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
31 #include "sync_chain.h"
33 #include "event_analysis_chull.h"
37 #define g_info(format...) g_log (G_LOG_DOMAIN, G_LOG_LEVEL_INFO, format)
55 // Functions common to all analysis modules
56 static void initAnalysisCHull(SyncState
* const syncState
);
57 static void destroyAnalysisCHull(SyncState
* const syncState
);
59 static void analyzeMessageCHull(SyncState
* const syncState
, Message
* const
61 static GArray
* finalizeAnalysisCHull(SyncState
* const syncState
);
62 static void printAnalysisStatsCHull(SyncState
* const syncState
);
63 static void writeAnalysisGraphsPlotsCHull(SyncState
* const syncState
, const
64 unsigned int i
, const unsigned int j
);
66 // Functions specific to this module
67 static void registerAnalysisCHull() __attribute__((constructor (101)));
69 static void openGraphFiles(SyncState
* const syncState
);
70 static void closeGraphFiles(SyncState
* const syncState
);
71 static void writeGraphFiles(SyncState
* const syncState
);
72 static void gfDumpHullToFile(gpointer data
, gpointer userData
);
74 static void grahamScan(GQueue
* const hull
, Point
* const newPoint
, const
76 static int jointCmp(const Point
* const p1
, const Point
* const p2
, const Point
*
77 const p3
) __attribute__((pure
));
78 static double crossProductK(const Point
const* p1
, const Point
const* p2
,
79 const Point
const* p3
, const Point
const* p4
) __attribute__((pure
));
80 static Factors
* calculateFactorsExact(GQueue
* const cu
, GQueue
* const cl
, const
81 LineType lineType
) __attribute__((pure
));
82 static void calculateFactorsFallback(GQueue
* const cr
, GQueue
* const cs
,
83 FactorsCHull
* const result
);
84 static double slope(const Point
* const p1
, const Point
* const p2
)
85 __attribute__((pure
));
86 static double intercept(const Point
* const p1
, const Point
* const p2
)
87 __attribute__((pure
));
88 static GArray
* reduceFactors(SyncState
* const syncState
, FactorsCHull
**
90 static double verticalDistance(Point
* p1
, Point
* p2
, Point
* const point
)
91 __attribute__((pure
));
92 static void floydWarshall(SyncState
* const syncState
, FactorsCHull
** const
93 allFactors
, double*** const distances
, unsigned int*** const
95 static void getFactors(FactorsCHull
** const allFactors
, unsigned int** const
96 predecessors
, unsigned int* const references
, const unsigned int traceNum
,
97 Factors
* const factors
);
99 static void gfPointDestroy(gpointer data
, gpointer userData
);
102 static AnalysisModule analysisModuleCHull
= {
104 .initAnalysis
= &initAnalysisCHull
,
105 .destroyAnalysis
= &destroyAnalysisCHull
,
106 .analyzeMessage
= &analyzeMessageCHull
,
107 .finalizeAnalysis
= &finalizeAnalysisCHull
,
108 .printAnalysisStats
= &printAnalysisStatsCHull
,
110 .writeTraceTraceForePlots
= &writeAnalysisGraphsPlotsCHull
,
114 const char* const approxNames
[]= {
117 [FALLBACK
]= "Fallback",
118 [INCOMPLETE
]= "Incomplete",
120 [SCREWED
]= "Screwed",
125 * Analysis module registering function
127 static void registerAnalysisCHull()
129 g_queue_push_tail(&analysisModules
, &analysisModuleCHull
);
134 * Analysis init function
136 * This function is called at the beginning of a synchronization run for a set
139 * Allocate some of the analysis specific data structures
142 * syncState container for synchronization data.
143 * This function allocates or initializes these analysisData
148 static void initAnalysisCHull(SyncState
* const syncState
)
151 AnalysisDataCHull
* analysisData
;
153 analysisData
= malloc(sizeof(AnalysisDataCHull
));
154 syncState
->analysisData
= analysisData
;
156 analysisData
->hullArray
= malloc(syncState
->traceNb
* sizeof(GQueue
**));
157 for (i
= 0; i
< syncState
->traceNb
; i
++)
159 analysisData
->hullArray
[i
]= malloc(syncState
->traceNb
* sizeof(GQueue
*));
161 for (j
= 0; j
< syncState
->traceNb
; j
++)
163 analysisData
->hullArray
[i
][j
]= g_queue_new();
167 if (syncState
->stats
)
169 analysisData
->stats
= malloc(sizeof(AnalysisStatsCHull
));
170 analysisData
->stats
->dropped
= 0;
171 analysisData
->stats
->allFactors
= NULL
;
174 if (syncState
->graphsStream
)
176 analysisData
->graphsData
= malloc(sizeof(AnalysisGraphsDataCHull
));
177 openGraphFiles(syncState
);
178 analysisData
->graphsData
->allFactors
= NULL
;
184 * Create and open files used to store convex hull points to genereate
185 * graphs. Allocate and populate array to store file pointers.
188 * syncState: container for synchronization data
190 static void openGraphFiles(SyncState
* const syncState
)
196 AnalysisDataCHull
* analysisData
;
198 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
200 cwd
= changeToGraphDir(syncState
->graphsDir
);
202 analysisData
->graphsData
->hullPoints
= malloc(syncState
->traceNb
*
204 for (i
= 0; i
< syncState
->traceNb
; i
++)
206 analysisData
->graphsData
->hullPoints
[i
]= malloc(syncState
->traceNb
*
208 for (j
= 0; j
< syncState
->traceNb
; j
++)
212 retval
= snprintf(name
, sizeof(name
),
213 "analysis_chull-%03u_to_%03u.data", j
, i
);
214 if (retval
> sizeof(name
) - 1)
216 name
[sizeof(name
) - 1]= '\0';
218 if ((analysisData
->graphsData
->hullPoints
[i
][j
]= fopen(name
, "w")) ==
221 g_error(strerror(errno
));
230 g_error(strerror(errno
));
237 * Write hull points to files to generate graphs.
240 * syncState: container for synchronization data
242 static void writeGraphFiles(SyncState
* const syncState
)
245 AnalysisDataCHull
* analysisData
;
247 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
249 for (i
= 0; i
< syncState
->traceNb
; i
++)
251 for (j
= 0; j
< syncState
->traceNb
; j
++)
255 g_queue_foreach(analysisData
->hullArray
[i
][j
],
257 analysisData
->graphsData
->hullPoints
[i
][j
]);
265 * A GFunc for g_queue_foreach. Write a hull point to a file used to generate
269 * data: Point*, point to write to the file
270 * userData: FILE*, file pointer where to write the point
272 static void gfDumpHullToFile(gpointer data
, gpointer userData
)
276 point
= (Point
*) data
;
277 fprintf((FILE*) userData
, "%20llu %20llu\n", point
->x
, point
->y
);
282 * Close files used to store convex hull points to generate graphs.
283 * Deallocate array to store file pointers.
286 * syncState: container for synchronization data
288 static void closeGraphFiles(SyncState
* const syncState
)
291 AnalysisDataCHull
* analysisData
;
294 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
296 if (analysisData
->graphsData
->hullPoints
== NULL
)
301 for (i
= 0; i
< syncState
->traceNb
; i
++)
303 for (j
= 0; j
< syncState
->traceNb
; j
++)
307 retval
= fclose(analysisData
->graphsData
->hullPoints
[i
][j
]);
310 g_error(strerror(errno
));
314 free(analysisData
->graphsData
->hullPoints
[i
]);
316 free(analysisData
->graphsData
->hullPoints
);
317 analysisData
->graphsData
->hullPoints
= NULL
;
322 * Analysis destroy function
324 * Free the analysis specific data structures
327 * syncState container for synchronization data.
328 * This function deallocates these analysisData members:
332 static void destroyAnalysisCHull(SyncState
* const syncState
)
335 AnalysisDataCHull
* analysisData
;
337 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
339 if (analysisData
== NULL
)
344 for (i
= 0; i
< syncState
->traceNb
; i
++)
346 for (j
= 0; j
< syncState
->traceNb
; j
++)
348 g_queue_foreach(analysisData
->hullArray
[i
][j
], gfPointDestroy
, NULL
);
350 free(analysisData
->hullArray
[i
]);
352 free(analysisData
->hullArray
);
354 if (syncState
->stats
)
356 if (analysisData
->stats
->allFactors
!= NULL
)
358 freeAllFactors(syncState
->traceNb
, analysisData
->stats
->allFactors
);
361 free(analysisData
->stats
);
364 if (syncState
->graphsStream
)
366 if (analysisData
->graphsData
->hullPoints
!= NULL
)
368 closeGraphFiles(syncState
);
371 if (!syncState
->stats
&& analysisData
->graphsData
->allFactors
!= NULL
)
373 freeAllFactors(syncState
->traceNb
, analysisData
->graphsData
->allFactors
);
376 free(analysisData
->graphsData
);
379 free(syncState
->analysisData
);
380 syncState
->analysisData
= NULL
;
385 * Perform analysis on an event pair.
388 * syncState container for synchronization data
389 * message structure containing the events
391 static void analyzeMessageCHull(SyncState
* const syncState
, Message
* const message
)
393 AnalysisDataCHull
* analysisData
;
398 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
400 newPoint
= malloc(sizeof(Point
));
401 if (message
->inE
->traceNum
< message
->outE
->traceNum
)
403 // CA is inE->traceNum
404 newPoint
->x
= message
->inE
->cpuTime
;
405 newPoint
->y
= message
->outE
->cpuTime
;
407 g_debug("Reception point hullArray[%lu][%lu] x= inE->time= %llu y= outE->time= %llu",
408 message
->inE
->traceNum
, message
->outE
->traceNum
, newPoint
->x
,
413 // CA is outE->traceNum
414 newPoint
->x
= message
->outE
->cpuTime
;
415 newPoint
->y
= message
->inE
->cpuTime
;
417 g_debug("Send point hullArray[%lu][%lu] x= inE->time= %llu y= outE->time= %llu",
418 message
->inE
->traceNum
, message
->outE
->traceNum
, newPoint
->x
,
423 analysisData
->hullArray
[message
->inE
->traceNum
][message
->outE
->traceNum
];
425 if (hull
->length
>= 1 && newPoint
->x
< ((Point
*)
426 g_queue_peek_tail(hull
))->x
)
428 if (syncState
->stats
)
430 analysisData
->stats
->dropped
++;
437 grahamScan(hull
, newPoint
, hullType
);
443 * Construct one half of a convex hull from abscissa-sorted points
446 * hull: the points already in the hull
447 * newPoint: a new point to consider
448 * type: which half of the hull to construct
450 static void grahamScan(GQueue
* const hull
, Point
* const newPoint
, const
455 g_debug("grahamScan(hull (length: %u), newPoint, %s)", hull
->length
, type
456 == LOWER
? "LOWER" : "UPPER");
467 if (hull
->length
>= 2)
469 g_debug("jointCmp(hull[%u], hull[%u], newPoint) * inversionFactor = %d * %d = %d",
472 jointCmp(g_queue_peek_nth(hull
, hull
->length
- 2),
473 g_queue_peek_tail(hull
), newPoint
),
475 jointCmp(g_queue_peek_nth(hull
, hull
->length
- 2),
476 g_queue_peek_tail(hull
), newPoint
) * inversionFactor
);
478 while (hull
->length
>= 2 && jointCmp(g_queue_peek_nth(hull
, hull
->length
-
479 2), g_queue_peek_tail(hull
), newPoint
) * inversionFactor
<= 0)
481 g_debug("Removing hull[%u]", hull
->length
);
482 free((Point
*) g_queue_pop_tail(hull
));
484 if (hull
->length
>= 2)
486 g_debug("jointCmp(hull[%u], hull[%u], newPoint) * inversionFactor = %d * %d = %d",
489 jointCmp(g_queue_peek_nth(hull
, hull
->length
- 2),
490 g_queue_peek_tail(hull
), newPoint
),
492 jointCmp(g_queue_peek_nth(hull
, hull
->length
- 2),
493 g_queue_peek_tail(hull
), newPoint
) * inversionFactor
);
496 g_queue_push_tail(hull
, newPoint
);
501 * Finalize the factor calculations
504 * syncState container for synchronization data.
507 * Factors[traceNb] synchronization factors for each trace
509 static GArray
* finalizeAnalysisCHull(SyncState
* const syncState
)
511 AnalysisDataCHull
* analysisData
;
513 FactorsCHull
** allFactors
;
515 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
517 if (syncState
->graphsStream
&& analysisData
->graphsData
->hullPoints
!= NULL
)
519 writeGraphFiles(syncState
);
520 closeGraphFiles(syncState
);
523 allFactors
= calculateAllFactors(syncState
);
525 factors
= reduceFactors(syncState
, allFactors
);
527 if (syncState
->stats
|| syncState
->graphsStream
)
529 if (syncState
->stats
)
531 analysisData
->stats
->allFactors
= allFactors
;
534 if (syncState
->graphsStream
)
536 analysisData
->graphsData
->allFactors
= allFactors
;
541 freeAllFactors(syncState
->traceNb
, allFactors
);
549 * Print statistics related to analysis. Must be called after
553 * syncState container for synchronization data.
555 static void printAnalysisStatsCHull(SyncState
* const syncState
)
557 AnalysisDataCHull
* analysisData
;
560 if (!syncState
->stats
)
565 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
567 printf("Convex hull analysis stats:\n");
568 printf("\tout of order packets dropped from analysis: %u\n",
569 analysisData
->stats
->dropped
);
571 printf("\tNumber of points in convex hulls:\n");
573 for (i
= 0; i
< syncState
->traceNb
; i
++)
575 for (j
= i
+ 1; j
< syncState
->traceNb
; j
++)
577 printf("\t\t%3d - %-3d: lower half-hull %-5u upper half-hull %-5u\n",
578 i
, j
, analysisData
->hullArray
[j
][i
]->length
,
579 analysisData
->hullArray
[i
][j
]->length
);
583 printf("\tIndividual synchronization factors:\n");
585 for (i
= 0; i
< syncState
->traceNb
; i
++)
587 for (j
= i
+ 1; j
< syncState
->traceNb
; j
++)
589 FactorsCHull
* factorsCHull
;
591 factorsCHull
= &analysisData
->stats
->allFactors
[j
][i
];
592 printf("\t\t%3d - %-3d: ", i
, j
);
594 if (factorsCHull
->type
== EXACT
)
596 printf("Exact a0= % 7g a1= 1 %c %7g\n",
597 factorsCHull
->approx
->offset
,
598 factorsCHull
->approx
->drift
< 0. ? '-' : '+',
599 fabs(factorsCHull
->approx
->drift
));
601 else if (factorsCHull
->type
== MIDDLE
)
603 printf("Middle a0= % 7g a1= 1 %c %7g accuracy %7g\n",
604 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
605 - 1. < 0. ? '-' : '+', fabs(factorsCHull
->approx
->drift
-
606 1.), factorsCHull
->accuracy
);
607 printf("\t\t a0: % 7g to % 7g (delta= %7g)\n",
608 factorsCHull
->max
->offset
, factorsCHull
->min
->offset
,
609 factorsCHull
->min
->offset
- factorsCHull
->max
->offset
);
610 printf("\t\t a1: 1 %+7g to %+7g (delta= %7g)\n",
611 factorsCHull
->min
->drift
- 1., factorsCHull
->max
->drift
-
612 1., factorsCHull
->max
->drift
- factorsCHull
->min
->drift
);
614 else if (factorsCHull
->type
== FALLBACK
)
616 printf("Fallback a0= % 7g a1= 1 %c %7g error= %7g\n",
617 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
618 - 1. < 0. ? '-' : '+', fabs(factorsCHull
->approx
->drift
-
619 1.), factorsCHull
->accuracy
);
621 else if (factorsCHull
->type
== INCOMPLETE
)
623 printf("Incomplete\n");
625 if (factorsCHull
->min
->drift
!= -INFINITY
)
627 printf("\t\t min: a0: % 7g a1: 1 %c %7g\n",
628 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
-
629 1. < 0 ? '-' : '+', fabs(factorsCHull
->min
->drift
-
632 if (factorsCHull
->max
->drift
!= INFINITY
)
634 printf("\t\t max: a0: % 7g a1: 1 %c %7g\n",
635 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
-
636 1. < 0 ? '-' : '+', fabs(factorsCHull
->max
->drift
-
640 else if (factorsCHull
->type
== SCREWED
)
644 if (factorsCHull
->min
!= NULL
&& factorsCHull
->min
->drift
!= -INFINITY
)
646 printf("\t\t min: a0: % 7g a1: 1 %c %7g\n",
647 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
-
648 1. < 0 ? '-' : '+', fabs(factorsCHull
->min
->drift
-
651 if (factorsCHull
->max
!= NULL
&& factorsCHull
->max
->drift
!= INFINITY
)
653 printf("\t\t max: a0: % 7g a1: 1 %c %7g\n",
654 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
-
655 1. < 0 ? '-' : '+', fabs(factorsCHull
->max
->drift
-
659 else if (factorsCHull
->type
== ABSENT
)
665 g_assert_not_reached();
673 * A GFunc for g_queue_foreach()
676 * data Point*, point to destroy
679 static void gfPointDestroy(gpointer data
, gpointer userData
)
683 point
= (Point
*) data
;
689 * Find out if a sequence of three points constitutes a "left turn" or a
693 * p1, p2, p3: The three points.
697 * 0 colinear (unlikely result since this uses floating point
701 static int jointCmp(const Point
const* p1
, const Point
const* p2
, const
705 const double fuzzFactor
= 0.;
707 result
= crossProductK(p1
, p2
, p1
, p3
);
708 g_debug("crossProductK(p1= (%llu, %llu), p2= (%llu, %llu), p1= (%llu, %llu), p3= (%llu, %llu))= %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= %llu y= %llu c2[i2]: x= %llu y= %llu",
1081 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
, result
->offset
);
1094 * Analyze the convex hulls to determine approximate synchronization factors
1095 * between one pair of trace when there is no line that can fit in the
1096 * corridor separating them.
1098 * This implements the algorithm in [Ashton, P.: Algorithms for Off-line Clock
1099 * Synchronisation, University of Canterbury, December 1995, 26] Section 4.2.2
1102 * For each point p1 in cr
1103 * For each point p2 in cs
1105 * Calculate the line paramaters
1106 * For each point p3 in each convex hull
1107 * If p3 is on the wrong side of the line
1109 * If error < errorMin
1113 * cr: the upper half-convex hull
1114 * cs: the lower half-convex hull
1115 * result: a pointer to the pre-allocated struct where the results
1118 static void calculateFactorsFallback(GQueue
* const cr
, GQueue
* const cs
,
1119 FactorsCHull
* const result
)
1121 unsigned int i
, j
, k
;
1126 approx
= malloc(sizeof(Factors
));
1128 for (i
= 0; i
< cs
->length
; i
++)
1130 for (j
= 0; j
< cr
->length
; j
++)
1137 if (((Point
*) g_queue_peek_nth(cs
, i
))->x
< ((Point
*)g_queue_peek_nth(cr
, j
))->x
)
1139 p1
= *(Point
*)g_queue_peek_nth(cs
, i
);
1140 p2
= *(Point
*)g_queue_peek_nth(cr
, j
);
1144 p1
= *(Point
*)g_queue_peek_nth(cr
, j
);
1145 p2
= *(Point
*)g_queue_peek_nth(cs
, i
);
1148 // The lower hull should be above the point
1149 for (k
= 0; k
< cs
->length
; k
++)
1151 if (jointCmp(&p1
, &p2
, g_queue_peek_nth(cs
, k
)) < 0.)
1153 error
+= verticalDistance(&p1
, &p2
, g_queue_peek_nth(cs
, k
));
1157 // The upper hull should be below the point
1158 for (k
= 0; k
< cr
->length
; k
++)
1160 if (jointCmp(&p1
, &p2
, g_queue_peek_nth(cr
, k
)) > 0.)
1162 error
+= verticalDistance(&p1
, &p2
, g_queue_peek_nth(cr
, k
));
1166 if (error
< errorMin
)
1168 g_debug("Fallback: i= %u j= %u is a better match (error= %g)", i
, j
, error
);
1169 approx
->drift
= slope(&p1
, &p2
);
1170 approx
->offset
= intercept(&p1
, &p2
);
1176 result
->approx
= approx
;
1177 result
->accuracy
= errorMin
;
1182 * Calculate the vertical distance between a line and a point
1185 * p1, p2: Two points defining the line
1189 * the vertical distance
1191 static double verticalDistance(Point
* p1
, Point
* p2
, Point
* const point
)
1193 return fabs(slope(p1
, p2
) * point
->x
+ intercept(p1
, p2
) - point
->y
);
1198 * Calculate the slope between two points
1201 * p1, p2 the two points
1206 static double slope(const Point
* const p1
, const Point
* const p2
)
1208 return ((double) p2
->y
- p1
->y
) / (p2
->x
- p1
->x
);
1212 /* Calculate the y-intercept of a line that passes by two points
1215 * p1, p2 the two points
1220 static double intercept(const Point
* const p1
, const Point
* const p2
)
1222 return ((double) p2
->y
* p1
->x
- (double) p1
->y
* p2
->x
) / ((double) p1
->x
- p2
->x
);
1227 * Calculate a resulting offset and drift for each trace.
1229 * Traces are assembled in groups. A group is an "island" of nodes/traces that
1230 * exchanged messages. A reference is determined for each group by using a
1231 * shortest path search based on the accuracy of the approximation. This also
1232 * forms a tree of the best way to relate each node's clock to the reference's
1233 * based on the accuracy. Sometimes it may be necessary or advantageous to
1234 * propagate the factors through intermediary clocks. Resulting factors for
1235 * each trace are determined based on this tree.
1237 * This part was not the focus of my research. The algorithm used here is
1238 * inexact in some ways:
1239 * 1) The reference used may not actually be the best one to use. This is
1240 * because the accuracy is not corrected based on the drift during the
1241 * shortest path search.
1242 * 2) The min and max factors are not propagated and are no longer valid.
1243 * 3) Approximations of different types (MIDDLE and FALLBACK) are compared
1244 * together. The "accuracy" parameters of these have different meanings and
1245 * are not readily comparable.
1247 * Nevertheless, the result is satisfactory. You just can't tell "how much" it
1250 * Two alternative (and subtly different) ways of propagating factors to
1251 * preserve min and max bondaries have been proposed, see:
1252 * [Duda, A., Harrus, G., Haddad, Y., and Bernard, G.: Estimating global time
1253 * in distributed systems, Proc. 7th Int. Conf. on Distributed Computing
1254 * Systems, Berlin, volume 18, 1987] p.304
1256 * [Jezequel, J.M., and Jard, C.: Building a global clock for observing
1257 * computations in distributed memory parallel computers, Concurrency:
1258 * Practice and Experience 8(1), volume 8, John Wiley & Sons, Ltd Chichester,
1259 * 1996, 32] Section 5; which is mostly the same as
1260 * [Jezequel, J.M.: Building a global time on parallel machines, Proceedings
1261 * of the 3rd International Workshop on Distributed Algorithms, LNCS, volume
1262 * 392, 136–147, 1989] Section 5
1265 * syncState: container for synchronization data.
1266 * allFactors: offset and drift between each pair of traces
1269 * Factors[traceNb] synchronization factors for each trace
1271 static GArray
* reduceFactors(SyncState
* const syncState
, FactorsCHull
** const
1276 unsigned int** predecessors
;
1277 double* distanceSums
;
1278 unsigned int* references
;
1281 // Solve the all-pairs shortest path problem using the Floyd-Warshall
1283 floydWarshall(syncState
, allFactors
, &distances
, &predecessors
);
1285 /* Find the reference for each node
1287 * First calculate, for each node, the sum of the distances to each other
1288 * node it can reach.
1290 * Then, go through each "island" of traces to find the trace that has the
1291 * lowest distance sum. Assign this trace as the reference to each trace
1294 distanceSums
= malloc(syncState
->traceNb
* sizeof(double));
1295 for (i
= 0; i
< syncState
->traceNb
; i
++)
1297 distanceSums
[i
]= 0.;
1298 for (j
= 0; j
< syncState
->traceNb
; j
++)
1300 distanceSums
[i
]+= distances
[i
][j
];
1304 references
= malloc(syncState
->traceNb
* sizeof(unsigned int));
1305 for (i
= 0; i
< syncState
->traceNb
; i
++)
1307 references
[i
]= UINT_MAX
;
1309 for (i
= 0; i
< syncState
->traceNb
; i
++)
1311 if (references
[i
] == UINT_MAX
)
1313 unsigned int reference
;
1314 double distanceSumMin
;
1316 // A node is its own reference by default
1318 distanceSumMin
= INFINITY
;
1319 for (j
= 0; j
< syncState
->traceNb
; j
++)
1321 if (distances
[i
][j
] != INFINITY
&& distanceSums
[j
] <
1325 distanceSumMin
= distanceSums
[j
];
1328 for (j
= 0; j
< syncState
->traceNb
; j
++)
1330 if (distances
[i
][j
] != INFINITY
)
1332 references
[j
]= reference
;
1338 for (i
= 0; i
< syncState
->traceNb
; i
++)
1345 /* For each trace, calculate the factors based on their corresponding
1346 * tree. The tree is rooted at the reference and the shortest path to each
1347 * other nodes are the branches.
1349 factors
= g_array_sized_new(FALSE
, FALSE
, sizeof(Factors
),
1350 syncState
->traceNb
);
1351 g_array_set_size(factors
, syncState
->traceNb
);
1352 for (i
= 0; i
< syncState
->traceNb
; i
++)
1354 getFactors(allFactors
, predecessors
, references
, i
, &g_array_index(factors
,
1358 for (i
= 0; i
< syncState
->traceNb
; i
++)
1360 free(predecessors
[i
]);
1370 * Perform an all-source shortest path search using the Floyd-Warshall
1373 * The algorithm is implemented accoding to the description here:
1374 * http://web.mit.edu/urban_or_book/www/book/chapter6/6.2.2.html
1377 * syncState: container for synchronization data.
1378 * allFactors: offset and drift between each pair of traces
1379 * distances: resulting matrix of the length of the shortest path between
1380 * two nodes. If there is no path between two nodes, the
1381 * length is INFINITY
1382 * predecessors: resulting matrix of each node's predecessor on the shortest
1383 * path between two nodes
1385 static void floydWarshall(SyncState
* const syncState
, FactorsCHull
** const
1386 allFactors
, double*** const distances
, unsigned int*** const
1389 unsigned int i
, j
, k
;
1391 // Setup initial conditions
1392 *distances
= malloc(syncState
->traceNb
* sizeof(double*));
1393 *predecessors
= malloc(syncState
->traceNb
* sizeof(unsigned int*));
1394 for (i
= 0; i
< syncState
->traceNb
; i
++)
1396 (*distances
)[i
]= malloc(syncState
->traceNb
* sizeof(double));
1397 for (j
= 0; j
< syncState
->traceNb
; j
++)
1401 g_assert(allFactors
[i
][j
].type
== EXACT
);
1403 (*distances
)[i
][j
]= 0.;
1407 unsigned int row
, col
;
1420 if (allFactors
[row
][col
].type
== MIDDLE
||
1421 allFactors
[row
][col
].type
== FALLBACK
)
1423 (*distances
)[i
][j
]= allFactors
[row
][col
].accuracy
;
1425 else if (allFactors
[row
][col
].type
== INCOMPLETE
||
1426 allFactors
[row
][col
].type
== SCREWED
||
1427 allFactors
[row
][col
].type
== ABSENT
)
1429 (*distances
)[i
][j
]= INFINITY
;
1433 g_assert_not_reached();
1438 (*predecessors
)[i
]= malloc(syncState
->traceNb
* sizeof(unsigned int));
1439 for (j
= 0; j
< syncState
->traceNb
; j
++)
1443 (*predecessors
)[i
][j
]= i
;
1447 (*predecessors
)[i
][j
]= UINT_MAX
;
1452 // Run the iterations
1453 for (k
= 0; k
< syncState
->traceNb
; k
++)
1455 for (i
= 0; i
< syncState
->traceNb
; i
++)
1457 for (j
= 0; j
< syncState
->traceNb
; j
++)
1461 distanceMin
= MIN((*distances
)[i
][j
], (*distances
)[i
][k
] +
1462 (*distances
)[k
][j
]);
1464 if (distanceMin
!= (*distances
)[i
][j
])
1466 (*predecessors
)[i
][j
]= (*predecessors
)[k
][j
];
1469 (*distances
)[i
][j
]= distanceMin
;
1477 * Cummulate the time correction factors to convert a node's time to its
1479 * This function recursively calls itself until it reaches the reference node.
1482 * allFactors: offset and drift between each pair of traces
1483 * predecessors: matrix of each node's predecessor on the shortest
1484 * path between two nodes
1485 * references: reference node for each node
1486 * traceNum: node for which to find the factors
1487 * factors: resulting factors
1489 static void getFactors(FactorsCHull
** const allFactors
, unsigned int** const
1490 predecessors
, unsigned int* const references
, const unsigned int traceNum
,
1491 Factors
* const factors
)
1493 unsigned int reference
;
1495 reference
= references
[traceNum
];
1497 if (reference
== traceNum
)
1499 factors
->offset
= 0.;
1504 Factors previousVertexFactors
;
1506 getFactors(allFactors
, predecessors
, references
,
1507 predecessors
[reference
][traceNum
], &previousVertexFactors
);
1509 // convertir de traceNum à reference
1511 // allFactors convertit de col à row
1513 if (reference
> traceNum
)
1515 factors
->offset
= previousVertexFactors
.drift
*
1516 allFactors
[reference
][traceNum
].approx
->offset
+
1517 previousVertexFactors
.offset
;
1518 factors
->drift
= previousVertexFactors
.drift
*
1519 allFactors
[reference
][traceNum
].approx
->drift
;
1523 factors
->offset
= previousVertexFactors
.drift
* (-1. *
1524 allFactors
[traceNum
][reference
].approx
->offset
/
1525 allFactors
[traceNum
][reference
].approx
->drift
) +
1526 previousVertexFactors
.offset
;
1527 factors
->drift
= previousVertexFactors
.drift
* (1. /
1528 allFactors
[traceNum
][reference
].approx
->drift
);
1535 * Write the analysis-specific graph lines in the gnuplot script.
1538 * syncState: container for synchronization data
1539 * i: first trace number
1540 * j: second trace number, garanteed to be larger than i
1542 void writeAnalysisGraphsPlotsCHull(SyncState
* const syncState
, const unsigned
1543 int i
, const unsigned int j
)
1545 AnalysisDataCHull
* analysisData
;
1546 FactorsCHull
* factorsCHull
;
1548 analysisData
= (AnalysisDataCHull
*) syncState
->analysisData
;
1550 fprintf(syncState
->graphsStream
,
1551 "\t\"analysis_chull-%1$03d_to_%2$03d.data\" "
1552 "title \"Lower half-hull\" with linespoints "
1553 "linecolor rgb \"#015a01\" linetype 4 pointtype 8 pointsize 0.8, \\\n"
1554 "\t\"analysis_chull-%2$03d_to_%1$03d.data\" "
1555 "title \"Upper half-hull\" with linespoints "
1556 "linecolor rgb \"#003366\" linetype 4 pointtype 10 pointsize 0.8, \\\n",
1559 factorsCHull
= &analysisData
->graphsData
->allFactors
[j
][i
];
1560 if (factorsCHull
->type
== EXACT
)
1562 fprintf(syncState
->graphsStream
,
1564 "title \"Exact conversion\" with lines "
1565 "linecolor rgb \"black\" linetype 1, \\\n",
1566 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
);
1568 else if (factorsCHull
->type
== MIDDLE
)
1570 fprintf(syncState
->graphsStream
,
1571 "\t%.2f + %.10f * x "
1572 "title \"Min conversion\" with lines "
1573 "linecolor rgb \"black\" linetype 5, \\\n",
1574 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
);
1575 fprintf(syncState
->graphsStream
,
1576 "\t%.2f + %.10f * x "
1577 "title \"Max conversion\" with lines "
1578 "linecolor rgb \"black\" linetype 8, \\\n",
1579 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
);
1580 fprintf(syncState
->graphsStream
,
1581 "\t%.2f + %.10f * x "
1582 "title \"Middle conversion\" with lines "
1583 "linecolor rgb \"black\" linetype 1, \\\n",
1584 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
);
1586 else if (factorsCHull
->type
== FALLBACK
)
1588 fprintf(syncState
->graphsStream
,
1589 "\t%.2f + %.10f * x "
1590 "title \"Fallback conversion\" with lines "
1591 "linecolor rgb \"gray60\" linetype 1, \\\n",
1592 factorsCHull
->approx
->offset
, factorsCHull
->approx
->drift
);
1594 else if (factorsCHull
->type
== INCOMPLETE
)
1596 if (factorsCHull
->min
->drift
!= -INFINITY
)
1598 fprintf(syncState
->graphsStream
,
1599 "\t%.2f + %.10f * x "
1600 "title \"Min conversion\" with lines "
1601 "linecolor rgb \"black\" linetype 5, \\\n",
1602 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
);
1605 if (factorsCHull
->max
->drift
!= INFINITY
)
1607 fprintf(syncState
->graphsStream
,
1608 "\t%.2f + %.10f * x "
1609 "title \"Max conversion\" with lines "
1610 "linecolor rgb \"black\" linetype 8, \\\n",
1611 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
);
1614 else if (factorsCHull
->type
== SCREWED
)
1616 if (factorsCHull
->min
!= NULL
&& factorsCHull
->min
->drift
!= -INFINITY
)
1618 fprintf(syncState
->graphsStream
,
1619 "\t%.2f + %.10f * x "
1620 "title \"Min conversion\" with lines "
1621 "linecolor rgb \"black\" linetype 5, \\\n",
1622 factorsCHull
->min
->offset
, factorsCHull
->min
->drift
);
1625 if (factorsCHull
->max
!= NULL
&& factorsCHull
->max
->drift
!= INFINITY
)
1627 fprintf(syncState
->graphsStream
,
1628 "\t%.2f + %.10f * x "
1629 "title \"Max conversion\" with lines "
1630 "linecolor rgb \"black\" linetype 8, \\\n",
1631 factorsCHull
->max
->offset
, factorsCHull
->max
->drift
);
1634 else if (factorsCHull
->type
== ABSENT
)
1639 g_assert_not_reached();