistance(&p1
, &p2
, g_queue_peek_nth(cs
, k
));
1158 // The upper hull should be below the point
1159 for (k
= 0; k
< cr
->length
; k
++)
1161 if (jointCmp(&p1
, &p2
, g_queue_peek_nth(cr
, k
)) > 0.)
1163 error
+= verticalDistance(&p1
, &p2
, g_queue_peek_nth(cr
, k
));
1167 if (error
< errorMin
)
1169 g_debug("Fallback: i= %u j= %u is a better match (error= %g)", i
, j
, error
);
1170 approx
->drift
= slope(&p1
, &p2
);
1171 approx
->offset
= intercept(&p1
, &p2
);
1177 result
->approx
= approx
;
1178 result
->accuracy
= errorMin
;
1183 * Calculate the vertical distance between a line and a point
1186 * p1, p2: Two points defining the line
1190 * the vertical distance
1192 static double verticalDistance(Point
* p1
, Point
* p2
, Point
* const point
)
1194 return fabs(slope(p1
, p2
) * point
->x
+ intercept(p1
, p2
) - point
->y
);
1199 * Calculate the slope between two points
1202 * p1, p2 the two points
1207 static double slope(const Point
* const p1
, const Point
* const p2
)
1209 return ((double) p2
->y
- p1
->y
) / (p2
->x
- p1
->x
);
1213 /* Calculate the y-intercept of a line that passes by two points
1216 * p1, p2 the two points
1221 static double intercept(const Point
* const p1
, const Point
* const p2
)
1223 return ((double) p2
->y
* p1
->x
- (double) p1
->y
* p2
->x
) / ((double) p1
->x
- p2
->x
);
1228 * Calculate a resulting offset and drift for each trace.
1230 * Traces are assembled in groups. A group is an "island" of nodes/traces that
1231 * exchanged messages. A reference is determined for each group by using a
1232 * shortest path search based on the accuracy of the approximation. This also
1233 * forms a tree of the best way to relate each node's clock to the reference's
1234 * based on the accuracy. Sometimes it may be necessary or advantageous to
1235 * propagate the factors through intermediary clocks. Resulting factors for
1236 * each trace are determined based on this tree.
1238 * This part was not the focus of my research. The algorithm used here is
1239 * inexact in some ways:
1240 * 1) The reference used may not actually be the best one to use. This is
1241 * because the accuracy is not corrected based on the drift during the
1242 * shortest path search.
1243 * 2) The min and max factors are not propagated and are no longer valid.
1244 * 3) Approximations of different types (MIDDLE and FALLBACK) are compared
1245 * together. The "accuracy" parameters of these have different meanings and
1246 * are not readily comparable.
1248 * Nevertheless, the result is satisfactory. You just can't tell "how much" it
1251 * Two alternative (and subtly different) ways of propagating factors to
1252 * preserve min and max boundaries have been proposed, see:
1253 * [Duda, A., Harrus, G., Haddad, Y., and Bernard, G.: Estimating global time
1254 * in distributed systems, Proc. 7th Int. Conf. on Distributed Computing
1255 * Systems, Berlin, volume 18, 1987] p.304
1257 * [Jezequel, J.M., and Jard, C.: Building a global clock for observing
1258 * computations in distributed memory parallel computers, Concurrency:
1259 * Practice and Experience 8(1), volume 8, John Wiley & Sons, Ltd Chichester,
1260 * 1996, 32] Section 5; which is mostly the same as
1261 * [Jezequel, J.M.: Building a global time on parallel machines, Proceedings
1262 * of the 3rd International Workshop on Distributed Algorithms, LNCS, volume
1263 * 392, 136–147, 1989] Section 5
1266 * syncState: container for synchronization data.
1267 * allFactors: offset and drift between each pair of traces
1270 * Factors[traceNb] synchronization factors for each trace
1272 static GArray
* reduceFactors(SyncState
* const syncState
, FactorsCHull
** const
1277 unsigned int** predecessors
;
1278 double* distanceSums
;
1279 unsigned int* references
;
1282 // Solve the all-pairs shortest path problem using the Floyd-Warshall
1284 floydWarshall(syncState
, allFactors
, &distances
, &predecessors
);
1286 /* Find the reference for each node
1288 * First calculate, for each node, the sum of the distances to each other
1289 * node it can reach.
1291 * Then, go through each "island" of traces to find the trace that has the
1292 * lowest distance sum. Assign this trace as the reference to each trace
1295 distanceSums
= malloc(syncState
->traceNb
* sizeof(double));
1296 for (i
= 0; i
< syncState
->traceNb
; i
++)
1298 distanceSums
[i
]= 0.;
1299 for (j
= 0; j
< syncState
->traceNb
; j
++)
1301 distanceSums
[i
]+= distances
[i
][j
];
1305 references
= malloc(syncState
->traceNb
* sizeof(unsigned int));
1306 for (i
= 0; i
< syncState
->traceNb
; i
++)
1308 references
[i
]= UINT_MAX
;
1310 for (i
= 0; i
< syncState
->traceNb
; i
++)
1312 if (references
[i
] == UINT_MAX
)
1314 unsigned int reference
;
1315 double distanceSumMin
;
1317 // A node is its own reference by default
1319 distanceSumMin
= INFINITY
;
1320 for (j
= 0; j
< syncState
->traceNb
; j
++)
1322 if (distances
[i
][j
] != INFINITY
&& distanceSums
[j
] <
1326 distanceSumMin
= distanceSums
[j
];
1329 for (j
= 0; j
< syncState
->traceNb
; j
++)
1331 if (distances
[i
][j
] != INFINITY
)
1333 references
[j
]= reference
;
1339 for (i
= 0; i
< syncState
->traceNb
; i
++)
1346 /* For each trace, calculate the factors based on their corresponding
1347 * tree. The tree is rooted at the reference and the shortest path to each
1348 * other nodes are the branches.
1350 factors
= g_array_sized_new(FALSE
, FALSE
, sizeof(Factors
),
1351 syncState
->traceNb
);
1352 g_array_set_size(factors
, syncState
->traceNb
);
1353 for (i
= 0; i
< syncState
->traceNb
; i
++)
1355 getFactors(allFactors
, predecessors
, references
, i
, &g_array_index(factors
,
1359 for (i
= 0; i
< syncState
->traceNb
; i
++)
1361 free(predecessors
[i
]);
1371 * Perform an all-source shortest path search using the Floyd-Warshall
1374 * The algorithm is implemented accoding to the description here:
1375 * http://web.mit.edu/urban_or_book/www/book/chapter6/6.2.2.html
1378 * syncState: container for synchronization data.
1379 * allFactors: offset and drift between each pair of traces
1380 * distances: resulting matrix of the length of the shortest path between
1381 * two nodes. If there is no path between two nodes, the
1382 * length is INFINITY
1383 * predecessors: resulting matrix of each node's predecessor on the shortest
1384 * path between two nodes
1386 static void floydWarshall(SyncState
* const syncState
, FactorsCHull
** const
1387 allFactors
, double*** const distances
, unsigned int*** const
1390 unsigned int i
, j
, k
;
1392 // Setup initial conditions
1393 *distances
= malloc(syncState
->traceNb
* sizeof(double*));
1394 *predecessors
= malloc(syncState
->traceNb
* sizeof(unsigned int*));
1395 for (i
= 0; i
< syncState
->traceNb
; i
++)
1397 (*distances
)[i
]= malloc(syncState
->traceNb
* sizeof(double));
1398 for (j
= 0; j
< syncState
->traceNb
; j
++)
1402 g_assert(allFactors
[i
][j
].type
== EXACT
);
1404 (*distances
)[i
][j
]= 0.;
1408 unsigned int row
, col
;
1421 if (allFactors
[row
][col
].type
== MIDDLE
||
1422 allFactors
[row
][col
].type
== FALLBACK
)
1424 (*distances
)[i
][j
]= allFactors
[row
][col
].accuracy
;
1426 else if (allFactors
[row
][col
].type
== INCOMPLETE
||
1427 allFactors
[row
][col
].type
== SCREWED
||
1428 allFactors
[row
][col
].type
== ABSENT
)
1430 (*distances
)[i
][j
]= INFINITY
;
1434 g_assert_not_reached();
1439 (*predecessors
)[i
]= malloc(syncState
->traceNb
* sizeof(unsigned int));
1440 for (j
= 0; j
< syncState
->traceNb
; j
++)
1444 (*predecessors
)[i
][j
]= i
;
1448 (*predecessors
)[i
][j
]= UINT_MAX
;
1453 // Run the iterations
1454 for (k
= 0; k
< syncState
->traceNb
; k
++)
1456 for (i
= 0; i
< syncState
->traceNb
; i
++)
1458 for (j
= 0; j
< syncState
->traceNb
; j
++)
1462 distanceMin
= MIN((*distances
)[i
][j
], (*distances
)[i
][k
] +
1463 (*distances
)[k
][j
]);
1465 if (distanceMin
!= (*distances
)[i
][j
])
1467 (*predecessors
)[i
][j
]= (*predecessors
)[k
][j
];
1470 (*distances
)[i
][j
]= distanceMin
;
1478 * Cummulate the time correction factors to convert a node's time to its
1480 * This function recursively calls itself until it reaches the reference node.
1483 * allFactors: offset and drift between each pair of traces
1484 * predecessors: matrix of each node's predecessor on the shortest
1485 * path between two nodes
1486 * references: reference node for each node
1487 * traceNum: node for which to find the factors
1488 * factors: resulting factors
1490 static void getFactors(FactorsCHull
** const allFactors
, unsigned int** const
1491 predecessors
, unsigned int* const references
, const unsigned int traceNum
,
1492 Factors
* const factors
)
1494 unsigned int reference
;
1496 reference
= references
[traceNum
];
1498 if (reference
== traceNum
)
1500 factors
->offset
= 0.;
1505 Factors previousVertexFactors
;
1507 getFactors(allFactors
, predecessors
, references
,
1508 predecessors
[reference
][traceNum
], &previousVertexFactors
);
1510 // convertir de traceNum à reference
1512 // allFactors convertit de col à row
1514 if (reference
> traceNum
)
1516 factors
->offset
= previousVertexFactors
.drift
*
1517 allFactors
[reference
][traceNum
].approx
->offset
+
1518 previousVertexFactors
.offset
;
1519 factors
->drift
= previousVertexFactors
.drift
*
1520 allFactors
[reference
][traceNum
].approx
->drift
;
1524 factors
->offset
= previousVertexFactors
.drift
* (-1. *
1525 allFactors
[traceNum
][reference
].approx
->offset
/
1526 allFactors
[traceNum
][reference
].approx
->drift
) +
1527 previousVertexFactors
.offset
;
1528 factors
->drift
= previousVertexFactors
.drift
* (1. /
1529 allFactors
[traceNum
][reference
].approx
->drift
);
1536 * Write the analysis-specific graph lines in the gnuplot script.
1539 * syncState: container for synchronization data
1540 * i: first trace number
1541 * j: second trace number, garanteed to be larger than i
1543 void writeAnalysisGraphsPlotsCHull(SyncState
* const syncState
, const unsigned
1544 int i
, const unsigned int j
)
1546 AnalysisDataCHull
* analysisData
;
1547 FactorsCHull
* factorsCHull
;
1549 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
1551 fprintf(syncState
->graphsStream
,
1552 "\t\"analysis_chull-%1$03d_to_%2$03d.data\" "
1553 "title \"Lower half-hull\" with linespoints "
1554 "linecolor rgb \"#015a01\" linetype 4 pointtype 8 pointsize 0.8, \\\n"
1555 "\t\"analysis_chull-%2$03d_to_%1$03d.data\" "
1556 "title \"Upper half-hull\" with linespoints "
1557 "linecolor rgb \"#003366\" linetype 4 pointtype 10 pointsize 0.8, \\\n",
1560 factorsCHull
= &analysisData
->graphsData
->allFactors
[j
][i
];
1561 if (factorsCHull
->type
== EXACT
)
1563 fprintf(syncState
->graphsStream
,
1565 "title \"Exact conversion\" with lines "
1566 "linecolor rgb \"black\" linetype 1, \\\n",
1567 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
);
1569 else if (factorsCHull
->type
== MIDDLE
)
1571 fprintf(syncState
->graphsStream
,
1572 "\t%.2f + %.10f * x "
1573 "title \"Min conversion\" with lines "
1574 "linecolor rgb \"black\" linetype 5, \\\n",
1575 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
);
1576 fprintf(syncState
->graphsStream
,
1577 "\t%.2f + %.10f * x "
1578 "title \"Max conversion\" with lines "
1579 "linecolor rgb \"black\" linetype 8, \\\n",
1580 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
);
1581 fprintf(syncState
->graphsStream
,
1582 "\t%.2f + %.10f * x "
1583 "title \"Middle conversion\" with lines "
1584 "linecolor rgb \"black\" linetype 1, \\\n",
1585 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
);
1587 else if (factorsCHull
->type
== FALLBACK
)
1589 fprintf(syncState
->graphsStream
,
1590 "\t%.2f + %.10f * x "
1591 "title \"Fallback conversion\" with lines "
1592 "linecolor rgb \"gray60\" linetype 1, \\\n",
1593 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
);
1595 else if (factorsCHull
->type
== INCOMPLETE
)
1597 if (factorsCHull
->min
->drift
!= -INFINITY
)
1599 fprintf(syncState
->graphsStream
,
1600 "\t%.2f + %.10f * x "
1601 "title \"Min conversion\" with lines "
1602 "linecolor rgb \"black\" linetype 5, \\\n",
1603 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
);
1606 if (factorsCHull
->max
->drift
!= INFINITY
)
1608 fprintf(syncState
->graphsStream
,
1609 "\t%.2f + %.10f * x "
1610 "title \"Max conversion\" with lines "
1611 "linecolor rgb \"black\" linetype 8, \\\n",
1612 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
);
1615 else if (factorsCHull
->type
== SCREWED
)
1617 if (factorsCHull
->min
!= NULL
&& factorsCHull
->min
->drift
!= -INFINITY
)
1619 fprintf(syncState
->graphsStream
,
1620 "\t%.2f + %.10f * x "
1621 "title \"Min conversion\" with lines "
1622 "linecolor rgb \"black\" linetype 5, \\\n",
1623 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
);
1626 if (factorsCHull
->max
!= NULL
&& factorsCHull
->max
->drift
!= INFINITY
)
1628 fprintf(syncState
->graphsStream
,
1629 "\t%.2f + %.10f * x "
1630 "title \"Max conversion\" with lines "
1631 "linecolor rgb \"black\" linetype 8, \\\n",
1632 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
);
1635 else if (factorsCHull
->type
== ABSENT
)
1640 g_assert_not_reached();