1 /* This file is part of the Linux Trace Toolkit viewer
2 * Copyright (C) 2009 Benjamin Poirier <benjamin.poirier@polymtl.ca>
4 * This program is free software; you can redistribute it and/or modify
5 * it under the terms of the GNU General Public License Version 2 as
6 * published by the Free Software Foundation;
8 * This program is distributed in the hope that it will be useful,
9 * but WITHOUT ANY WARRANTY; without even the implied warranty of
10 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
11 * GNU General Public License for more details.
13 * You should have received a copy of the GNU General Public License
14 * along with this program; if not, write to the Free Software
15 * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
18 #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 registerAnalysisCHull() __attribute__((constructor (101)));
65 static void openGraphFiles(SyncState
* const syncState
);
66 static void closeGraphFiles(SyncState
* const syncState
);
67 static void writeGraphFiles(SyncState
* const syncState
);
68 static void gfDumpHullToFile(gpointer data
, gpointer userData
);
70 static void grahamScan(GQueue
* const hull
, Point
* const newPoint
, const
72 static int jointCmp(const Point
* const p1
, const Point
* const p2
, const Point
*
73 const p3
) __attribute__((pure
));
74 static double crossProductK(const Point
const* p1
, const Point
const* p2
,
75 const Point
const* p3
, const Point
const* p4
) __attribute__((pure
));
76 static Factors
* calculateFactorsExact(GQueue
* const cu
, GQueue
* const cl
, const
77 LineType lineType
) __attribute__((pure
));
78 static void calculateFactorsFallback(GQueue
* const cr
, GQueue
* const cs
,
79 FactorsCHull
* const result
);
80 static double slope(const Point
* const p1
, const Point
* const p2
)
81 __attribute__((pure
));
82 static double intercept(const Point
* const p1
, const Point
* const p2
)
83 __attribute__((pure
));
84 static GArray
* reduceFactors(SyncState
* const syncState
, FactorsCHull
**
86 static double verticalDistance(Point
* p1
, Point
* p2
, Point
* const point
)
87 __attribute__((pure
));
88 static void floydWarshall(SyncState
* const syncState
, FactorsCHull
** const
89 allFactors
, double*** const distances
, unsigned int*** const
91 static void getFactors(FactorsCHull
** const allFactors
, unsigned int** const
92 predecessors
, unsigned int* const references
, const unsigned int traceNum
,
93 Factors
* const factors
);
95 static void gfPointDestroy(gpointer data
, gpointer userData
);
98 static AnalysisModule analysisModuleCHull
= {
100 .initAnalysis
= &initAnalysisCHull
,
101 .destroyAnalysis
= &destroyAnalysisCHull
,
102 .analyzeMessage
= &analyzeMessageCHull
,
103 .finalizeAnalysis
= &finalizeAnalysisCHull
,
104 .printAnalysisStats
= &printAnalysisStatsCHull
,
106 .writeTraceTraceForePlots
= &writeAnalysisGraphsPlotsCHull
,
110 const char* const approxNames
[]= {
113 [FALLBACK
]= "Fallback",
114 [INCOMPLETE
]= "Incomplete",
116 [SCREWED
]= "Screwed",
121 * Analysis module registering function
123 static void registerAnalysisCHull()
125 g_queue_push_tail(&analysisModules
, &analysisModuleCHull
);
130 * Analysis init function
132 * This function is called at the beginning of a synchronization run for a set
135 * Allocate some of the analysis specific data structures
138 * syncState container for synchronization data.
139 * This function allocates or initializes these analysisData
144 static void initAnalysisCHull(SyncState
* const syncState
)
147 AnalysisDataCHull
* analysisData
;
149 analysisData
= malloc(sizeof(AnalysisDataCHull
));
150 syncState
->analysisData
= analysisData
;
152 analysisData
->hullArray
= malloc(syncState
->traceNb
* sizeof(GQueue
**));
153 for (i
= 0; i
< syncState
->traceNb
; i
++)
155 analysisData
->hullArray
[i
]= malloc(syncState
->traceNb
* sizeof(GQueue
*));
157 for (j
= 0; j
< syncState
->traceNb
; j
++)
159 analysisData
->hullArray
[i
][j
]= g_queue_new();
163 if (syncState
->stats
)
165 analysisData
->stats
= malloc(sizeof(AnalysisStatsCHull
));
166 analysisData
->stats
->dropped
= 0;
167 analysisData
->stats
->allFactors
= NULL
;
170 if (syncState
->graphsStream
)
172 analysisData
->graphsData
= malloc(sizeof(AnalysisGraphsDataCHull
));
173 openGraphFiles(syncState
);
174 analysisData
->graphsData
->allFactors
= NULL
;
180 * Create and open files used to store convex hull points to genereate
181 * graphs. Allocate and populate array to store file pointers.
184 * syncState: container for synchronization data
186 static void openGraphFiles(SyncState
* const syncState
)
192 AnalysisDataCHull
* analysisData
;
194 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
196 cwd
= changeToGraphsDir(syncState
->graphsDir
);
198 analysisData
->graphsData
->hullPoints
= malloc(syncState
->traceNb
*
200 for (i
= 0; i
< syncState
->traceNb
; i
++)
202 analysisData
->graphsData
->hullPoints
[i
]= malloc(syncState
->traceNb
*
204 for (j
= 0; j
< syncState
->traceNb
; j
++)
208 retval
= snprintf(name
, sizeof(name
),
209 "analysis_chull-%03u_to_%03u.data", j
, i
);
210 if (retval
> sizeof(name
) - 1)
212 name
[sizeof(name
) - 1]= '\0';
214 if ((analysisData
->graphsData
->hullPoints
[i
][j
]= fopen(name
, "w")) ==
217 g_error(strerror(errno
));
226 g_error(strerror(errno
));
233 * Write hull points to files to generate graphs.
236 * syncState: container for synchronization data
238 static void writeGraphFiles(SyncState
* const syncState
)
241 AnalysisDataCHull
* analysisData
;
243 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
245 for (i
= 0; i
< syncState
->traceNb
; i
++)
247 for (j
= 0; j
< syncState
->traceNb
; j
++)
251 g_queue_foreach(analysisData
->hullArray
[i
][j
],
253 analysisData
->graphsData
->hullPoints
[i
][j
]);
261 * A GFunc for g_queue_foreach. Write a hull point to a file used to generate
265 * data: Point*, point to write to the file
266 * userData: FILE*, file pointer where to write the point
268 static void gfDumpHullToFile(gpointer data
, gpointer userData
)
272 point
= (Point
*) data
;
273 fprintf((FILE*) userData
, "%20llu %20llu\n", point
->x
, point
->y
);
278 * Close files used to store convex hull points to generate graphs.
279 * Deallocate array to store file pointers.
282 * syncState: container for synchronization data
284 static void closeGraphFiles(SyncState
* const syncState
)
287 AnalysisDataCHull
* analysisData
;
290 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
292 if (analysisData
->graphsData
->hullPoints
== NULL
)
297 for (i
= 0; i
< syncState
->traceNb
; i
++)
299 for (j
= 0; j
< syncState
->traceNb
; j
++)
303 retval
= fclose(analysisData
->graphsData
->hullPoints
[i
][j
]);
306 g_error(strerror(errno
));
310 free(analysisData
->graphsData
->hullPoints
[i
]);
312 free(analysisData
->graphsData
->hullPoints
);
313 analysisData
->graphsData
->hullPoints
= NULL
;
318 * Analysis destroy function
320 * Free the analysis specific data structures
323 * syncState container for synchronization data.
324 * This function deallocates these analysisData members:
328 static void destroyAnalysisCHull(SyncState
* const syncState
)
331 AnalysisDataCHull
* analysisData
;
333 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
335 if (analysisData
== NULL
)
340 for (i
= 0; i
< syncState
->traceNb
; i
++)
342 for (j
= 0; j
< syncState
->traceNb
; j
++)
344 g_queue_foreach(analysisData
->hullArray
[i
][j
], gfPointDestroy
, NULL
);
345 g_queue_free(analysisData
->hullArray
[i
][j
]);
347 free(analysisData
->hullArray
[i
]);
349 free(analysisData
->hullArray
);
351 if (syncState
->stats
)
353 if (analysisData
->stats
->allFactors
!= NULL
)
355 freeAllFactors(syncState
->traceNb
, analysisData
->stats
->allFactors
);
358 free(analysisData
->stats
);
361 if (syncState
->graphsStream
)
363 if (analysisData
->graphsData
->hullPoints
!= NULL
)
365 closeGraphFiles(syncState
);
368 if (!syncState
->stats
&& analysisData
->graphsData
->allFactors
!= NULL
)
370 freeAllFactors(syncState
->traceNb
, analysisData
->graphsData
->allFactors
);
373 free(analysisData
->graphsData
);
376 free(syncState
->analysisData
);
377 syncState
->analysisData
= NULL
;
382 * Perform analysis on an event pair.
385 * syncState container for synchronization data
386 * message structure containing the events
388 static void analyzeMessageCHull(SyncState
* const syncState
, Message
* const message
)
390 AnalysisDataCHull
* analysisData
;
395 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
397 newPoint
= malloc(sizeof(Point
));
398 if (message
->inE
->traceNum
< message
->outE
->traceNum
)
400 // CA is inE->traceNum
401 newPoint
->x
= message
->inE
->cpuTime
;
402 newPoint
->y
= message
->outE
->cpuTime
;
404 g_debug("Reception point hullArray[%lu][%lu] x= inE->time= %llu y= outE->time= %llu",
405 message
->inE
->traceNum
, message
->outE
->traceNum
, newPoint
->x
,
410 // CA is outE->traceNum
411 newPoint
->x
= message
->outE
->cpuTime
;
412 newPoint
->y
= message
->inE
->cpuTime
;
414 g_debug("Send point hullArray[%lu][%lu] x= inE->time= %llu y= outE->time= %llu",
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= (%llu, %llu), p2= (%llu, %llu), p1= (%llu, %llu), p3= (%llu, %llu))= %g",
707 p1
->x
, p1
->y
, p2
->x
, p2
->y
, p1
->x
, p1
->y
, p3
->x
, p3
->y
, result
);
708 if (result
< fuzzFactor
)
712 else if (result
> fuzzFactor
)
724 * Calculate the k component of the cross product of two vectors.
727 * p1, p2: start and end points of the first vector
728 * p3, p4: start and end points of the second vector
731 * the k component of the cross product when considering the two vectors to
732 * be in the i-j plane. The direction (sign) of the result can be useful to
733 * determine the relative orientation of the two vectors.
735 static double crossProductK(const Point
const* p1
, const Point
const* p2
,
736 const Point
const* p3
, const Point
const* p4
)
738 return ((double) p2
->x
- p1
->x
) * ((double) p4
->y
- p3
->y
) - ((double)
739 p2
->y
- p1
->y
) * ((double) p4
->x
- p3
->x
);
744 * Free a container of FactorsCHull
747 * traceNb: number of traces
748 * allFactors: container of FactorsCHull
750 void freeAllFactors(const unsigned int traceNb
, FactorsCHull
** const
755 for (i
= 0; i
< traceNb
; i
++)
757 for (j
= 0; j
<= i
; j
++)
759 destroyFactorsCHull(&allFactors
[i
][j
]);
768 * Free a FactorsCHull
771 * factorsCHull: container of Factors
773 void destroyFactorsCHull(FactorsCHull
* factorsCHull
)
775 if (factorsCHull
->type
== MIDDLE
|| factorsCHull
->type
==
776 INCOMPLETE
|| factorsCHull
->type
== ABSENT
)
778 free(factorsCHull
->min
);
779 free(factorsCHull
->max
);
781 else if (factorsCHull
->type
== SCREWED
)
783 if (factorsCHull
->min
!= NULL
)
785 free(factorsCHull
->min
);
787 if (factorsCHull
->max
!= NULL
)
789 free(factorsCHull
->max
);
793 if (factorsCHull
->type
== EXACT
|| factorsCHull
->type
== MIDDLE
||
794 factorsCHull
->type
== FALLBACK
)
796 free(factorsCHull
->approx
);
802 * Analyze the convex hulls to determine the synchronization factors between
803 * each pair of trace.
806 * syncState container for synchronization data.
809 * FactorsCHull*[TraceNum][TraceNum] array. See the documentation for the
810 * member allFactors of AnalysisStatsCHull.
812 FactorsCHull
** calculateAllFactors(SyncState
* const syncState
)
814 unsigned int traceNumA
, traceNumB
;
815 FactorsCHull
** allFactors
;
816 AnalysisDataCHull
* analysisData
;
818 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
820 // Allocate allFactors and calculate min and max
821 allFactors
= malloc(syncState
->traceNb
* sizeof(FactorsCHull
*));
822 for (traceNumA
= 0; traceNumA
< syncState
->traceNb
; traceNumA
++)
824 allFactors
[traceNumA
]= malloc((traceNumA
+ 1) * sizeof(FactorsCHull
));
826 allFactors
[traceNumA
][traceNumA
].type
= EXACT
;
827 allFactors
[traceNumA
][traceNumA
].approx
= malloc(sizeof(Factors
));
828 allFactors
[traceNumA
][traceNumA
].approx
->drift
= 1.;
829 allFactors
[traceNumA
][traceNumA
].approx
->offset
= 0.;
831 for (traceNumB
= 0; traceNumB
< traceNumA
; traceNumB
++)
838 size_t factorsOffset
;
840 {MINIMUM
, offsetof(FactorsCHull
, min
)},
841 {MAXIMUM
, offsetof(FactorsCHull
, max
)}
844 cr
= analysisData
->hullArray
[traceNumB
][traceNumA
];
845 cs
= analysisData
->hullArray
[traceNumA
][traceNumB
];
847 for (i
= 0; i
< sizeof(loopValues
) / sizeof(*loopValues
); i
++)
849 g_debug("allFactors[%u][%u].%s = calculateFactorsExact(cr= hullArray[%u][%u], cs= hullArray[%u][%u], %s)",
850 traceNumA
, traceNumB
, loopValues
[i
].factorsOffset
==
851 offsetof(FactorsCHull
, min
) ? "min" : "max", traceNumB
,
852 traceNumA
, traceNumA
, traceNumB
, loopValues
[i
].lineType
==
853 MINIMUM
? "MINIMUM" : "MAXIMUM");
854 *((Factors
**) ((void*) &allFactors
[traceNumA
][traceNumB
] +
855 loopValues
[i
].factorsOffset
))=
856 calculateFactorsExact(cr
, cs
, loopValues
[i
].lineType
);
861 // Calculate approx when possible
862 for (traceNumA
= 0; traceNumA
< syncState
->traceNb
; traceNumA
++)
864 for (traceNumB
= 0; traceNumB
< traceNumA
; traceNumB
++)
866 FactorsCHull
* factorsCHull
;
868 factorsCHull
= &allFactors
[traceNumA
][traceNumB
];
869 if (factorsCHull
->min
== NULL
&& factorsCHull
->max
== NULL
)
871 factorsCHull
->type
= FALLBACK
;
872 calculateFactorsFallback(analysisData
->hullArray
[traceNumB
][traceNumA
],
873 analysisData
->hullArray
[traceNumA
][traceNumB
],
874 &allFactors
[traceNumA
][traceNumB
]);
876 else if (factorsCHull
->min
!= NULL
&& factorsCHull
->max
!= NULL
)
878 if (factorsCHull
->min
->drift
!= -INFINITY
&&
879 factorsCHull
->max
->drift
!= INFINITY
)
881 factorsCHull
->type
= MIDDLE
;
882 calculateFactorsMiddle(factorsCHull
);
884 else if (factorsCHull
->min
->drift
!= -INFINITY
||
885 factorsCHull
->max
->drift
!= INFINITY
)
887 factorsCHull
->type
= INCOMPLETE
;
891 factorsCHull
->type
= ABSENT
;
896 //g_assert_not_reached();
897 factorsCHull
->type
= SCREWED
;
906 /* Calculate approximative factors based on minimum and maximum limits. The
907 * best approximation to make is the interior bissector of the angle formed by
908 * the minimum and maximum lines.
910 * The formulae used come from [Haddad, Yoram: Performance dans les systèmes
911 * répartis: des outils pour les mesures, Université de Paris-Sud, Centre
912 * d'Orsay, September 1988] Section 6.1 p.44
914 * The reasoning for choosing this estimator comes from [Duda, A., Harrus, G.,
915 * Haddad, Y., and Bernard, G.: Estimating global time in distributed systems,
916 * Proc. 7th Int. Conf. on Distributed Computing Systems, Berlin, volume 18,
920 * factors: contains the min and max limits, used to store the result
922 void calculateFactorsMiddle(FactorsCHull
* const factors
)
924 double amin
, amax
, bmin
, bmax
, bhat
;
926 amin
= factors
->max
->offset
;
927 amax
= factors
->min
->offset
;
928 bmin
= factors
->min
->drift
;
929 bmax
= factors
->max
->drift
;
931 g_assert_cmpfloat(bmax
, >=, bmin
);
933 factors
->approx
= malloc(sizeof(Factors
));
934 bhat
= (bmax
* bmin
- 1. + sqrt(1. + pow(bmax
, 2.) * pow(bmin
, 2.) +
935 pow(bmax
, 2.) + pow(bmin
, 2.))) / (bmax
+ bmin
);
936 factors
->approx
->offset
= amax
- (amax
- amin
) / 2. * (pow(bhat
, 2.) + 1.)
937 / (1. + bhat
* bmax
);
938 factors
->approx
->drift
= bhat
;
939 factors
->accuracy
= bmax
- bmin
;
944 * Analyze the convex hulls to determine the minimum or maximum
945 * synchronization factors between one pair of trace.
947 * This implements and improves upon the algorithm in [Haddad, Yoram:
948 * Performance dans les systèmes répartis: des outils pour les mesures,
949 * Université de Paris-Sud, Centre d'Orsay, September 1988] Section 6.2 p.47
951 * Some degenerate cases are possible:
952 * 1) the result is unbounded. In that case, when searching for the maximum
953 * factors, result->drift= INFINITY; result->offset= -INFINITY. When
954 * searching for the minimum factors, it is the opposite. It is not
955 * possible to improve the situation with this data.
956 * 2) no line can be above the upper hull and below the lower hull. This is
957 * because the hulls intersect each other or are reversed. This means that
958 * an assertion was false. Most probably, the clocks are not linear. It is
959 * possible to repeat the search with another algorithm that will find a
960 * "best effort" approximation. See calculateFactorsApprox().
963 * cu: the upper half-convex hull, the line must pass above this
964 * and touch it in one point
965 * cl: the lower half-convex hull, the line must pass below this
966 * and touch it in one point
967 * lineType: search for minimum or maximum factors
970 * If a result is found, a struct Factors is allocated, filed with the
971 * result and returned
972 * NULL otherwise, degenerate case 2 is in effect
974 static Factors
* calculateFactorsExact(GQueue
* const cu
, GQueue
* const cl
, const
980 double inversionFactor
;
983 g_debug("calculateFactorsExact(cu= %p, cl= %p, %s)", cu
, cl
, lineType
==
984 MINIMUM
? "MINIMUM" : "MAXIMUM");
986 if (lineType
== MINIMUM
)
990 inversionFactor
= -1.;
1002 // Check for degenerate case 1
1003 if (c1
->length
== 0 || c2
->length
== 0 || ((Point
*) g_queue_peek_nth(c1
,
1004 i1
))->x
>= ((Point
*) g_queue_peek_nth(c2
, i2
))->x
)
1006 result
= malloc(sizeof(Factors
));
1007 if (lineType
== MINIMUM
)
1009 result
->drift
= -INFINITY
;
1010 result
->offset
= INFINITY
;
1014 result
->drift
= INFINITY
;
1015 result
->offset
= -INFINITY
;
1027 g_queue_peek_nth(c1
, i1
),
1028 g_queue_peek_nth(c2
, i2
),
1029 g_queue_peek_nth(c1
, i1
),
1030 g_queue_peek_nth(c2
, i2
- 1)) * inversionFactor
< 0.
1033 if (((Point
*) g_queue_peek_nth(c1
, i1
))->x
1034 < ((Point
*) g_queue_peek_nth(c2
, i2
- 1))->x
)
1040 // Degenerate case 2
1046 i1
+ 1 < c1
->length
- 1
1048 g_queue_peek_nth(c1
, i1
),
1049 g_queue_peek_nth(c2
, i2
),
1050 g_queue_peek_nth(c1
, i1
+ 1),
1051 g_queue_peek_nth(c2
, i2
)) * inversionFactor
< 0.
1054 if (((Point
*) g_queue_peek_nth(c1
, i1
+ 1))->x
1055 < ((Point
*) g_queue_peek_nth(c2
, i2
))->x
)
1061 // Degenerate case 2
1069 g_queue_peek_nth(c1
, i1
),
1070 g_queue_peek_nth(c2
, i2
),
1071 g_queue_peek_nth(c1
, i1
),
1072 g_queue_peek_nth(c2
, i2
- 1)) * inversionFactor
< 0.
1075 p1
= g_queue_peek_nth(c1
, i1
);
1076 p2
= g_queue_peek_nth(c2
, i2
);
1078 g_debug("Resulting points are: c1[i1]: x= %llu y= %llu c2[i2]: x= %llu y= %llu",
1079 p1
->x
, p1
->y
, p2
->x
, p2
->y
);
1081 result
= malloc(sizeof(Factors
));
1082 result
->drift
= slope(p1
, p2
);
1083 result
->offset
= intercept(p1
, p2
);
1085 g_debug("Resulting factors are: drift= %g offset= %g", result
->drift
, result
->offset
);
1092 * Analyze the convex hulls to determine approximate synchronization factors
1093 * between one pair of trace when there is no line that can fit in the
1094 * corridor separating them.
1096 * This implements the algorithm in [Ashton, P.: Algorithms for Off-line Clock
1097 * Synchronisation, University of Canterbury, December 1995, 26] Section 4.2.2
1100 * For each point p1 in cr
1101 * For each point p2 in cs
1103 * Calculate the line paramaters
1104 * For each point p3 in each convex hull
1105 * If p3 is on the wrong side of the line
1107 * If error < errorMin
1111 * cr: the upper half-convex hull
1112 * cs: the lower half-convex hull
1113 * result: a pointer to the pre-allocated struct where the results
1116 static void calculateFactorsFallback(GQueue
* const cr
, GQueue
* const cs
,
1117 FactorsCHull
* const result
)
1119 unsigned int i
, j
, k
;
1124 approx
= malloc(sizeof(Factors
));
1126 for (i
= 0; i
< cs
->length
; i
++)
1128 for (j
= 0; j
< cr
->length
; j
++)
1135 if (((Point
*) g_queue_peek_nth(cs
, i
))->x
< ((Point
*)g_queue_peek_nth(cr
, j
))->x
)
1137 p1
= *(Point
*)g_queue_peek_nth(cs
, i
);
1138 p2
= *(Point
*)g_queue_peek_nth(cr
, j
);
1142 p1
= *(Point
*)g_queue_peek_nth(cr
, j
);
1143 p2
= *(Point
*)g_queue_peek_nth(cs
, i
);
1146 // The lower hull should be above the point
1147 for (k
= 0; k
< cs
->length
; k
++)
1149 if (jointCmp(&p1
, &p2
, g_queue_peek_nth(cs
, k
)) < 0.)
1151 error
+= verticalDistance(&p1
, &p2
, g_queue_peek_nth(cs
, k
));
1155 // The upper hull should be below the point
1156 for (k
= 0; k
< cr
->length
; k
++)
1158 if (jointCmp(&p1
, &p2
, g_queue_peek_nth(cr
, k
)) > 0.)
1160 error
+= verticalDistance(&p1
, &p2
, g_queue_peek_nth(cr
, k
));
1164 if (error
< errorMin
)
1166 g_debug("Fallback: i= %u j= %u is a better match (error= %g)", i
, j
, error
);
1167 approx
->drift
= slope(&p1
, &p2
);
1168 approx
->offset
= intercept(&p1
, &p2
);
1174 result
->approx
= approx
;
1175 result
->accuracy
= errorMin
;
1180 * Calculate the vertical distance between a line and a point
1183 * p1, p2: Two points defining the line
1187 * the vertical distance
1189 static double verticalDistance(Point
* p1
, Point
* p2
, Point
* const point
)
1191 return fabs(slope(p1
, p2
) * point
->x
+ intercept(p1
, p2
) - point
->y
);
1196 * Calculate the slope between two points
1199 * p1, p2 the two points
1204 static double slope(const Point
* const p1
, const Point
* const p2
)
1206 return ((double) p2
->y
- p1
->y
) / (p2
->x
- p1
->x
);
1210 /* Calculate the y-intercept of a line that passes by two points
1213 * p1, p2 the two points
1218 static double intercept(const Point
* const p1
, const Point
* const p2
)
1220 return ((double) p2
->y
* p1
->x
- (double) p1
->y
* p2
->x
) / ((double) p1
->x
- p2
->x
);
1225 * Calculate a resulting offset and drift for each trace.
1227 * Traces are assembled in groups. A group is an "island" of nodes/traces that
1228 * exchanged messages. A reference is determined for each group by using a
1229 * shortest path search based on the accuracy of the approximation. This also
1230 * forms a tree of the best way to relate each node's clock to the reference's
1231 * based on the accuracy. Sometimes it may be necessary or advantageous to
1232 * propagate the factors through intermediary clocks. Resulting factors for
1233 * each trace are determined based on this tree.
1235 * This part was not the focus of my research. The algorithm used here is
1236 * inexact in some ways:
1237 * 1) The reference used may not actually be the best one to use. This is
1238 * because the accuracy is not corrected based on the drift during the
1239 * shortest path search.
1240 * 2) The min and max factors are not propagated and are no longer valid.
1241 * 3) Approximations of different types (MIDDLE and FALLBACK) are compared
1242 * together. The "accuracy" parameters of these have different meanings and
1243 * are not readily comparable.
1245 * Nevertheless, the result is satisfactory. You just can't tell "how much" it
1248 * Two alternative (and subtly different) ways of propagating factors to
1249 * preserve min and max bondaries have been proposed, see:
1250 * [Duda, A., Harrus, G., Haddad, Y., and Bernard, G.: Estimating global time
1251 * in distributed systems, Proc. 7th Int. Conf. on Distributed Computing
1252 * Systems, Berlin, volume 18, 1987] p.304
1254 * [Jezequel, J.M., and Jard, C.: Building a global clock for observing
1255 * computations in distributed memory parallel computers, Concurrency:
1256 * Practice and Experience 8(1), volume 8, John Wiley & Sons, Ltd Chichester,
1257 * 1996, 32] Section 5; which is mostly the same as
1258 * [Jezequel, J.M.: Building a global time on parallel machines, Proceedings
1259 * of the 3rd International Workshop on Distributed Algorithms, LNCS, volume
1260 * 392, 136–147, 1989] Section 5
1263 * syncState: container for synchronization data.
1264 * allFactors: offset and drift between each pair of traces
1267 * Factors[traceNb] synchronization factors for each trace
1269 static GArray
* reduceFactors(SyncState
* const syncState
, FactorsCHull
** const
1274 unsigned int** predecessors
;
1275 double* distanceSums
;
1276 unsigned int* references
;
1279 // Solve the all-pairs shortest path problem using the Floyd-Warshall
1281 floydWarshall(syncState
, allFactors
, &distances
, &predecessors
);
1283 /* Find the reference for each node
1285 * First calculate, for each node, the sum of the distances to each other
1286 * node it can reach.
1288 * Then, go through each "island" of traces to find the trace that has the
1289 * lowest distance sum. Assign this trace as the reference to each trace
1292 distanceSums
= malloc(syncState
->traceNb
* sizeof(double));
1293 for (i
= 0; i
< syncState
->traceNb
; i
++)
1295 distanceSums
[i
]= 0.;
1296 for (j
= 0; j
< syncState
->traceNb
; j
++)
1298 distanceSums
[i
]+= distances
[i
][j
];
1302 references
= malloc(syncState
->traceNb
* sizeof(unsigned int));
1303 for (i
= 0; i
< syncState
->traceNb
; i
++)
1305 references
[i
]= UINT_MAX
;
1307 for (i
= 0; i
< syncState
->traceNb
; i
++)
1309 if (references
[i
] == UINT_MAX
)
1311 unsigned int reference
;
1312 double distanceSumMin
;
1314 // A node is its own reference by default
1316 distanceSumMin
= INFINITY
;
1317 for (j
= 0; j
< syncState
->traceNb
; j
++)
1319 if (distances
[i
][j
] != INFINITY
&& distanceSums
[j
] <
1323 distanceSumMin
= distanceSums
[j
];
1326 for (j
= 0; j
< syncState
->traceNb
; j
++)
1328 if (distances
[i
][j
] != INFINITY
)
1330 references
[j
]= reference
;
1336 for (i
= 0; i
< syncState
->traceNb
; i
++)
1343 /* For each trace, calculate the factors based on their corresponding
1344 * tree. The tree is rooted at the reference and the shortest path to each
1345 * other nodes are the branches.
1347 factors
= g_array_sized_new(FALSE
, FALSE
, sizeof(Factors
),
1348 syncState
->traceNb
);
1349 g_array_set_size(factors
, syncState
->traceNb
);
1350 for (i
= 0; i
< syncState
->traceNb
; i
++)
1352 getFactors(allFactors
, predecessors
, references
, i
, &g_array_index(factors
,
1356 for (i
= 0; i
< syncState
->traceNb
; i
++)
1358 free(predecessors
[i
]);
1368 * Perform an all-source shortest path search using the Floyd-Warshall
1371 * The algorithm is implemented accoding to the description here:
1372 * http://web.mit.edu/urban_or_book/www/book/chapter6/6.2.2.html
1375 * syncState: container for synchronization data.
1376 * allFactors: offset and drift between each pair of traces
1377 * distances: resulting matrix of the length of the shortest path between
1378 * two nodes. If there is no path between two nodes, the
1379 * length is INFINITY
1380 * predecessors: resulting matrix of each node's predecessor on the shortest
1381 * path between two nodes
1383 static void floydWarshall(SyncState
* const syncState
, FactorsCHull
** const
1384 allFactors
, double*** const distances
, unsigned int*** const
1387 unsigned int i
, j
, k
;
1389 // Setup initial conditions
1390 *distances
= malloc(syncState
->traceNb
* sizeof(double*));
1391 *predecessors
= malloc(syncState
->traceNb
* sizeof(unsigned int*));
1392 for (i
= 0; i
< syncState
->traceNb
; i
++)
1394 (*distances
)[i
]= malloc(syncState
->traceNb
* sizeof(double));
1395 for (j
= 0; j
< syncState
->traceNb
; j
++)
1399 g_assert(allFactors
[i
][j
].type
== EXACT
);
1401 (*distances
)[i
][j
]= 0.;
1405 unsigned int row
, col
;
1418 if (allFactors
[row
][col
].type
== MIDDLE
||
1419 allFactors
[row
][col
].type
== FALLBACK
)
1421 (*distances
)[i
][j
]= allFactors
[row
][col
].accuracy
;
1423 else if (allFactors
[row
][col
].type
== INCOMPLETE
||
1424 allFactors
[row
][col
].type
== SCREWED
||
1425 allFactors
[row
][col
].type
== ABSENT
)
1427 (*distances
)[i
][j
]= INFINITY
;
1431 g_assert_not_reached();
1436 (*predecessors
)[i
]= malloc(syncState
->traceNb
* sizeof(unsigned int));
1437 for (j
= 0; j
< syncState
->traceNb
; j
++)
1441 (*predecessors
)[i
][j
]= i
;
1445 (*predecessors
)[i
][j
]= UINT_MAX
;
1450 // Run the iterations
1451 for (k
= 0; k
< syncState
->traceNb
; k
++)
1453 for (i
= 0; i
< syncState
->traceNb
; i
++)
1455 for (j
= 0; j
< syncState
->traceNb
; j
++)
1459 distanceMin
= MIN((*distances
)[i
][j
], (*distances
)[i
][k
] +
1460 (*distances
)[k
][j
]);
1462 if (distanceMin
!= (*distances
)[i
][j
])
1464 (*predecessors
)[i
][j
]= (*predecessors
)[k
][j
];
1467 (*distances
)[i
][j
]= distanceMin
;
1475 * Cummulate the time correction factors to convert a node's time to its
1477 * This function recursively calls itself until it reaches the reference node.
1480 * allFactors: offset and drift between each pair of traces
1481 * predecessors: matrix of each node's predecessor on the shortest
1482 * path between two nodes
1483 * references: reference node for each node
1484 * traceNum: node for which to find the factors
1485 * factors: resulting factors
1487 static void getFactors(FactorsCHull
** const allFactors
, unsigned int** const
1488 predecessors
, unsigned int* const references
, const unsigned int traceNum
,
1489 Factors
* const factors
)
1491 unsigned int reference
;
1493 reference
= references
[traceNum
];
1495 if (reference
== traceNum
)
1497 factors
->offset
= 0.;
1502 Factors previousVertexFactors
;
1504 getFactors(allFactors
, predecessors
, references
,
1505 predecessors
[reference
][traceNum
], &previousVertexFactors
);
1507 // convertir de traceNum à reference
1509 // allFactors convertit de col à row
1511 if (reference
> traceNum
)
1513 factors
->offset
= previousVertexFactors
.drift
*
1514 allFactors
[reference
][traceNum
].approx
->offset
+
1515 previousVertexFactors
.offset
;
1516 factors
->drift
= previousVertexFactors
.drift
*
1517 allFactors
[reference
][traceNum
].approx
->drift
;
1521 factors
->offset
= previousVertexFactors
.drift
* (-1. *
1522 allFactors
[traceNum
][reference
].approx
->offset
/
1523 allFactors
[traceNum
][reference
].approx
->drift
) +
1524 previousVertexFactors
.offset
;
1525 factors
->drift
= previousVertexFactors
.drift
* (1. /
1526 allFactors
[traceNum
][reference
].approx
->drift
);
1533 * Write the analysis-specific graph lines in the gnuplot script.
1536 * syncState: container for synchronization data
1537 * i: first trace number
1538 * j: second trace number, garanteed to be larger than i
1540 void writeAnalysisGraphsPlotsCHull(SyncState
* const syncState
, const unsigned
1541 int i
, const unsigned int j
)
1543 AnalysisDataCHull
* analysisData
;
1544 FactorsCHull
* factorsCHull
;
1546 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
1548 fprintf(syncState
->graphsStream
,
1549 "\t\"analysis_chull-%1$03d_to_%2$03d.data\" "
1550 "title \"Lower half-hull\" with linespoints "
1551 "linecolor rgb \"#015a01\" linetype 4 pointtype 8 pointsize 0.8, \\\n"
1552 "\t\"analysis_chull-%2$03d_to_%1$03d.data\" "
1553 "title \"Upper half-hull\" with linespoints "
1554 "linecolor rgb \"#003366\" linetype 4 pointtype 10 pointsize 0.8, \\\n",
1557 factorsCHull
= &analysisData
->graphsData
->allFactors
[j
][i
];
1558 if (factorsCHull
->type
== EXACT
)
1560 fprintf(syncState
->graphsStream
,
1562 "title \"Exact conversion\" with lines "
1563 "linecolor rgb \"black\" linetype 1, \\\n",
1564 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
);
1566 else if (factorsCHull
->type
== MIDDLE
)
1568 fprintf(syncState
->graphsStream
,
1569 "\t%.2f + %.10f * x "
1570 "title \"Min conversion\" with lines "
1571 "linecolor rgb \"black\" linetype 5, \\\n",
1572 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
);
1573 fprintf(syncState
->graphsStream
,
1574 "\t%.2f + %.10f * x "
1575 "title \"Max conversion\" with lines "
1576 "linecolor rgb \"black\" linetype 8, \\\n",
1577 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
);
1578 fprintf(syncState
->graphsStream
,
1579 "\t%.2f + %.10f * x "
1580 "title \"Middle conversion\" with lines "
1581 "linecolor rgb \"black\" linetype 1, \\\n",
1582 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
);
1584 else if (factorsCHull
->type
== FALLBACK
)
1586 fprintf(syncState
->graphsStream
,
1587 "\t%.2f + %.10f * x "
1588 "title \"Fallback conversion\" with lines "
1589 "linecolor rgb \"gray60\" linetype 1, \\\n",
1590 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
);
1592 else if (factorsCHull
->type
== INCOMPLETE
)
1594 if (factorsCHull
->min
->drift
!= -INFINITY
)
1596 fprintf(syncState
->graphsStream
,
1597 "\t%.2f + %.10f * x "
1598 "title \"Min conversion\" with lines "
1599 "linecolor rgb \"black\" linetype 5, \\\n",
1600 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
);
1603 if (factorsCHull
->max
->drift
!= INFINITY
)
1605 fprintf(syncState
->graphsStream
,
1606 "\t%.2f + %.10f * x "
1607 "title \"Max conversion\" with lines "
1608 "linecolor rgb \"black\" linetype 8, \\\n",
1609 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
);
1612 else if (factorsCHull
->type
== SCREWED
)
1614 if (factorsCHull
->min
!= NULL
&& factorsCHull
->min
->drift
!= -INFINITY
)
1616 fprintf(syncState
->graphsStream
,
1617 "\t%.2f + %.10f * x "
1618 "title \"Min conversion\" with lines "
1619 "linecolor rgb \"black\" linetype 5, \\\n",
1620 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
);
1623 if (factorsCHull
->max
!= NULL
&& factorsCHull
->max
->drift
!= INFINITY
)
1625 fprintf(syncState
->graphsStream
,
1626 "\t%.2f + %.10f * x "
1627 "title \"Max conversion\" with lines "
1628 "linecolor rgb \"black\" linetype 8, \\\n",
1629 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
);
1632 else if (factorsCHull
->type
== ABSENT
)
1637 g_assert_not_reached();