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
);
346 free(analysisData
->hullArray
[i
]);
348 free(analysisData
->hullArray
);
350 if (syncState
->stats
)
352 if (analysisData
->stats
->allFactors
!= NULL
)
354 freeAllFactors(syncState
->traceNb
, analysisData
->stats
->allFactors
);
357 free(analysisData
->stats
);
360 if (syncState
->graphsStream
)
362 if (analysisData
->graphsData
->hullPoints
!= NULL
)
364 closeGraphFiles(syncState
);
367 if (!syncState
->stats
&& analysisData
->graphsData
->allFactors
!= NULL
)
369 freeAllFactors(syncState
->traceNb
, analysisData
->graphsData
->allFactors
);
372 free(analysisData
->graphsData
);
375 free(syncState
->analysisData
);
376 syncState
->analysisData
= NULL
;
381 * Perform analysis on an event pair.
384 * syncState container for synchronization data
385 * message structure containing the events
387 static void analyzeMessageCHull(SyncState
* const syncState
, Message
* const message
)
389 AnalysisDataCHull
* analysisData
;
394 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
396 newPoint
= malloc(sizeof(Point
));
397 if (message
->inE
->traceNum
< message
->outE
->traceNum
)
399 // CA is inE->traceNum
400 newPoint
->x
= message
->inE
->cpuTime
;
401 newPoint
->y
= message
->outE
->cpuTime
;
403 g_debug("Reception point hullArray[%lu][%lu] x= inE->time= %llu y= outE->time= %llu",
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] x= inE->time= %llu y= outE->time= %llu",
414 message
->inE
->traceNum
, message
->outE
->traceNum
, newPoint
->x
,
419 analysisData
->hullArray
[message
->inE
->traceNum
][message
->outE
->traceNum
];
421 if (hull
->length
>= 1 && newPoint
->x
< ((Point
*)
422 g_queue_peek_tail(hull
))->x
)
424 if (syncState
->stats
)
426 analysisData
->stats
->dropped
++;
433 grahamScan(hull
, newPoint
, hullType
);
439 * Construct one half of a convex hull from abscissa-sorted points
442 * hull: the points already in the hull
443 * newPoint: a new point to consider
444 * type: which half of the hull to construct
446 static void grahamScan(GQueue
* const hull
, Point
* const newPoint
, const
451 g_debug("grahamScan(hull (length: %u), newPoint, %s)", hull
->length
, type
452 == LOWER
? "LOWER" : "UPPER");
463 if (hull
->length
>= 2)
465 g_debug("jointCmp(hull[%u], hull[%u], newPoint) * inversionFactor = %d * %d = %d",
468 jointCmp(g_queue_peek_nth(hull
, hull
->length
- 2),
469 g_queue_peek_tail(hull
), newPoint
),
471 jointCmp(g_queue_peek_nth(hull
, hull
->length
- 2),
472 g_queue_peek_tail(hull
), newPoint
) * inversionFactor
);
474 while (hull
->length
>= 2 && jointCmp(g_queue_peek_nth(hull
, hull
->length
-
475 2), g_queue_peek_tail(hull
), newPoint
) * inversionFactor
<= 0)
477 g_debug("Removing hull[%u]", hull
->length
);
478 free((Point
*) g_queue_pop_tail(hull
));
480 if (hull
->length
>= 2)
482 g_debug("jointCmp(hull[%u], hull[%u], newPoint) * inversionFactor = %d * %d = %d",
485 jointCmp(g_queue_peek_nth(hull
, hull
->length
- 2),
486 g_queue_peek_tail(hull
), newPoint
),
488 jointCmp(g_queue_peek_nth(hull
, hull
->length
- 2),
489 g_queue_peek_tail(hull
), newPoint
) * inversionFactor
);
492 g_queue_push_tail(hull
, newPoint
);
497 * Finalize the factor calculations
500 * syncState container for synchronization data.
503 * Factors[traceNb] synchronization factors for each trace
505 static GArray
* finalizeAnalysisCHull(SyncState
* const syncState
)
507 AnalysisDataCHull
* analysisData
;
509 FactorsCHull
** allFactors
;
511 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
513 if (syncState
->graphsStream
&& analysisData
->graphsData
->hullPoints
!= NULL
)
515 writeGraphFiles(syncState
);
516 closeGraphFiles(syncState
);
519 allFactors
= calculateAllFactors(syncState
);
521 factors
= reduceFactors(syncState
, allFactors
);
523 if (syncState
->stats
|| syncState
->graphsStream
)
525 if (syncState
->stats
)
527 analysisData
->stats
->allFactors
= allFactors
;
530 if (syncState
->graphsStream
)
532 analysisData
->graphsData
->allFactors
= allFactors
;
537 freeAllFactors(syncState
->traceNb
, allFactors
);
545 * Print statistics related to analysis. Must be called after
549 * syncState container for synchronization data.
551 static void printAnalysisStatsCHull(SyncState
* const syncState
)
553 AnalysisDataCHull
* analysisData
;
556 if (!syncState
->stats
)
561 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
563 printf("Convex hull analysis stats:\n");
564 printf("\tout of order packets dropped from analysis: %u\n",
565 analysisData
->stats
->dropped
);
567 printf("\tNumber of points in convex hulls:\n");
569 for (i
= 0; i
< syncState
->traceNb
; i
++)
571 for (j
= i
+ 1; j
< syncState
->traceNb
; j
++)
573 printf("\t\t%3d - %-3d: lower half-hull %-5u upper half-hull %-5u\n",
574 i
, j
, analysisData
->hullArray
[j
][i
]->length
,
575 analysisData
->hullArray
[i
][j
]->length
);
579 printf("\tIndividual synchronization factors:\n");
581 for (i
= 0; i
< syncState
->traceNb
; i
++)
583 for (j
= i
+ 1; j
< syncState
->traceNb
; j
++)
585 FactorsCHull
* factorsCHull
;
587 factorsCHull
= &analysisData
->stats
->allFactors
[j
][i
];
588 printf("\t\t%3d - %-3d: %s", i
, j
,
589 approxNames
[factorsCHull
->type
]);
591 if (factorsCHull
->type
== EXACT
)
593 printf(" a0= % 7g a1= 1 %c %7g\n",
594 factorsCHull
->approx
->offset
,
595 factorsCHull
->approx
->drift
< 0. ? '-' : '+',
596 fabs(factorsCHull
->approx
->drift
));
598 else if (factorsCHull
->type
== MIDDLE
)
600 printf(" a0= % 7g a1= 1 %c %7g accuracy %7g\n",
601 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
602 - 1. < 0. ? '-' : '+', fabs(factorsCHull
->approx
->drift
-
603 1.), factorsCHull
->accuracy
);
604 printf("\t\t a0: % 7g to % 7g (delta= %7g)\n",
605 factorsCHull
->max
->offset
, factorsCHull
->min
->offset
,
606 factorsCHull
->min
->offset
- factorsCHull
->max
->offset
);
607 printf("\t\t a1: 1 %+7g to %+7g (delta= %7g)\n",
608 factorsCHull
->min
->drift
- 1., factorsCHull
->max
->drift
-
609 1., factorsCHull
->max
->drift
- factorsCHull
->min
->drift
);
611 else if (factorsCHull
->type
== FALLBACK
)
613 printf(" a0= % 7g a1= 1 %c %7g error= %7g\n",
614 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
615 - 1. < 0. ? '-' : '+', fabs(factorsCHull
->approx
->drift
-
616 1.), factorsCHull
->accuracy
);
618 else if (factorsCHull
->type
== INCOMPLETE
)
622 if (factorsCHull
->min
->drift
!= -INFINITY
)
624 printf("\t\t min: a0: % 7g a1: 1 %c %7g\n",
625 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
-
626 1. < 0 ? '-' : '+', fabs(factorsCHull
->min
->drift
-
629 if (factorsCHull
->max
->drift
!= INFINITY
)
631 printf("\t\t max: a0: % 7g a1: 1 %c %7g\n",
632 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
-
633 1. < 0 ? '-' : '+', fabs(factorsCHull
->max
->drift
-
637 else if (factorsCHull
->type
== SCREWED
)
641 if (factorsCHull
->min
!= NULL
&& factorsCHull
->min
->drift
!= -INFINITY
)
643 printf("\t\t min: a0: % 7g a1: 1 %c %7g\n",
644 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
-
645 1. < 0 ? '-' : '+', fabs(factorsCHull
->min
->drift
-
648 if (factorsCHull
->max
!= NULL
&& factorsCHull
->max
->drift
!= INFINITY
)
650 printf("\t\t max: a0: % 7g a1: 1 %c %7g\n",
651 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
-
652 1. < 0 ? '-' : '+', fabs(factorsCHull
->max
->drift
-
656 else if (factorsCHull
->type
== ABSENT
)
662 g_assert_not_reached();
670 * A GFunc for g_queue_foreach()
673 * data Point*, point to destroy
676 static void gfPointDestroy(gpointer data
, gpointer userData
)
680 point
= (Point
*) data
;
686 * Find out if a sequence of three points constitutes a "left turn" or a
690 * p1, p2, p3: The three points.
694 * 0 colinear (unlikely result since this uses floating point
698 static int jointCmp(const Point
const* p1
, const Point
const* p2
, const
702 const double fuzzFactor
= 0.;
704 result
= crossProductK(p1
, p2
, p1
, p3
);
705 g_debug("crossProductK(p1= (%llu, %llu), p2= (%llu, %llu), p1= (%llu, %llu), p3= (%llu, %llu))= %g",
706 p1
->x
, p1
->y
, p2
->x
, p2
->y
, p1
->x
, p1
->y
, p3
->x
, p3
->y
, result
);
707 if (result
< fuzzFactor
)
711 else if (result
> fuzzFactor
)
723 * Calculate the k component of the cross product of two vectors.
726 * p1, p2: start and end points of the first vector
727 * p3, p4: start and end points of the second vector
730 * the k component of the cross product when considering the two vectors to
731 * be in the i-j plane. The direction (sign) of the result can be useful to
732 * determine the relative orientation of the two vectors.
734 static double crossProductK(const Point
const* p1
, const Point
const* p2
,
735 const Point
const* p3
, const Point
const* p4
)
737 return ((double) p2
->x
- p1
->x
) * ((double) p4
->y
- p3
->y
) - ((double)
738 p2
->y
- p1
->y
) * ((double) p4
->x
- p3
->x
);
743 * Free a container of FactorsCHull
746 * traceNb: number of traces
747 * allFactors: container of FactorsCHull
749 void freeAllFactors(const unsigned int traceNb
, FactorsCHull
** const
754 for (i
= 0; i
< traceNb
; i
++)
756 for (j
= 0; j
<= i
; j
++)
758 destroyFactorsCHull(&allFactors
[i
][j
]);
767 * Free a FactorsCHull
770 * factorsCHull: container of Factors
772 void destroyFactorsCHull(FactorsCHull
* factorsCHull
)
774 if (factorsCHull
->type
== MIDDLE
|| factorsCHull
->type
==
775 INCOMPLETE
|| factorsCHull
->type
== ABSENT
)
777 free(factorsCHull
->min
);
778 free(factorsCHull
->max
);
780 else if (factorsCHull
->type
== SCREWED
)
782 if (factorsCHull
->min
!= NULL
)
784 free(factorsCHull
->min
);
786 if (factorsCHull
->max
!= NULL
)
788 free(factorsCHull
->max
);
792 if (factorsCHull
->type
== EXACT
|| factorsCHull
->type
== MIDDLE
||
793 factorsCHull
->type
== FALLBACK
)
795 free(factorsCHull
->approx
);
801 * Analyze the convex hulls to determine the synchronization factors between
802 * each pair of trace.
805 * syncState container for synchronization data.
808 * FactorsCHull*[TraceNum][TraceNum] array. See the documentation for the
809 * member allFactors of AnalysisStatsCHull.
811 FactorsCHull
** calculateAllFactors(SyncState
* const syncState
)
813 unsigned int traceNumA
, traceNumB
;
814 FactorsCHull
** allFactors
;
815 AnalysisDataCHull
* analysisData
;
817 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
819 // Allocate allFactors and calculate min and max
820 allFactors
= malloc(syncState
->traceNb
* sizeof(FactorsCHull
*));
821 for (traceNumA
= 0; traceNumA
< syncState
->traceNb
; traceNumA
++)
823 allFactors
[traceNumA
]= malloc((traceNumA
+ 1) * sizeof(FactorsCHull
));
825 allFactors
[traceNumA
][traceNumA
].type
= EXACT
;
826 allFactors
[traceNumA
][traceNumA
].approx
= malloc(sizeof(Factors
));
827 allFactors
[traceNumA
][traceNumA
].approx
->drift
= 1.;
828 allFactors
[traceNumA
][traceNumA
].approx
->offset
= 0.;
830 for (traceNumB
= 0; traceNumB
< traceNumA
; traceNumB
++)
837 size_t factorsOffset
;
839 {MINIMUM
, offsetof(FactorsCHull
, min
)},
840 {MAXIMUM
, offsetof(FactorsCHull
, max
)}
843 cr
= analysisData
->hullArray
[traceNumB
][traceNumA
];
844 cs
= analysisData
->hullArray
[traceNumA
][traceNumB
];
846 for (i
= 0; i
< sizeof(loopValues
) / sizeof(*loopValues
); i
++)
848 g_debug("allFactors[%u][%u].%s = calculateFactorsExact(cr= hullArray[%u][%u], cs= hullArray[%u][%u], %s)",
849 traceNumA
, traceNumB
, loopValues
[i
].factorsOffset
==
850 offsetof(FactorsCHull
, min
) ? "min" : "max", traceNumB
,
851 traceNumA
, traceNumA
, traceNumB
, loopValues
[i
].lineType
==
852 MINIMUM
? "MINIMUM" : "MAXIMUM");
853 *((Factors
**) ((void*) &allFactors
[traceNumA
][traceNumB
] +
854 loopValues
[i
].factorsOffset
))=
855 calculateFactorsExact(cr
, cs
, loopValues
[i
].lineType
);
860 // Calculate approx when possible
861 for (traceNumA
= 0; traceNumA
< syncState
->traceNb
; traceNumA
++)
863 for (traceNumB
= 0; traceNumB
< traceNumA
; traceNumB
++)
865 FactorsCHull
* factorsCHull
;
867 factorsCHull
= &allFactors
[traceNumA
][traceNumB
];
868 if (factorsCHull
->min
== NULL
&& factorsCHull
->max
== NULL
)
870 factorsCHull
->type
= FALLBACK
;
871 calculateFactorsFallback(analysisData
->hullArray
[traceNumB
][traceNumA
],
872 analysisData
->hullArray
[traceNumA
][traceNumB
],
873 &allFactors
[traceNumA
][traceNumB
]);
875 else if (factorsCHull
->min
!= NULL
&& factorsCHull
->max
!= NULL
)
877 if (factorsCHull
->min
->drift
!= -INFINITY
&&
878 factorsCHull
->max
->drift
!= INFINITY
)
880 factorsCHull
->type
= MIDDLE
;
881 calculateFactorsMiddle(factorsCHull
);
883 else if (factorsCHull
->min
->drift
!= -INFINITY
||
884 factorsCHull
->max
->drift
!= INFINITY
)
886 factorsCHull
->type
= INCOMPLETE
;
890 factorsCHull
->type
= ABSENT
;
895 //g_assert_not_reached();
896 factorsCHull
->type
= SCREWED
;
905 /* Calculate approximative factors based on minimum and maximum limits. The
906 * best approximation to make is the interior bissector of the angle formed by
907 * the minimum and maximum lines.
909 * The formulae used come from [Haddad, Yoram: Performance dans les systèmes
910 * répartis: des outils pour les mesures, Université de Paris-Sud, Centre
911 * d'Orsay, September 1988] Section 6.1 p.44
913 * The reasoning for choosing this estimator comes from [Duda, A., Harrus, G.,
914 * Haddad, Y., and Bernard, G.: Estimating global time in distributed systems,
915 * Proc. 7th Int. Conf. on Distributed Computing Systems, Berlin, volume 18,
919 * factors: contains the min and max limits, used to store the result
921 void calculateFactorsMiddle(FactorsCHull
* const factors
)
923 double amin
, amax
, bmin
, bmax
, bhat
;
925 amin
= factors
->max
->offset
;
926 amax
= factors
->min
->offset
;
927 bmin
= factors
->min
->drift
;
928 bmax
= factors
->max
->drift
;
930 g_assert_cmpfloat(bmax
, >, bmin
);
932 factors
->approx
= malloc(sizeof(Factors
));
933 bhat
= (bmax
* bmin
- 1. + sqrt(1. + pow(bmax
, 2.) * pow(bmin
, 2.) +
934 pow(bmax
, 2.) + pow(bmin
, 2.))) / (bmax
+ bmin
);
935 factors
->approx
->offset
= amax
- (amax
- amin
) / 2. * (pow(bhat
, 2.) + 1.)
936 / (1. + bhat
* bmax
);
937 factors
->approx
->drift
= bhat
;
938 factors
->accuracy
= bmax
- bmin
;
943 * Analyze the convex hulls to determine the minimum or maximum
944 * synchronization factors between one pair of trace.
946 * This implements and improves upon the algorithm in [Haddad, Yoram:
947 * Performance dans les systèmes répartis: des outils pour les mesures,
948 * Université de Paris-Sud, Centre d'Orsay, September 1988] Section 6.2 p.47
950 * Some degenerate cases are possible:
951 * 1) the result is unbounded. In that case, when searching for the maximum
952 * factors, result->drift= INFINITY; result->offset= -INFINITY. When
953 * searching for the minimum factors, it is the opposite. It is not
954 * possible to improve the situation with this data.
955 * 2) no line can be above the upper hull and below the lower hull. This is
956 * because the hulls intersect each other or are reversed. This means that
957 * an assertion was false. Most probably, the clocks are not linear. It is
958 * possible to repeat the search with another algorithm that will find a
959 * "best effort" approximation. See calculateFactorsApprox().
962 * cu: the upper half-convex hull, the line must pass above this
963 * and touch it in one point
964 * cl: the lower half-convex hull, the line must pass below this
965 * and touch it in one point
966 * lineType: search for minimum or maximum factors
969 * If a result is found, a struct Factors is allocated, filed with the
970 * result and returned
971 * NULL otherwise, degenerate case 2 is in effect
973 static Factors
* calculateFactorsExact(GQueue
* const cu
, GQueue
* const cl
, const
979 double inversionFactor
;
982 g_debug("calculateFactorsExact(cu= %p, cl= %p, %s)", cu
, cl
, lineType
==
983 MINIMUM
? "MINIMUM" : "MAXIMUM");
985 if (lineType
== MINIMUM
)
989 inversionFactor
= -1.;
1001 // Check for degenerate case 1
1002 if (c1
->length
== 0 || c2
->length
== 0 || ((Point
*) g_queue_peek_nth(c1
,
1003 i1
))->x
>= ((Point
*) g_queue_peek_nth(c2
, i2
))->x
)
1005 result
= malloc(sizeof(Factors
));
1006 if (lineType
== MINIMUM
)
1008 result
->drift
= -INFINITY
;
1009 result
->offset
= INFINITY
;
1013 result
->drift
= INFINITY
;
1014 result
->offset
= -INFINITY
;
1026 g_queue_peek_nth(c1
, i1
),
1027 g_queue_peek_nth(c2
, i2
),
1028 g_queue_peek_nth(c1
, i1
),
1029 g_queue_peek_nth(c2
, i2
- 1)) * inversionFactor
< 0.
1032 if (((Point
*) g_queue_peek_nth(c1
, i1
))->x
1033 < ((Point
*) g_queue_peek_nth(c2
, i2
- 1))->x
)
1039 // Degenerate case 2
1045 i1
+ 1 < c1
->length
- 1
1047 g_queue_peek_nth(c1
, i1
),
1048 g_queue_peek_nth(c2
, i2
),
1049 g_queue_peek_nth(c1
, i1
+ 1),
1050 g_queue_peek_nth(c2
, i2
)) * inversionFactor
< 0.
1053 if (((Point
*) g_queue_peek_nth(c1
, i1
+ 1))->x
1054 < ((Point
*) g_queue_peek_nth(c2
, i2
))->x
)
1060 // Degenerate case 2
1068 g_queue_peek_nth(c1
, i1
),
1069 g_queue_peek_nth(c2
, i2
),
1070 g_queue_peek_nth(c1
, i1
),
1071 g_queue_peek_nth(c2
, i2
- 1)) * inversionFactor
< 0.
1074 p1
= g_queue_peek_nth(c1
, i1
);
1075 p2
= g_queue_peek_nth(c2
, i2
);
1077 g_debug("Resulting points are: c1[i1]: x= %llu y= %llu c2[i2]: x= %llu y= %llu",
1078 p1
->x
, p1
->y
, p2
->x
, p2
->y
);
1080 result
= malloc(sizeof(Factors
));
1081 result
->drift
= slope(p1
, p2
);
1082 result
->offset
= intercept(p1
, p2
);
1084 g_debug("Resulting factors are: drift= %g offset= %g", result
->drift
, result
->offset
);
1091 * Analyze the convex hulls to determine approximate synchronization factors
1092 * between one pair of trace when there is no line that can fit in the
1093 * corridor separating them.
1095 * This implements the algorithm in [Ashton, P.: Algorithms for Off-line Clock
1096 * Synchronisation, University of Canterbury, December 1995, 26] Section 4.2.2
1099 * For each point p1 in cr
1100 * For each point p2 in cs
1102 * Calculate the line paramaters
1103 * For each point p3 in each convex hull
1104 * If p3 is on the wrong side of the line
1106 * If error < errorMin
1110 * cr: the upper half-convex hull
1111 * cs: the lower half-convex hull
1112 * result: a pointer to the pre-allocated struct where the results
1115 static void calculateFactorsFallback(GQueue
* const cr
, GQueue
* const cs
,
1116 FactorsCHull
* const result
)
1118 unsigned int i
, j
, k
;
1123 approx
= malloc(sizeof(Factors
));
1125 for (i
= 0; i
< cs
->length
; i
++)
1127 for (j
= 0; j
< cr
->length
; j
++)
1134 if (((Point
*) g_queue_peek_nth(cs
, i
))->x
< ((Point
*)g_queue_peek_nth(cr
, j
))->x
)
1136 p1
= *(Point
*)g_queue_peek_nth(cs
, i
);
1137 p2
= *(Point
*)g_queue_peek_nth(cr
, j
);
1141 p1
= *(Point
*)g_queue_peek_nth(cr
, j
);
1142 p2
= *(Point
*)g_queue_peek_nth(cs
, i
);
1145 // The lower hull should be above the point
1146 for (k
= 0; k
< cs
->length
; k
++)
1148 if (jointCmp(&p1
, &p2
, g_queue_peek_nth(cs
, k
)) < 0.)
1150 error
+= verticalDistance(&p1
, &p2
, g_queue_peek_nth(cs
, k
));
1154 // The upper hull should be below the point
1155 for (k
= 0; k
< cr
->length
; k
++)
1157 if (jointCmp(&p1
, &p2
, g_queue_peek_nth(cr
, k
)) > 0.)
1159 error
+= verticalDistance(&p1
, &p2
, g_queue_peek_nth(cr
, k
));
1163 if (error
< errorMin
)
1165 g_debug("Fallback: i= %u j= %u is a better match (error= %g)", i
, j
, error
);
1166 approx
->drift
= slope(&p1
, &p2
);
1167 approx
->offset
= intercept(&p1
, &p2
);
1173 result
->approx
= approx
;
1174 result
->accuracy
= errorMin
;
1179 * Calculate the vertical distance between a line and a point
1182 * p1, p2: Two points defining the line
1186 * the vertical distance
1188 static double verticalDistance(Point
* p1
, Point
* p2
, Point
* const point
)
1190 return fabs(slope(p1
, p2
) * point
->x
+ intercept(p1
, p2
) - point
->y
);
1195 * Calculate the slope between two points
1198 * p1, p2 the two points
1203 static double slope(const Point
* const p1
, const Point
* const p2
)
1205 return ((double) p2
->y
- p1
->y
) / (p2
->x
- p1
->x
);
1209 /* Calculate the y-intercept of a line that passes by two points
1212 * p1, p2 the two points
1217 static double intercept(const Point
* const p1
, const Point
* const p2
)
1219 return ((double) p2
->y
* p1
->x
- (double) p1
->y
* p2
->x
) / ((double) p1
->x
- p2
->x
);
1224 * Calculate a resulting offset and drift for each trace.
1226 * Traces are assembled in groups. A group is an "island" of nodes/traces that
1227 * exchanged messages. A reference is determined for each group by using a
1228 * shortest path search based on the accuracy of the approximation. This also
1229 * forms a tree of the best way to relate each node's clock to the reference's
1230 * based on the accuracy. Sometimes it may be necessary or advantageous to
1231 * propagate the factors through intermediary clocks. Resulting factors for
1232 * each trace are determined based on this tree.
1234 * This part was not the focus of my research. The algorithm used here is
1235 * inexact in some ways:
1236 * 1) The reference used may not actually be the best one to use. This is
1237 * because the accuracy is not corrected based on the drift during the
1238 * shortest path search.
1239 * 2) The min and max factors are not propagated and are no longer valid.
1240 * 3) Approximations of different types (MIDDLE and FALLBACK) are compared
1241 * together. The "accuracy" parameters of these have different meanings and
1242 * are not readily comparable.
1244 * Nevertheless, the result is satisfactory. You just can't tell "how much" it
1247 * Two alternative (and subtly different) ways of propagating factors to
1248 * preserve min and max bondaries have been proposed, see:
1249 * [Duda, A., Harrus, G., Haddad, Y., and Bernard, G.: Estimating global time
1250 * in distributed systems, Proc. 7th Int. Conf. on Distributed Computing
1251 * Systems, Berlin, volume 18, 1987] p.304
1253 * [Jezequel, J.M., and Jard, C.: Building a global clock for observing
1254 * computations in distributed memory parallel computers, Concurrency:
1255 * Practice and Experience 8(1), volume 8, John Wiley & Sons, Ltd Chichester,
1256 * 1996, 32] Section 5; which is mostly the same as
1257 * [Jezequel, J.M.: Building a global time on parallel machines, Proceedings
1258 * of the 3rd International Workshop on Distributed Algorithms, LNCS, volume
1259 * 392, 136–147, 1989] Section 5
1262 * syncState: container for synchronization data.
1263 * allFactors: offset and drift between each pair of traces
1266 * Factors[traceNb] synchronization factors for each trace
1268 static GArray
* reduceFactors(SyncState
* const syncState
, FactorsCHull
** const
1273 unsigned int** predecessors
;
1274 double* distanceSums
;
1275 unsigned int* references
;
1278 // Solve the all-pairs shortest path problem using the Floyd-Warshall
1280 floydWarshall(syncState
, allFactors
, &distances
, &predecessors
);
1282 /* Find the reference for each node
1284 * First calculate, for each node, the sum of the distances to each other
1285 * node it can reach.
1287 * Then, go through each "island" of traces to find the trace that has the
1288 * lowest distance sum. Assign this trace as the reference to each trace
1291 distanceSums
= malloc(syncState
->traceNb
* sizeof(double));
1292 for (i
= 0; i
< syncState
->traceNb
; i
++)
1294 distanceSums
[i
]= 0.;
1295 for (j
= 0; j
< syncState
->traceNb
; j
++)
1297 distanceSums
[i
]+= distances
[i
][j
];
1301 references
= malloc(syncState
->traceNb
* sizeof(unsigned int));
1302 for (i
= 0; i
< syncState
->traceNb
; i
++)
1304 references
[i
]= UINT_MAX
;
1306 for (i
= 0; i
< syncState
->traceNb
; i
++)
1308 if (references
[i
] == UINT_MAX
)
1310 unsigned int reference
;
1311 double distanceSumMin
;
1313 // A node is its own reference by default
1315 distanceSumMin
= INFINITY
;
1316 for (j
= 0; j
< syncState
->traceNb
; j
++)
1318 if (distances
[i
][j
] != INFINITY
&& distanceSums
[j
] <
1322 distanceSumMin
= distanceSums
[j
];
1325 for (j
= 0; j
< syncState
->traceNb
; j
++)
1327 if (distances
[i
][j
] != INFINITY
)
1329 references
[j
]= reference
;
1335 for (i
= 0; i
< syncState
->traceNb
; i
++)
1342 /* For each trace, calculate the factors based on their corresponding
1343 * tree. The tree is rooted at the reference and the shortest path to each
1344 * other nodes are the branches.
1346 factors
= g_array_sized_new(FALSE
, FALSE
, sizeof(Factors
),
1347 syncState
->traceNb
);
1348 g_array_set_size(factors
, syncState
->traceNb
);
1349 for (i
= 0; i
< syncState
->traceNb
; i
++)
1351 getFactors(allFactors
, predecessors
, references
, i
, &g_array_index(factors
,
1355 for (i
= 0; i
< syncState
->traceNb
; i
++)
1357 free(predecessors
[i
]);
1367 * Perform an all-source shortest path search using the Floyd-Warshall
1370 * The algorithm is implemented accoding to the description here:
1371 * http://web.mit.edu/urban_or_book/www/book/chapter6/6.2.2.html
1374 * syncState: container for synchronization data.
1375 * allFactors: offset and drift between each pair of traces
1376 * distances: resulting matrix of the length of the shortest path between
1377 * two nodes. If there is no path between two nodes, the
1378 * length is INFINITY
1379 * predecessors: resulting matrix of each node's predecessor on the shortest
1380 * path between two nodes
1382 static void floydWarshall(SyncState
* const syncState
, FactorsCHull
** const
1383 allFactors
, double*** const distances
, unsigned int*** const
1386 unsigned int i
, j
, k
;
1388 // Setup initial conditions
1389 *distances
= malloc(syncState
->traceNb
* sizeof(double*));
1390 *predecessors
= malloc(syncState
->traceNb
* sizeof(unsigned int*));
1391 for (i
= 0; i
< syncState
->traceNb
; i
++)
1393 (*distances
)[i
]= malloc(syncState
->traceNb
* sizeof(double));
1394 for (j
= 0; j
< syncState
->traceNb
; j
++)
1398 g_assert(allFactors
[i
][j
].type
== EXACT
);
1400 (*distances
)[i
][j
]= 0.;
1404 unsigned int row
, col
;
1417 if (allFactors
[row
][col
].type
== MIDDLE
||
1418 allFactors
[row
][col
].type
== FALLBACK
)
1420 (*distances
)[i
][j
]= allFactors
[row
][col
].accuracy
;
1422 else if (allFactors
[row
][col
].type
== INCOMPLETE
||
1423 allFactors
[row
][col
].type
== SCREWED
||
1424 allFactors
[row
][col
].type
== ABSENT
)
1426 (*distances
)[i
][j
]= INFINITY
;
1430 g_assert_not_reached();
1435 (*predecessors
)[i
]= malloc(syncState
->traceNb
* sizeof(unsigned int));
1436 for (j
= 0; j
< syncState
->traceNb
; j
++)
1440 (*predecessors
)[i
][j
]= i
;
1444 (*predecessors
)[i
][j
]= UINT_MAX
;
1449 // Run the iterations
1450 for (k
= 0; k
< syncState
->traceNb
; k
++)
1452 for (i
= 0; i
< syncState
->traceNb
; i
++)
1454 for (j
= 0; j
< syncState
->traceNb
; j
++)
1458 distanceMin
= MIN((*distances
)[i
][j
], (*distances
)[i
][k
] +
1459 (*distances
)[k
][j
]);
1461 if (distanceMin
!= (*distances
)[i
][j
])
1463 (*predecessors
)[i
][j
]= (*predecessors
)[k
][j
];
1466 (*distances
)[i
][j
]= distanceMin
;
1474 * Cummulate the time correction factors to convert a node's time to its
1476 * This function recursively calls itself until it reaches the reference node.
1479 * allFactors: offset and drift between each pair of traces
1480 * predecessors: matrix of each node's predecessor on the shortest
1481 * path between two nodes
1482 * references: reference node for each node
1483 * traceNum: node for which to find the factors
1484 * factors: resulting factors
1486 static void getFactors(FactorsCHull
** const allFactors
, unsigned int** const
1487 predecessors
, unsigned int* const references
, const unsigned int traceNum
,
1488 Factors
* const factors
)
1490 unsigned int reference
;
1492 reference
= references
[traceNum
];
1494 if (reference
== traceNum
)
1496 factors
->offset
= 0.;
1501 Factors previousVertexFactors
;
1503 getFactors(allFactors
, predecessors
, references
,
1504 predecessors
[reference
][traceNum
], &previousVertexFactors
);
1506 // convertir de traceNum à reference
1508 // allFactors convertit de col à row
1510 if (reference
> traceNum
)
1512 factors
->offset
= previousVertexFactors
.drift
*
1513 allFactors
[reference
][traceNum
].approx
->offset
+
1514 previousVertexFactors
.offset
;
1515 factors
->drift
= previousVertexFactors
.drift
*
1516 allFactors
[reference
][traceNum
].approx
->drift
;
1520 factors
->offset
= previousVertexFactors
.drift
* (-1. *
1521 allFactors
[traceNum
][reference
].approx
->offset
/
1522 allFactors
[traceNum
][reference
].approx
->drift
) +
1523 previousVertexFactors
.offset
;
1524 factors
->drift
= previousVertexFactors
.drift
* (1. /
1525 allFactors
[traceNum
][reference
].approx
->drift
);
1532 * Write the analysis-specific graph lines in the gnuplot script.
1535 * syncState: container for synchronization data
1536 * i: first trace number
1537 * j: second trace number, garanteed to be larger than i
1539 void writeAnalysisGraphsPlotsCHull(SyncState
* const syncState
, const unsigned
1540 int i
, const unsigned int j
)
1542 AnalysisDataCHull
* analysisData
;
1543 FactorsCHull
* factorsCHull
;
1545 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
1547 fprintf(syncState
->graphsStream
,
1548 "\t\"analysis_chull-%1$03d_to_%2$03d.data\" "
1549 "title \"Lower half-hull\" with linespoints "
1550 "linecolor rgb \"#015a01\" linetype 4 pointtype 8 pointsize 0.8, \\\n"
1551 "\t\"analysis_chull-%2$03d_to_%1$03d.data\" "
1552 "title \"Upper half-hull\" with linespoints "
1553 "linecolor rgb \"#003366\" linetype 4 pointtype 10 pointsize 0.8, \\\n",
1556 factorsCHull
= &analysisData
->graphsData
->allFactors
[j
][i
];
1557 if (factorsCHull
->type
== EXACT
)
1559 fprintf(syncState
->graphsStream
,
1561 "title \"Exact conversion\" with lines "
1562 "linecolor rgb \"black\" linetype 1, \\\n",
1563 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
);
1565 else if (factorsCHull
->type
== MIDDLE
)
1567 fprintf(syncState
->graphsStream
,
1568 "\t%.2f + %.10f * x "
1569 "title \"Min conversion\" with lines "
1570 "linecolor rgb \"black\" linetype 5, \\\n",
1571 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
);
1572 fprintf(syncState
->graphsStream
,
1573 "\t%.2f + %.10f * x "
1574 "title \"Max conversion\" with lines "
1575 "linecolor rgb \"black\" linetype 8, \\\n",
1576 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
);
1577 fprintf(syncState
->graphsStream
,
1578 "\t%.2f + %.10f * x "
1579 "title \"Middle conversion\" with lines "
1580 "linecolor rgb \"black\" linetype 1, \\\n",
1581 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
);
1583 else if (factorsCHull
->type
== FALLBACK
)
1585 fprintf(syncState
->graphsStream
,
1586 "\t%.2f + %.10f * x "
1587 "title \"Fallback conversion\" with lines "
1588 "linecolor rgb \"gray60\" linetype 1, \\\n",
1589 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
);
1591 else if (factorsCHull
->type
== INCOMPLETE
)
1593 if (factorsCHull
->min
->drift
!= -INFINITY
)
1595 fprintf(syncState
->graphsStream
,
1596 "\t%.2f + %.10f * x "
1597 "title \"Min conversion\" with lines "
1598 "linecolor rgb \"black\" linetype 5, \\\n",
1599 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
);
1602 if (factorsCHull
->max
->drift
!= INFINITY
)
1604 fprintf(syncState
->graphsStream
,
1605 "\t%.2f + %.10f * x "
1606 "title \"Max conversion\" with lines "
1607 "linecolor rgb \"black\" linetype 8, \\\n",
1608 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
);
1611 else if (factorsCHull
->type
== SCREWED
)
1613 if (factorsCHull
->min
!= NULL
&& factorsCHull
->min
->drift
!= -INFINITY
)
1615 fprintf(syncState
->graphsStream
,
1616 "\t%.2f + %.10f * x "
1617 "title \"Min conversion\" with lines "
1618 "linecolor rgb \"black\" linetype 5, \\\n",
1619 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
);
1622 if (factorsCHull
->max
!= NULL
&& factorsCHull
->max
->drift
!= INFINITY
)
1624 fprintf(syncState
->graphsStream
,
1625 "\t%.2f + %.10f * x "
1626 "title \"Max conversion\" with lines "
1627 "linecolor rgb \"black\" linetype 8, \\\n",
1628 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
);
1631 else if (factorsCHull
->type
== ABSENT
)
1636 g_assert_not_reached();