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08365995 BP |
1 | /* This file is part of the Linux Trace Toolkit viewer |
2 | * Copyright (C) 2009 Benjamin Poirier <benjamin.poirier@polymtl.ca> | |
3 | * | |
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; | |
7 | * | |
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. | |
12 | * | |
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, | |
16 | * MA 02111-1307, USA. | |
17 | */ | |
18 | #define _ISOC99_SOURCE | |
19 | ||
20 | #ifdef HAVE_CONFIG_H | |
21 | #include <config.h> | |
22 | #endif | |
23 | ||
24 | #include <errno.h> | |
25 | #include <math.h> | |
26 | #include <float.h> | |
27 | #include <stdlib.h> | |
28 | #include <stdio.h> | |
29 | #include <unistd.h> | |
30 | ||
2bd4b3e4 | 31 | #include "sync_chain.h" |
08365995 BP |
32 | |
33 | #include "event_analysis_chull.h" | |
34 | ||
35 | ||
36 | #ifndef g_info | |
37 | #define g_info(format...) g_log (G_LOG_DOMAIN, G_LOG_LEVEL_INFO, format) | |
38 | #endif | |
39 | ||
40 | ||
41 | typedef enum | |
42 | { | |
43 | LOWER, | |
44 | UPPER | |
45 | } HullType; | |
46 | ||
47 | ||
48 | typedef enum | |
49 | { | |
50 | MINIMUM, | |
51 | MAXIMUM | |
52 | } LineType; | |
53 | ||
54 | ||
55 | // Functions common to all analysis modules | |
56 | static void initAnalysisCHull(SyncState* const syncState); | |
57 | static void destroyAnalysisCHull(SyncState* const syncState); | |
58 | ||
10341d26 BP |
59 | static void analyzeMessageCHull(SyncState* const syncState, Message* const |
60 | message); | |
08365995 BP |
61 | static GArray* finalizeAnalysisCHull(SyncState* const syncState); |
62 | static void printAnalysisStatsCHull(SyncState* const syncState); | |
8d7d16dd BP |
63 | static void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const |
64 | unsigned int i, const unsigned int j); | |
08365995 BP |
65 | |
66 | // Functions specific to this module | |
67 | static void registerAnalysisCHull() __attribute__((constructor (101))); | |
68 | ||
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); | |
73 | ||
74 | static void grahamScan(GQueue* const hull, Point* const newPoint, const | |
75 | HullType type); | |
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)); | |
08365995 BP |
80 | static Factors* calculateFactorsExact(GQueue* const cu, GQueue* const cl, const |
81 | LineType lineType) __attribute__((pure)); | |
08365995 BP |
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** | |
89 | allFactors); | |
08365995 BP |
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 | |
94 | predecessors); | |
95 | static void getFactors(FactorsCHull** const allFactors, unsigned int** const | |
96 | predecessors, unsigned int* const references, const unsigned int traceNum, | |
97 | Factors* const factors); | |
98 | ||
99 | static void gfPointDestroy(gpointer data, gpointer userData); | |
100 | ||
101 | ||
102 | static AnalysisModule analysisModuleCHull= { | |
103 | .name= "chull", | |
104 | .initAnalysis= &initAnalysisCHull, | |
105 | .destroyAnalysis= &destroyAnalysisCHull, | |
10341d26 | 106 | .analyzeMessage= &analyzeMessageCHull, |
08365995 BP |
107 | .finalizeAnalysis= &finalizeAnalysisCHull, |
108 | .printAnalysisStats= &printAnalysisStatsCHull, | |
467066ee | 109 | .graphFunctions= { |
c6356aa7 | 110 | .writeTraceTraceForePlots= &writeAnalysisGraphsPlotsCHull, |
467066ee | 111 | } |
08365995 BP |
112 | }; |
113 | ||
66eaf2eb BP |
114 | const char* const approxNames[]= { |
115 | [EXACT]= "Exact", | |
116 | [MIDDLE]= "Middle", | |
117 | [FALLBACK]= "Fallback", | |
118 | [INCOMPLETE]= "Incomplete", | |
119 | [ABSENT]= "Absent", | |
120 | [SCREWED]= "Screwed", | |
121 | }; | |
08365995 | 122 | |
c6356aa7 | 123 | |
08365995 BP |
124 | /* |
125 | * Analysis module registering function | |
126 | */ | |
127 | static void registerAnalysisCHull() | |
128 | { | |
129 | g_queue_push_tail(&analysisModules, &analysisModuleCHull); | |
130 | } | |
131 | ||
132 | ||
133 | /* | |
134 | * Analysis init function | |
135 | * | |
136 | * This function is called at the beginning of a synchronization run for a set | |
137 | * of traces. | |
138 | * | |
139 | * Allocate some of the analysis specific data structures | |
140 | * | |
141 | * Args: | |
142 | * syncState container for synchronization data. | |
143 | * This function allocates or initializes these analysisData | |
144 | * members: | |
145 | * hullArray | |
146 | * dropped | |
147 | */ | |
148 | static void initAnalysisCHull(SyncState* const syncState) | |
149 | { | |
150 | unsigned int i, j; | |
151 | AnalysisDataCHull* analysisData; | |
152 | ||
153 | analysisData= malloc(sizeof(AnalysisDataCHull)); | |
154 | syncState->analysisData= analysisData; | |
155 | ||
156 | analysisData->hullArray= malloc(syncState->traceNb * sizeof(GQueue**)); | |
157 | for (i= 0; i < syncState->traceNb; i++) | |
158 | { | |
159 | analysisData->hullArray[i]= malloc(syncState->traceNb * sizeof(GQueue*)); | |
160 | ||
161 | for (j= 0; j < syncState->traceNb; j++) | |
162 | { | |
163 | analysisData->hullArray[i][j]= g_queue_new(); | |
164 | } | |
165 | } | |
166 | ||
167 | if (syncState->stats) | |
168 | { | |
169 | analysisData->stats= malloc(sizeof(AnalysisStatsCHull)); | |
170 | analysisData->stats->dropped= 0; | |
171 | analysisData->stats->allFactors= NULL; | |
172 | } | |
173 | ||
8d7d16dd | 174 | if (syncState->graphsStream) |
08365995 BP |
175 | { |
176 | analysisData->graphsData= malloc(sizeof(AnalysisGraphsDataCHull)); | |
177 | openGraphFiles(syncState); | |
178 | analysisData->graphsData->allFactors= NULL; | |
179 | } | |
180 | } | |
181 | ||
182 | ||
183 | /* | |
184 | * Create and open files used to store convex hull points to genereate | |
185 | * graphs. Allocate and populate array to store file pointers. | |
186 | * | |
187 | * Args: | |
188 | * syncState: container for synchronization data | |
189 | */ | |
190 | static void openGraphFiles(SyncState* const syncState) | |
191 | { | |
192 | unsigned int i, j; | |
193 | int retval; | |
194 | char* cwd; | |
195 | char name[31]; | |
196 | AnalysisDataCHull* analysisData; | |
197 | ||
198 | analysisData= (AnalysisDataCHull*) syncState->analysisData; | |
199 | ||
8d7d16dd | 200 | cwd= changeToGraphDir(syncState->graphsDir); |
08365995 BP |
201 | |
202 | analysisData->graphsData->hullPoints= malloc(syncState->traceNb * | |
203 | sizeof(FILE**)); | |
204 | for (i= 0; i < syncState->traceNb; i++) | |
205 | { | |
206 | analysisData->graphsData->hullPoints[i]= malloc(syncState->traceNb * | |
207 | sizeof(FILE*)); | |
208 | for (j= 0; j < syncState->traceNb; j++) | |
209 | { | |
210 | if (i != j) | |
211 | { | |
212 | retval= snprintf(name, sizeof(name), | |
213 | "analysis_chull-%03u_to_%03u.data", j, i); | |
214 | if (retval > sizeof(name) - 1) | |
215 | { | |
216 | name[sizeof(name) - 1]= '\0'; | |
217 | } | |
218 | if ((analysisData->graphsData->hullPoints[i][j]= fopen(name, "w")) == | |
219 | NULL) | |
220 | { | |
221 | g_error(strerror(errno)); | |
222 | } | |
223 | } | |
224 | } | |
225 | } | |
226 | ||
227 | retval= chdir(cwd); | |
228 | if (retval == -1) | |
229 | { | |
230 | g_error(strerror(errno)); | |
231 | } | |
232 | free(cwd); | |
233 | } | |
234 | ||
235 | ||
236 | /* | |
237 | * Write hull points to files to generate graphs. | |
238 | * | |
239 | * Args: | |
240 | * syncState: container for synchronization data | |
241 | */ | |
242 | static void writeGraphFiles(SyncState* const syncState) | |
243 | { | |
244 | unsigned int i, j; | |
245 | AnalysisDataCHull* analysisData; | |
246 | ||
247 | analysisData= (AnalysisDataCHull*) syncState->analysisData; | |
248 | ||
249 | for (i= 0; i < syncState->traceNb; i++) | |
250 | { | |
251 | for (j= 0; j < syncState->traceNb; j++) | |
252 | { | |
253 | if (i != j) | |
254 | { | |
255 | g_queue_foreach(analysisData->hullArray[i][j], | |
256 | &gfDumpHullToFile, | |
257 | analysisData->graphsData->hullPoints[i][j]); | |
258 | } | |
259 | } | |
260 | } | |
261 | } | |
262 | ||
263 | ||
264 | /* | |
265 | * A GFunc for g_queue_foreach. Write a hull point to a file used to generate | |
266 | * graphs | |
267 | * | |
268 | * Args: | |
269 | * data: Point*, point to write to the file | |
270 | * userData: FILE*, file pointer where to write the point | |
271 | */ | |
272 | static void gfDumpHullToFile(gpointer data, gpointer userData) | |
273 | { | |
274 | Point* point; | |
275 | ||
276 | point= (Point*) data; | |
277 | fprintf((FILE*) userData, "%20llu %20llu\n", point->x, point->y); | |
278 | } | |
279 | ||
280 | ||
281 | /* | |
282 | * Close files used to store convex hull points to generate graphs. | |
283 | * Deallocate array to store file pointers. | |
284 | * | |
285 | * Args: | |
286 | * syncState: container for synchronization data | |
287 | */ | |
288 | static void closeGraphFiles(SyncState* const syncState) | |
289 | { | |
290 | unsigned int i, j; | |
291 | AnalysisDataCHull* analysisData; | |
292 | int retval; | |
293 | ||
294 | analysisData= (AnalysisDataCHull*) syncState->analysisData; | |
295 | ||
296 | if (analysisData->graphsData->hullPoints == NULL) | |
297 | { | |
298 | return; | |
299 | } | |
300 | ||
301 | for (i= 0; i < syncState->traceNb; i++) | |
302 | { | |
303 | for (j= 0; j < syncState->traceNb; j++) | |
304 | { | |
305 | if (i != j) | |
306 | { | |
307 | retval= fclose(analysisData->graphsData->hullPoints[i][j]); | |
308 | if (retval != 0) | |
309 | { | |
310 | g_error(strerror(errno)); | |
311 | } | |
312 | } | |
313 | } | |
314 | free(analysisData->graphsData->hullPoints[i]); | |
315 | } | |
316 | free(analysisData->graphsData->hullPoints); | |
317 | analysisData->graphsData->hullPoints= NULL; | |
318 | } | |
319 | ||
320 | ||
321 | /* | |
322 | * Analysis destroy function | |
323 | * | |
324 | * Free the analysis specific data structures | |
325 | * | |
326 | * Args: | |
327 | * syncState container for synchronization data. | |
328 | * This function deallocates these analysisData members: | |
329 | * hullArray | |
330 | * stDev | |
331 | */ | |
332 | static void destroyAnalysisCHull(SyncState* const syncState) | |
333 | { | |
334 | unsigned int i, j; | |
335 | AnalysisDataCHull* analysisData; | |
336 | ||
337 | analysisData= (AnalysisDataCHull*) syncState->analysisData; | |
338 | ||
339 | if (analysisData == NULL) | |
340 | { | |
341 | return; | |
342 | } | |
343 | ||
344 | for (i= 0; i < syncState->traceNb; i++) | |
345 | { | |
346 | for (j= 0; j < syncState->traceNb; j++) | |
347 | { | |
348 | g_queue_foreach(analysisData->hullArray[i][j], gfPointDestroy, NULL); | |
349 | } | |
350 | free(analysisData->hullArray[i]); | |
351 | } | |
352 | free(analysisData->hullArray); | |
353 | ||
354 | if (syncState->stats) | |
355 | { | |
356 | if (analysisData->stats->allFactors != NULL) | |
357 | { | |
66eaf2eb | 358 | freeAllFactors(syncState->traceNb, analysisData->stats->allFactors); |
08365995 BP |
359 | } |
360 | ||
361 | free(analysisData->stats); | |
362 | } | |
363 | ||
8d7d16dd | 364 | if (syncState->graphsStream) |
08365995 BP |
365 | { |
366 | if (analysisData->graphsData->hullPoints != NULL) | |
367 | { | |
368 | closeGraphFiles(syncState); | |
369 | } | |
370 | ||
371 | if (!syncState->stats && analysisData->graphsData->allFactors != NULL) | |
372 | { | |
66eaf2eb | 373 | freeAllFactors(syncState->traceNb, analysisData->graphsData->allFactors); |
08365995 BP |
374 | } |
375 | ||
376 | free(analysisData->graphsData); | |
377 | } | |
378 | ||
379 | free(syncState->analysisData); | |
380 | syncState->analysisData= NULL; | |
381 | } | |
382 | ||
383 | ||
384 | /* | |
385 | * Perform analysis on an event pair. | |
386 | * | |
387 | * Args: | |
388 | * syncState container for synchronization data | |
10341d26 | 389 | * message structure containing the events |
08365995 | 390 | */ |
10341d26 | 391 | static void analyzeMessageCHull(SyncState* const syncState, Message* const message) |
08365995 BP |
392 | { |
393 | AnalysisDataCHull* analysisData; | |
394 | Point* newPoint; | |
395 | HullType hullType; | |
396 | GQueue* hull; | |
397 | ||
398 | analysisData= (AnalysisDataCHull*) syncState->analysisData; | |
399 | ||
400 | newPoint= malloc(sizeof(Point)); | |
10341d26 | 401 | if (message->inE->traceNum < message->outE->traceNum) |
08365995 BP |
402 | { |
403 | // CA is inE->traceNum | |
76be6fc2 BP |
404 | newPoint->x= message->inE->cpuTime; |
405 | newPoint->y= message->outE->cpuTime; | |
08365995 | 406 | hullType= UPPER; |
10341d26 BP |
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, | |
08365995 BP |
409 | newPoint->y); |
410 | } | |
411 | else | |
412 | { | |
413 | // CA is outE->traceNum | |
76be6fc2 BP |
414 | newPoint->x= message->outE->cpuTime; |
415 | newPoint->y= message->inE->cpuTime; | |
08365995 | 416 | hullType= LOWER; |
10341d26 BP |
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, | |
08365995 BP |
419 | newPoint->y); |
420 | } | |
421 | ||
422 | hull= | |
10341d26 | 423 | analysisData->hullArray[message->inE->traceNum][message->outE->traceNum]; |
08365995 BP |
424 | |
425 | if (hull->length >= 1 && newPoint->x < ((Point*) | |
426 | g_queue_peek_tail(hull))->x) | |
427 | { | |
428 | if (syncState->stats) | |
429 | { | |
430 | analysisData->stats->dropped++; | |
431 | } | |
432 | ||
433 | free(newPoint); | |
434 | } | |
435 | else | |
436 | { | |
437 | grahamScan(hull, newPoint, hullType); | |
438 | } | |
439 | } | |
440 | ||
441 | ||
442 | /* | |
443 | * Construct one half of a convex hull from abscissa-sorted points | |
444 | * | |
445 | * Args: | |
446 | * hull: the points already in the hull | |
447 | * newPoint: a new point to consider | |
448 | * type: which half of the hull to construct | |
449 | */ | |
450 | static void grahamScan(GQueue* const hull, Point* const newPoint, const | |
451 | HullType type) | |
452 | { | |
453 | int inversionFactor; | |
454 | ||
455 | g_debug("grahamScan(hull (length: %u), newPoint, %s)", hull->length, type | |
456 | == LOWER ? "LOWER" : "UPPER"); | |
457 | ||
458 | if (type == LOWER) | |
459 | { | |
460 | inversionFactor= 1; | |
461 | } | |
462 | else | |
463 | { | |
464 | inversionFactor= -1; | |
465 | } | |
466 | ||
467 | if (hull->length >= 2) | |
468 | { | |
469 | g_debug("jointCmp(hull[%u], hull[%u], newPoint) * inversionFactor = %d * %d = %d", | |
470 | hull->length - 2, | |
471 | hull->length - 1, | |
472 | jointCmp(g_queue_peek_nth(hull, hull->length - 2), | |
473 | g_queue_peek_tail(hull), newPoint), | |
474 | inversionFactor, | |
475 | jointCmp(g_queue_peek_nth(hull, hull->length - 2), | |
476 | g_queue_peek_tail(hull), newPoint) * inversionFactor); | |
477 | } | |
478 | while (hull->length >= 2 && jointCmp(g_queue_peek_nth(hull, hull->length - | |
479 | 2), g_queue_peek_tail(hull), newPoint) * inversionFactor <= 0) | |
480 | { | |
481 | g_debug("Removing hull[%u]", hull->length); | |
482 | free((Point*) g_queue_pop_tail(hull)); | |
483 | ||
484 | if (hull->length >= 2) | |
485 | { | |
486 | g_debug("jointCmp(hull[%u], hull[%u], newPoint) * inversionFactor = %d * %d = %d", | |
487 | hull->length - 2, | |
488 | hull->length - 1, | |
489 | jointCmp(g_queue_peek_nth(hull, hull->length - 2), | |
490 | g_queue_peek_tail(hull), newPoint), | |
491 | inversionFactor, | |
492 | jointCmp(g_queue_peek_nth(hull, hull->length - 2), | |
493 | g_queue_peek_tail(hull), newPoint) * inversionFactor); | |
494 | } | |
495 | } | |
496 | g_queue_push_tail(hull, newPoint); | |
497 | } | |
498 | ||
499 | ||
500 | /* | |
501 | * Finalize the factor calculations | |
502 | * | |
503 | * Args: | |
504 | * syncState container for synchronization data. | |
505 | * | |
506 | * Returns: | |
507 | * Factors[traceNb] synchronization factors for each trace | |
508 | */ | |
509 | static GArray* finalizeAnalysisCHull(SyncState* const syncState) | |
510 | { | |
511 | AnalysisDataCHull* analysisData; | |
512 | GArray* factors; | |
513 | FactorsCHull** allFactors; | |
514 | ||
515 | analysisData= (AnalysisDataCHull*) syncState->analysisData; | |
516 | ||
8d7d16dd | 517 | if (syncState->graphsStream && analysisData->graphsData->hullPoints != NULL) |
08365995 BP |
518 | { |
519 | writeGraphFiles(syncState); | |
520 | closeGraphFiles(syncState); | |
521 | } | |
522 | ||
523 | allFactors= calculateAllFactors(syncState); | |
524 | ||
525 | factors= reduceFactors(syncState, allFactors); | |
526 | ||
8d7d16dd | 527 | if (syncState->stats || syncState->graphsStream) |
08365995 BP |
528 | { |
529 | if (syncState->stats) | |
530 | { | |
531 | analysisData->stats->allFactors= allFactors; | |
532 | } | |
533 | ||
8d7d16dd | 534 | if (syncState->graphsStream) |
08365995 BP |
535 | { |
536 | analysisData->graphsData->allFactors= allFactors; | |
537 | } | |
538 | } | |
539 | else | |
540 | { | |
66eaf2eb | 541 | freeAllFactors(syncState->traceNb, allFactors); |
08365995 BP |
542 | } |
543 | ||
544 | return factors; | |
545 | } | |
546 | ||
547 | ||
548 | /* | |
549 | * Print statistics related to analysis. Must be called after | |
550 | * finalizeAnalysis. | |
551 | * | |
552 | * Args: | |
553 | * syncState container for synchronization data. | |
554 | */ | |
555 | static void printAnalysisStatsCHull(SyncState* const syncState) | |
556 | { | |
557 | AnalysisDataCHull* analysisData; | |
558 | unsigned int i, j; | |
559 | ||
560 | if (!syncState->stats) | |
561 | { | |
562 | return; | |
563 | } | |
564 | ||
565 | analysisData= (AnalysisDataCHull*) syncState->analysisData; | |
566 | ||
567 | printf("Convex hull analysis stats:\n"); | |
568 | printf("\tout of order packets dropped from analysis: %u\n", | |
569 | analysisData->stats->dropped); | |
570 | ||
571 | printf("\tNumber of points in convex hulls:\n"); | |
572 | ||
573 | for (i= 0; i < syncState->traceNb; i++) | |
574 | { | |
575 | for (j= i + 1; j < syncState->traceNb; j++) | |
576 | { | |
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); | |
580 | } | |
581 | } | |
582 | ||
583 | printf("\tIndividual synchronization factors:\n"); | |
584 | ||
585 | for (i= 0; i < syncState->traceNb; i++) | |
586 | { | |
587 | for (j= i + 1; j < syncState->traceNb; j++) | |
588 | { | |
589 | FactorsCHull* factorsCHull; | |
590 | ||
591 | factorsCHull= &analysisData->stats->allFactors[j][i]; | |
ce3dcf0e BP |
592 | printf("\t\t%3d - %-3d: %s", i, j, |
593 | approxNames[factorsCHull->type]); | |
08365995 BP |
594 | |
595 | if (factorsCHull->type == EXACT) | |
596 | { | |
ce3dcf0e | 597 | printf(" a0= % 7g a1= 1 %c %7g\n", |
08365995 BP |
598 | factorsCHull->approx->offset, |
599 | factorsCHull->approx->drift < 0. ? '-' : '+', | |
600 | fabs(factorsCHull->approx->drift)); | |
601 | } | |
602 | else if (factorsCHull->type == MIDDLE) | |
603 | { | |
ce3dcf0e | 604 | printf(" a0= % 7g a1= 1 %c %7g accuracy %7g\n", |
08365995 BP |
605 | factorsCHull->approx->offset, factorsCHull->approx->drift |
606 | - 1. < 0. ? '-' : '+', fabs(factorsCHull->approx->drift - | |
607 | 1.), factorsCHull->accuracy); | |
608 | printf("\t\t a0: % 7g to % 7g (delta= %7g)\n", | |
609 | factorsCHull->max->offset, factorsCHull->min->offset, | |
610 | factorsCHull->min->offset - factorsCHull->max->offset); | |
611 | printf("\t\t a1: 1 %+7g to %+7g (delta= %7g)\n", | |
612 | factorsCHull->min->drift - 1., factorsCHull->max->drift - | |
613 | 1., factorsCHull->max->drift - factorsCHull->min->drift); | |
614 | } | |
615 | else if (factorsCHull->type == FALLBACK) | |
616 | { | |
ce3dcf0e | 617 | printf(" a0= % 7g a1= 1 %c %7g error= %7g\n", |
08365995 BP |
618 | factorsCHull->approx->offset, factorsCHull->approx->drift |
619 | - 1. < 0. ? '-' : '+', fabs(factorsCHull->approx->drift - | |
620 | 1.), factorsCHull->accuracy); | |
621 | } | |
622 | else if (factorsCHull->type == INCOMPLETE) | |
623 | { | |
ce3dcf0e | 624 | printf("\n"); |
08365995 BP |
625 | |
626 | if (factorsCHull->min->drift != -INFINITY) | |
627 | { | |
628 | printf("\t\t min: a0: % 7g a1: 1 %c %7g\n", | |
629 | factorsCHull->min->offset, factorsCHull->min->drift - | |
630 | 1. < 0 ? '-' : '+', fabs(factorsCHull->min->drift - | |
631 | 1.)); | |
632 | } | |
633 | if (factorsCHull->max->drift != INFINITY) | |
634 | { | |
635 | printf("\t\t max: a0: % 7g a1: 1 %c %7g\n", | |
636 | factorsCHull->max->offset, factorsCHull->max->drift - | |
637 | 1. < 0 ? '-' : '+', fabs(factorsCHull->max->drift - | |
638 | 1.)); | |
639 | } | |
640 | } | |
641 | else if (factorsCHull->type == SCREWED) | |
642 | { | |
ce3dcf0e | 643 | printf("\n"); |
08365995 BP |
644 | |
645 | if (factorsCHull->min != NULL && factorsCHull->min->drift != -INFINITY) | |
646 | { | |
647 | printf("\t\t min: a0: % 7g a1: 1 %c %7g\n", | |
648 | factorsCHull->min->offset, factorsCHull->min->drift - | |
649 | 1. < 0 ? '-' : '+', fabs(factorsCHull->min->drift - | |
650 | 1.)); | |
651 | } | |
652 | if (factorsCHull->max != NULL && factorsCHull->max->drift != INFINITY) | |
653 | { | |
654 | printf("\t\t max: a0: % 7g a1: 1 %c %7g\n", | |
655 | factorsCHull->max->offset, factorsCHull->max->drift - | |
656 | 1. < 0 ? '-' : '+', fabs(factorsCHull->max->drift - | |
657 | 1.)); | |
658 | } | |
659 | } | |
660 | else if (factorsCHull->type == ABSENT) | |
661 | { | |
ce3dcf0e | 662 | printf("\n"); |
08365995 BP |
663 | } |
664 | else | |
665 | { | |
666 | g_assert_not_reached(); | |
667 | } | |
668 | } | |
669 | } | |
670 | } | |
671 | ||
672 | ||
673 | /* | |
674 | * A GFunc for g_queue_foreach() | |
675 | * | |
676 | * Args: | |
677 | * data Point*, point to destroy | |
678 | * user_data NULL | |
679 | */ | |
680 | static void gfPointDestroy(gpointer data, gpointer userData) | |
681 | { | |
682 | Point* point; | |
683 | ||
684 | point= (Point*) data; | |
685 | free(point); | |
686 | } | |
687 | ||
688 | ||
689 | /* | |
690 | * Find out if a sequence of three points constitutes a "left turn" or a | |
691 | * "right turn". | |
692 | * | |
693 | * Args: | |
694 | * p1, p2, p3: The three points. | |
695 | * | |
696 | * Returns: | |
697 | * < 0 right turn | |
698 | * 0 colinear (unlikely result since this uses floating point | |
699 | * arithmetic) | |
700 | * > 0 left turn | |
701 | */ | |
702 | static int jointCmp(const Point const* p1, const Point const* p2, const | |
703 | Point const* p3) | |
704 | { | |
705 | double result; | |
706 | const double fuzzFactor= 0.; | |
707 | ||
708 | result= crossProductK(p1, p2, p1, p3); | |
709 | g_debug("crossProductK(p1= (%llu, %llu), p2= (%llu, %llu), p1= (%llu, %llu), p3= (%llu, %llu))= %g", | |
710 | p1->x, p1->y, p2->x, p2->y, p1->x, p1->y, p3->x, p3->y, result); | |
711 | if (result < fuzzFactor) | |
712 | { | |
713 | return -1; | |
714 | } | |
715 | else if (result > fuzzFactor) | |
716 | { | |
717 | return 1; | |
718 | } | |
719 | else | |
720 | { | |
721 | return 0; | |
722 | } | |
723 | } | |
724 | ||
725 | ||
726 | /* | |
727 | * Calculate the k component of the cross product of two vectors. | |
728 | * | |
729 | * Args: | |
730 | * p1, p2: start and end points of the first vector | |
731 | * p3, p4: start and end points of the second vector | |
732 | * | |
733 | * Returns: | |
734 | * the k component of the cross product when considering the two vectors to | |
735 | * be in the i-j plane. The direction (sign) of the result can be useful to | |
736 | * determine the relative orientation of the two vectors. | |
737 | */ | |
738 | static double crossProductK(const Point const* p1, const Point const* p2, | |
739 | const Point const* p3, const Point const* p4) | |
740 | { | |
741 | return ((double) p2->x - p1->x) * ((double) p4->y - p3->y) - ((double) | |
742 | p2->y - p1->y) * ((double) p4->x - p3->x); | |
743 | } | |
744 | ||
745 | ||
746 | /* | |
747 | * Free a container of FactorsCHull | |
748 | * | |
749 | * Args: | |
66eaf2eb BP |
750 | * traceNb: number of traces |
751 | * allFactors: container of FactorsCHull | |
08365995 | 752 | */ |
66eaf2eb BP |
753 | void freeAllFactors(const unsigned int traceNb, FactorsCHull** const |
754 | allFactors) | |
08365995 BP |
755 | { |
756 | unsigned int i, j; | |
757 | ||
66eaf2eb | 758 | for (i= 0; i < traceNb; i++) |
08365995 BP |
759 | { |
760 | for (j= 0; j <= i; j++) | |
761 | { | |
66eaf2eb | 762 | destroyFactorsCHull(&allFactors[i][j]); |
08365995 BP |
763 | } |
764 | free(allFactors[i]); | |
765 | } | |
766 | free(allFactors); | |
767 | } | |
768 | ||
769 | ||
66eaf2eb BP |
770 | /* |
771 | * Free a FactorsCHull | |
772 | * | |
773 | * Args: | |
774 | * factorsCHull: container of Factors | |
775 | */ | |
776 | void destroyFactorsCHull(FactorsCHull* factorsCHull) | |
777 | { | |
778 | if (factorsCHull->type == MIDDLE || factorsCHull->type == | |
779 | INCOMPLETE || factorsCHull->type == ABSENT) | |
780 | { | |
781 | free(factorsCHull->min); | |
782 | free(factorsCHull->max); | |
783 | } | |
784 | else if (factorsCHull->type == SCREWED) | |
785 | { | |
786 | if (factorsCHull->min != NULL) | |
787 | { | |
788 | free(factorsCHull->min); | |
789 | } | |
790 | if (factorsCHull->max != NULL) | |
791 | { | |
792 | free(factorsCHull->max); | |
793 | } | |
794 | } | |
795 | ||
796 | if (factorsCHull->type == EXACT || factorsCHull->type == MIDDLE || | |
797 | factorsCHull->type == FALLBACK) | |
798 | { | |
799 | free(factorsCHull->approx); | |
800 | } | |
801 | } | |
802 | ||
803 | ||
08365995 BP |
804 | /* |
805 | * Analyze the convex hulls to determine the synchronization factors between | |
806 | * each pair of trace. | |
807 | * | |
808 | * Args: | |
809 | * syncState container for synchronization data. | |
810 | * | |
811 | * Returns: | |
812 | * FactorsCHull*[TraceNum][TraceNum] array. See the documentation for the | |
813 | * member allFactors of AnalysisStatsCHull. | |
814 | */ | |
66eaf2eb | 815 | FactorsCHull** calculateAllFactors(SyncState* const syncState) |
08365995 BP |
816 | { |
817 | unsigned int traceNumA, traceNumB; | |
818 | FactorsCHull** allFactors; | |
819 | AnalysisDataCHull* analysisData; | |
820 | ||
821 | analysisData= (AnalysisDataCHull*) syncState->analysisData; | |
822 | ||
823 | // Allocate allFactors and calculate min and max | |
824 | allFactors= malloc(syncState->traceNb * sizeof(FactorsCHull*)); | |
825 | for (traceNumA= 0; traceNumA < syncState->traceNb; traceNumA++) | |
826 | { | |
827 | allFactors[traceNumA]= malloc((traceNumA + 1) * sizeof(FactorsCHull)); | |
828 | ||
829 | allFactors[traceNumA][traceNumA].type= EXACT; | |
830 | allFactors[traceNumA][traceNumA].approx= malloc(sizeof(Factors)); | |
831 | allFactors[traceNumA][traceNumA].approx->drift= 1.; | |
832 | allFactors[traceNumA][traceNumA].approx->offset= 0.; | |
833 | ||
834 | for (traceNumB= 0; traceNumB < traceNumA; traceNumB++) | |
835 | { | |
836 | unsigned int i; | |
837 | GQueue* cs, * cr; | |
838 | const struct | |
839 | { | |
840 | LineType lineType; | |
841 | size_t factorsOffset; | |
842 | } loopValues[]= { | |
843 | {MINIMUM, offsetof(FactorsCHull, min)}, | |
844 | {MAXIMUM, offsetof(FactorsCHull, max)} | |
845 | }; | |
846 | ||
847 | cr= analysisData->hullArray[traceNumB][traceNumA]; | |
848 | cs= analysisData->hullArray[traceNumA][traceNumB]; | |
849 | ||
850 | for (i= 0; i < sizeof(loopValues) / sizeof(*loopValues); i++) | |
851 | { | |
852 | g_debug("allFactors[%u][%u].%s = calculateFactorsExact(cr= hullArray[%u][%u], cs= hullArray[%u][%u], %s)", | |
853 | traceNumA, traceNumB, loopValues[i].factorsOffset == | |
854 | offsetof(FactorsCHull, min) ? "min" : "max", traceNumB, | |
855 | traceNumA, traceNumA, traceNumB, loopValues[i].lineType == | |
856 | MINIMUM ? "MINIMUM" : "MAXIMUM"); | |
857 | *((Factors**) ((void*) &allFactors[traceNumA][traceNumB] + | |
858 | loopValues[i].factorsOffset))= | |
859 | calculateFactorsExact(cr, cs, loopValues[i].lineType); | |
860 | } | |
861 | } | |
862 | } | |
863 | ||
864 | // Calculate approx when possible | |
865 | for (traceNumA= 0; traceNumA < syncState->traceNb; traceNumA++) | |
866 | { | |
867 | for (traceNumB= 0; traceNumB < traceNumA; traceNumB++) | |
868 | { | |
869 | FactorsCHull* factorsCHull; | |
870 | ||
871 | factorsCHull= &allFactors[traceNumA][traceNumB]; | |
872 | if (factorsCHull->min == NULL && factorsCHull->max == NULL) | |
873 | { | |
874 | factorsCHull->type= FALLBACK; | |
875 | calculateFactorsFallback(analysisData->hullArray[traceNumB][traceNumA], | |
876 | analysisData->hullArray[traceNumA][traceNumB], | |
877 | &allFactors[traceNumA][traceNumB]); | |
878 | } | |
879 | else if (factorsCHull->min != NULL && factorsCHull->max != NULL) | |
880 | { | |
881 | if (factorsCHull->min->drift != -INFINITY && | |
882 | factorsCHull->max->drift != INFINITY) | |
883 | { | |
884 | factorsCHull->type= MIDDLE; | |
885 | calculateFactorsMiddle(factorsCHull); | |
886 | } | |
887 | else if (factorsCHull->min->drift != -INFINITY || | |
888 | factorsCHull->max->drift != INFINITY) | |
889 | { | |
890 | factorsCHull->type= INCOMPLETE; | |
891 | } | |
892 | else | |
893 | { | |
894 | factorsCHull->type= ABSENT; | |
895 | } | |
896 | } | |
897 | else | |
898 | { | |
899 | //g_assert_not_reached(); | |
900 | factorsCHull->type= SCREWED; | |
901 | } | |
902 | } | |
903 | } | |
904 | ||
905 | return allFactors; | |
906 | } | |
907 | ||
908 | ||
909 | /* Calculate approximative factors based on minimum and maximum limits. The | |
910 | * best approximation to make is the interior bissector of the angle formed by | |
911 | * the minimum and maximum lines. | |
912 | * | |
913 | * The formulae used come from [Haddad, Yoram: Performance dans les systèmes | |
914 | * répartis: des outils pour les mesures, Université de Paris-Sud, Centre | |
915 | * d'Orsay, September 1988] Section 6.1 p.44 | |
916 | * | |
917 | * The reasoning for choosing this estimator comes from [Duda, A., Harrus, G., | |
918 | * Haddad, Y., and Bernard, G.: Estimating global time in distributed systems, | |
919 | * Proc. 7th Int. Conf. on Distributed Computing Systems, Berlin, volume 18, | |
920 | * 1987] p.303 | |
921 | * | |
922 | * Args: | |
923 | * factors: contains the min and max limits, used to store the result | |
924 | */ | |
66eaf2eb | 925 | void calculateFactorsMiddle(FactorsCHull* const factors) |
08365995 BP |
926 | { |
927 | double amin, amax, bmin, bmax, bhat; | |
928 | ||
929 | amin= factors->max->offset; | |
930 | amax= factors->min->offset; | |
931 | bmin= factors->min->drift; | |
932 | bmax= factors->max->drift; | |
933 | ||
934 | g_assert_cmpfloat(bmax, >, bmin); | |
935 | ||
936 | factors->approx= malloc(sizeof(Factors)); | |
937 | bhat= (bmax * bmin - 1. + sqrt(1. + pow(bmax, 2.) * pow(bmin, 2.) + | |
938 | pow(bmax, 2.) + pow(bmin, 2.))) / (bmax + bmin); | |
939 | factors->approx->offset= amax - (amax - amin) / 2. * (pow(bhat, 2.) + 1.) | |
940 | / (1. + bhat * bmax); | |
941 | factors->approx->drift= bhat; | |
942 | factors->accuracy= bmax - bmin; | |
943 | } | |
944 | ||
945 | ||
946 | /* | |
947 | * Analyze the convex hulls to determine the minimum or maximum | |
948 | * synchronization factors between one pair of trace. | |
949 | * | |
950 | * This implements and improves upon the algorithm in [Haddad, Yoram: | |
951 | * Performance dans les systèmes répartis: des outils pour les mesures, | |
952 | * Université de Paris-Sud, Centre d'Orsay, September 1988] Section 6.2 p.47 | |
953 | * | |
954 | * Some degenerate cases are possible: | |
955 | * 1) the result is unbounded. In that case, when searching for the maximum | |
956 | * factors, result->drift= INFINITY; result->offset= -INFINITY. When | |
957 | * searching for the minimum factors, it is the opposite. It is not | |
958 | * possible to improve the situation with this data. | |
959 | * 2) no line can be above the upper hull and below the lower hull. This is | |
960 | * because the hulls intersect each other or are reversed. This means that | |
961 | * an assertion was false. Most probably, the clocks are not linear. It is | |
962 | * possible to repeat the search with another algorithm that will find a | |
963 | * "best effort" approximation. See calculateFactorsApprox(). | |
964 | * | |
965 | * Args: | |
966 | * cu: the upper half-convex hull, the line must pass above this | |
967 | * and touch it in one point | |
968 | * cl: the lower half-convex hull, the line must pass below this | |
969 | * and touch it in one point | |
970 | * lineType: search for minimum or maximum factors | |
971 | * | |
972 | * Returns: | |
973 | * If a result is found, a struct Factors is allocated, filed with the | |
974 | * result and returned | |
975 | * NULL otherwise, degenerate case 2 is in effect | |
976 | */ | |
977 | static Factors* calculateFactorsExact(GQueue* const cu, GQueue* const cl, const | |
978 | LineType lineType) | |
979 | { | |
980 | GQueue* c1, * c2; | |
981 | unsigned int i1, i2; | |
982 | Point* p1, * p2; | |
983 | double inversionFactor; | |
984 | Factors* result; | |
985 | ||
986 | g_debug("calculateFactorsExact(cu= %p, cl= %p, %s)", cu, cl, lineType == | |
987 | MINIMUM ? "MINIMUM" : "MAXIMUM"); | |
988 | ||
989 | if (lineType == MINIMUM) | |
990 | { | |
991 | c1= cl; | |
992 | c2= cu; | |
993 | inversionFactor= -1.; | |
994 | } | |
995 | else | |
996 | { | |
997 | c1= cu; | |
998 | c2= cl; | |
999 | inversionFactor= 1.; | |
1000 | } | |
1001 | ||
1002 | i1= 0; | |
1003 | i2= c2->length - 1; | |
1004 | ||
1005 | // Check for degenerate case 1 | |
1006 | if (c1->length == 0 || c2->length == 0 || ((Point*) g_queue_peek_nth(c1, | |
1007 | i1))->x >= ((Point*) g_queue_peek_nth(c2, i2))->x) | |
1008 | { | |
1009 | result= malloc(sizeof(Factors)); | |
1010 | if (lineType == MINIMUM) | |
1011 | { | |
1012 | result->drift= -INFINITY; | |
1013 | result->offset= INFINITY; | |
1014 | } | |
1015 | else | |
1016 | { | |
1017 | result->drift= INFINITY; | |
1018 | result->offset= -INFINITY; | |
1019 | } | |
1020 | ||
1021 | return result; | |
1022 | } | |
1023 | ||
1024 | do | |
1025 | { | |
1026 | while | |
1027 | ( | |
1028 | (int) i2 - 1 > 0 | |
1029 | && crossProductK( | |
1030 | g_queue_peek_nth(c1, i1), | |
1031 | g_queue_peek_nth(c2, i2), | |
1032 | g_queue_peek_nth(c1, i1), | |
1033 | g_queue_peek_nth(c2, i2 - 1)) * inversionFactor < 0. | |
1034 | ) | |
1035 | { | |
1036 | if (((Point*) g_queue_peek_nth(c1, i1))->x | |
1037 | < ((Point*) g_queue_peek_nth(c2, i2 - 1))->x) | |
1038 | { | |
1039 | i2--; | |
1040 | } | |
1041 | else | |
1042 | { | |
1043 | // Degenerate case 2 | |
1044 | return NULL; | |
1045 | } | |
1046 | } | |
1047 | while | |
1048 | ( | |
1049 | i1 + 1 < c1->length - 1 | |
1050 | && crossProductK( | |
1051 | g_queue_peek_nth(c1, i1), | |
1052 | g_queue_peek_nth(c2, i2), | |
1053 | g_queue_peek_nth(c1, i1 + 1), | |
1054 | g_queue_peek_nth(c2, i2)) * inversionFactor < 0. | |
1055 | ) | |
1056 | { | |
1057 | if (((Point*) g_queue_peek_nth(c1, i1 + 1))->x | |
1058 | < ((Point*) g_queue_peek_nth(c2, i2))->x) | |
1059 | { | |
1060 | i1++; | |
1061 | } | |
1062 | else | |
1063 | { | |
1064 | // Degenerate case 2 | |
1065 | return NULL; | |
1066 | } | |
1067 | } | |
1068 | } while | |
1069 | ( | |
1070 | (int) i2 - 1 > 0 | |
1071 | && crossProductK( | |
1072 | g_queue_peek_nth(c1, i1), | |
1073 | g_queue_peek_nth(c2, i2), | |
1074 | g_queue_peek_nth(c1, i1), | |
1075 | g_queue_peek_nth(c2, i2 - 1)) * inversionFactor < 0. | |
1076 | ); | |
1077 | ||
1078 | p1= g_queue_peek_nth(c1, i1); | |
1079 | p2= g_queue_peek_nth(c2, i2); | |
1080 | ||
1081 | g_debug("Resulting points are: c1[i1]: x= %llu y= %llu c2[i2]: x= %llu y= %llu", | |
1082 | p1->x, p1->y, p2->x, p2->y); | |
1083 | ||
1084 | result= malloc(sizeof(Factors)); | |
1085 | result->drift= slope(p1, p2); | |
1086 | result->offset= intercept(p1, p2); | |
1087 | ||
1088 | g_debug("Resulting factors are: drift= %g offset= %g", result->drift, result->offset); | |
1089 | ||
1090 | return result; | |
1091 | } | |
1092 | ||
1093 | ||
1094 | /* | |
1095 | * Analyze the convex hulls to determine approximate synchronization factors | |
1096 | * between one pair of trace when there is no line that can fit in the | |
1097 | * corridor separating them. | |
1098 | * | |
1099 | * This implements the algorithm in [Ashton, P.: Algorithms for Off-line Clock | |
1100 | * Synchronisation, University of Canterbury, December 1995, 26] Section 4.2.2 | |
1101 | * p.7 | |
1102 | * | |
1103 | * For each point p1 in cr | |
1104 | * For each point p2 in cs | |
1105 | * errorMin= 0 | |
1106 | * Calculate the line paramaters | |
1107 | * For each point p3 in each convex hull | |
1108 | * If p3 is on the wrong side of the line | |
1109 | * error+= distance | |
1110 | * If error < errorMin | |
1111 | * Update results | |
1112 | * | |
1113 | * Args: | |
1114 | * cr: the upper half-convex hull | |
1115 | * cs: the lower half-convex hull | |
1116 | * result: a pointer to the pre-allocated struct where the results | |
1117 | * will be stored | |
1118 | */ | |
1119 | static void calculateFactorsFallback(GQueue* const cr, GQueue* const cs, | |
1120 | FactorsCHull* const result) | |
1121 | { | |
1122 | unsigned int i, j, k; | |
1123 | double errorMin; | |
1124 | Factors* approx; | |
1125 | ||
1126 | errorMin= INFINITY; | |
1127 | approx= malloc(sizeof(Factors)); | |
1128 | ||
1129 | for (i= 0; i < cs->length; i++) | |
1130 | { | |
1131 | for (j= 0; j < cr->length; j++) | |
1132 | { | |
1133 | double error; | |
1134 | Point p1, p2; | |
1135 | ||
1136 | error= 0.; | |
1137 | ||
1138 | if (((Point*) g_queue_peek_nth(cs, i))->x < ((Point*)g_queue_peek_nth(cr, j))->x) | |
1139 | { | |
1140 | p1= *(Point*)g_queue_peek_nth(cs, i); | |
1141 | p2= *(Point*)g_queue_peek_nth(cr, j); | |
1142 | } | |
1143 | else | |
1144 | { | |
1145 | p1= *(Point*)g_queue_peek_nth(cr, j); | |
1146 | p2= *(Point*)g_queue_peek_nth(cs, i); | |
1147 | } | |
1148 | ||
1149 | // The lower hull should be above the point | |
1150 | for (k= 0; k < cs->length; k++) | |
1151 | { | |
1152 | if (jointCmp(&p1, &p2, g_queue_peek_nth(cs, k)) < 0.) | |
1153 | { | |
1154 | error+= verticalDistance(&p1, &p2, g_queue_peek_nth(cs, k)); | |
1155 | } | |
1156 | } | |
1157 | ||
1158 | // The upper hull should be below the point | |
1159 | for (k= 0; k < cr->length; k++) | |
1160 | { | |
1161 | if (jointCmp(&p1, &p2, g_queue_peek_nth(cr, k)) > 0.) | |
1162 | { | |
1163 | error+= verticalDistance(&p1, &p2, g_queue_peek_nth(cr, k)); | |
1164 | } | |
1165 | } | |
1166 | ||
1167 | if (error < errorMin) | |
1168 | { | |
1169 | g_debug("Fallback: i= %u j= %u is a better match (error= %g)", i, j, error); | |
1170 | approx->drift= slope(&p1, &p2); | |
1171 | approx->offset= intercept(&p1, &p2); | |
1172 | errorMin= error; | |
1173 | } | |
1174 | } | |
1175 | } | |
1176 | ||
1177 | result->approx= approx; | |
1178 | result->accuracy= errorMin; | |
1179 | } | |
1180 | ||
1181 | ||
1182 | /* | |
1183 | * Calculate the vertical distance between a line and a point | |
1184 | * | |
1185 | * Args: | |
1186 | * p1, p2: Two points defining the line | |
1187 | * point: a point | |
1188 | * | |
1189 | * Return: | |
1190 | * the vertical distance | |
1191 | */ | |
1192 | static double verticalDistance(Point* p1, Point* p2, Point* const point) | |
1193 | { | |
1194 | return fabs(slope(p1, p2) * point->x + intercept(p1, p2) - point->y); | |
1195 | } | |
1196 | ||
1197 | ||
1198 | /* | |
1199 | * Calculate the slope between two points | |
1200 | * | |
1201 | * Args: | |
1202 | * p1, p2 the two points | |
1203 | * | |
1204 | * Returns: | |
1205 | * the slope | |
1206 | */ | |
1207 | static double slope(const Point* const p1, const Point* const p2) | |
1208 | { | |
1209 | return ((double) p2->y - p1->y) / (p2->x - p1->x); | |
1210 | } | |
1211 | ||
1212 | ||
1213 | /* Calculate the y-intercept of a line that passes by two points | |
1214 | * | |
1215 | * Args: | |
1216 | * p1, p2 the two points | |
1217 | * | |
1218 | * Returns: | |
1219 | * the y-intercept | |
1220 | */ | |
1221 | static double intercept(const Point* const p1, const Point* const p2) | |
1222 | { | |
1223 | return ((double) p2->y * p1->x - (double) p1->y * p2->x) / ((double) p1->x - p2->x); | |
1224 | } | |
1225 | ||
1226 | ||
1227 | /* | |
1228 | * Calculate a resulting offset and drift for each trace. | |
1229 | * | |
1230 | * Traces are assembled in groups. A group is an "island" of nodes/traces that | |
1231 | * exchanged messages. A reference is determined for each group by using a | |
1232 | * shortest path search based on the accuracy of the approximation. This also | |
1233 | * forms a tree of the best way to relate each node's clock to the reference's | |
1234 | * based on the accuracy. Sometimes it may be necessary or advantageous to | |
1235 | * propagate the factors through intermediary clocks. Resulting factors for | |
1236 | * each trace are determined based on this tree. | |
1237 | * | |
1238 | * This part was not the focus of my research. The algorithm used here is | |
1239 | * inexact in some ways: | |
1240 | * 1) The reference used may not actually be the best one to use. This is | |
1241 | * because the accuracy is not corrected based on the drift during the | |
1242 | * shortest path search. | |
1243 | * 2) The min and max factors are not propagated and are no longer valid. | |
1244 | * 3) Approximations of different types (MIDDLE and FALLBACK) are compared | |
1245 | * together. The "accuracy" parameters of these have different meanings and | |
1246 | * are not readily comparable. | |
1247 | * | |
1248 | * Nevertheless, the result is satisfactory. You just can't tell "how much" it | |
1249 | * is. | |
1250 | * | |
1251 | * Two alternative (and subtly different) ways of propagating factors to | |
1252 | * preserve min and max bondaries have been proposed, see: | |
1253 | * [Duda, A., Harrus, G., Haddad, Y., and Bernard, G.: Estimating global time | |
1254 | * in distributed systems, Proc. 7th Int. Conf. on Distributed Computing | |
1255 | * Systems, Berlin, volume 18, 1987] p.304 | |
1256 | * | |
1257 | * [Jezequel, J.M., and Jard, C.: Building a global clock for observing | |
1258 | * computations in distributed memory parallel computers, Concurrency: | |
1259 | * Practice and Experience 8(1), volume 8, John Wiley & Sons, Ltd Chichester, | |
1260 | * 1996, 32] Section 5; which is mostly the same as | |
1261 | * [Jezequel, J.M.: Building a global time on parallel machines, Proceedings | |
1262 | * of the 3rd International Workshop on Distributed Algorithms, LNCS, volume | |
1263 | * 392, 136–147, 1989] Section 5 | |
1264 | * | |
1265 | * Args: | |
1266 | * syncState: container for synchronization data. | |
1267 | * allFactors: offset and drift between each pair of traces | |
1268 | * | |
1269 | * Returns: | |
1270 | * Factors[traceNb] synchronization factors for each trace | |
1271 | */ | |
1272 | static GArray* reduceFactors(SyncState* const syncState, FactorsCHull** const | |
1273 | allFactors) | |
1274 | { | |
1275 | GArray* factors; | |
1276 | double** distances; | |
1277 | unsigned int** predecessors; | |
1278 | double* distanceSums; | |
1279 | unsigned int* references; | |
1280 | unsigned int i, j; | |
1281 | ||
1282 | // Solve the all-pairs shortest path problem using the Floyd-Warshall | |
1283 | // algorithm | |
1284 | floydWarshall(syncState, allFactors, &distances, &predecessors); | |
1285 | ||
1286 | /* Find the reference for each node | |
1287 | * | |
1288 | * First calculate, for each node, the sum of the distances to each other | |
1289 | * node it can reach. | |
1290 | * | |
1291 | * Then, go through each "island" of traces to find the trace that has the | |
1292 | * lowest distance sum. Assign this trace as the reference to each trace | |
1293 | * of the island. | |
1294 | */ | |
1295 | distanceSums= malloc(syncState->traceNb * sizeof(double)); | |
1296 | for (i= 0; i < syncState->traceNb; i++) | |
1297 | { | |
1298 | distanceSums[i]= 0.; | |
1299 | for (j= 0; j < syncState->traceNb; j++) | |
1300 | { | |
1301 | distanceSums[i]+= distances[i][j]; | |
1302 | } | |
1303 | } | |
1304 | ||
1305 | references= malloc(syncState->traceNb * sizeof(unsigned int)); | |
1306 | for (i= 0; i < syncState->traceNb; i++) | |
1307 | { | |
1308 | references[i]= UINT_MAX; | |
1309 | } | |
1310 | for (i= 0; i < syncState->traceNb; i++) | |
1311 | { | |
1312 | if (references[i] == UINT_MAX) | |
1313 | { | |
1314 | unsigned int reference; | |
1315 | double distanceSumMin; | |
1316 | ||
1317 | // A node is its own reference by default | |
1318 | reference= i; | |
1319 | distanceSumMin= INFINITY; | |
1320 | for (j= 0; j < syncState->traceNb; j++) | |
1321 | { | |
1322 | if (distances[i][j] != INFINITY && distanceSums[j] < | |
1323 | distanceSumMin) | |
1324 | { | |
1325 | reference= j; | |
1326 | distanceSumMin= distanceSums[j]; | |
1327 | } | |
1328 | } | |
1329 | for (j= 0; j < syncState->traceNb; j++) | |
1330 | { | |
1331 | if (distances[i][j] != INFINITY) | |
1332 | { | |
1333 | references[j]= reference; | |
1334 | } | |
1335 | } | |
1336 | } | |
1337 | } | |
1338 | ||
1339 | for (i= 0; i < syncState->traceNb; i++) | |
1340 | { | |
1341 | free(distances[i]); | |
1342 | } | |
1343 | free(distances); | |
1344 | free(distanceSums); | |
1345 | ||
1346 | /* For each trace, calculate the factors based on their corresponding | |
1347 | * tree. The tree is rooted at the reference and the shortest path to each | |
1348 | * other nodes are the branches. | |
1349 | */ | |
1350 | factors= g_array_sized_new(FALSE, FALSE, sizeof(Factors), | |
1351 | syncState->traceNb); | |
1352 | g_array_set_size(factors, syncState->traceNb); | |
1353 | for (i= 0; i < syncState->traceNb; i++) | |
1354 | { | |
1355 | getFactors(allFactors, predecessors, references, i, &g_array_index(factors, | |
1356 | Factors, i)); | |
1357 | } | |
1358 | ||
1359 | for (i= 0; i < syncState->traceNb; i++) | |
1360 | { | |
1361 | free(predecessors[i]); | |
1362 | } | |
1363 | free(predecessors); | |
1364 | free(references); | |
1365 | ||
1366 | return factors; | |
1367 | } | |
1368 | ||
1369 | ||
1370 | /* | |
1371 | * Perform an all-source shortest path search using the Floyd-Warshall | |
1372 | * algorithm. | |
1373 | * | |
1374 | * The algorithm is implemented accoding to the description here: | |
1375 | * http://web.mit.edu/urban_or_book/www/book/chapter6/6.2.2.html | |
1376 | * | |
1377 | * Args: | |
1378 | * syncState: container for synchronization data. | |
1379 | * allFactors: offset and drift between each pair of traces | |
1380 | * distances: resulting matrix of the length of the shortest path between | |
1381 | * two nodes. If there is no path between two nodes, the | |
1382 | * length is INFINITY | |
1383 | * predecessors: resulting matrix of each node's predecessor on the shortest | |
1384 | * path between two nodes | |
1385 | */ | |
1386 | static void floydWarshall(SyncState* const syncState, FactorsCHull** const | |
1387 | allFactors, double*** const distances, unsigned int*** const | |
1388 | predecessors) | |
1389 | { | |
1390 | unsigned int i, j, k; | |
1391 | ||
1392 | // Setup initial conditions | |
1393 | *distances= malloc(syncState->traceNb * sizeof(double*)); | |
1394 | *predecessors= malloc(syncState->traceNb * sizeof(unsigned int*)); | |
1395 | for (i= 0; i < syncState->traceNb; i++) | |
1396 | { | |
1397 | (*distances)[i]= malloc(syncState->traceNb * sizeof(double)); | |
1398 | for (j= 0; j < syncState->traceNb; j++) | |
1399 | { | |
1400 | if (i == j) | |
1401 | { | |
1402 | g_assert(allFactors[i][j].type == EXACT); | |
1403 | ||
1404 | (*distances)[i][j]= 0.; | |
1405 | } | |
1406 | else | |
1407 | { | |
1408 | unsigned int row, col; | |
1409 | ||
1410 | if (i > j) | |
1411 | { | |
1412 | row= i; | |
1413 | col= j; | |
1414 | } | |
1415 | else if (i < j) | |
1416 | { | |
1417 | row= j; | |
1418 | col= i; | |
1419 | } | |
1420 | ||
1421 | if (allFactors[row][col].type == MIDDLE || | |
1422 | allFactors[row][col].type == FALLBACK) | |
1423 | { | |
1424 | (*distances)[i][j]= allFactors[row][col].accuracy; | |
1425 | } | |
1426 | else if (allFactors[row][col].type == INCOMPLETE || | |
1427 | allFactors[row][col].type == SCREWED || | |
1428 | allFactors[row][col].type == ABSENT) | |
1429 | { | |
1430 | (*distances)[i][j]= INFINITY; | |
1431 | } | |
1432 | else | |
1433 | { | |
1434 | g_assert_not_reached(); | |
1435 | } | |
1436 | } | |
1437 | } | |
1438 | ||
1439 | (*predecessors)[i]= malloc(syncState->traceNb * sizeof(unsigned int)); | |
1440 | for (j= 0; j < syncState->traceNb; j++) | |
1441 | { | |
1442 | if (i != j) | |
1443 | { | |
1444 | (*predecessors)[i][j]= i; | |
1445 | } | |
1446 | else | |
1447 | { | |
1448 | (*predecessors)[i][j]= UINT_MAX; | |
1449 | } | |
1450 | } | |
1451 | } | |
1452 | ||
1453 | // Run the iterations | |
1454 | for (k= 0; k < syncState->traceNb; k++) | |
1455 | { | |
1456 | for (i= 0; i < syncState->traceNb; i++) | |
1457 | { | |
1458 | for (j= 0; j < syncState->traceNb; j++) | |
1459 | { | |
1460 | double distanceMin; | |
1461 | ||
1462 | distanceMin= MIN((*distances)[i][j], (*distances)[i][k] + | |
1463 | (*distances)[k][j]); | |
1464 | ||
1465 | if (distanceMin != (*distances)[i][j]) | |
1466 | { | |
1467 | (*predecessors)[i][j]= (*predecessors)[k][j]; | |
1468 | } | |
1469 | ||
1470 | (*distances)[i][j]= distanceMin; | |
1471 | } | |
1472 | } | |
1473 | } | |
1474 | } | |
1475 | ||
1476 | ||
1477 | /* | |
1478 | * Cummulate the time correction factors to convert a node's time to its | |
1479 | * reference's time. | |
1480 | * This function recursively calls itself until it reaches the reference node. | |
1481 | * | |
1482 | * Args: | |
1483 | * allFactors: offset and drift between each pair of traces | |
1484 | * predecessors: matrix of each node's predecessor on the shortest | |
1485 | * path between two nodes | |
1486 | * references: reference node for each node | |
1487 | * traceNum: node for which to find the factors | |
1488 | * factors: resulting factors | |
1489 | */ | |
1490 | static void getFactors(FactorsCHull** const allFactors, unsigned int** const | |
1491 | predecessors, unsigned int* const references, const unsigned int traceNum, | |
1492 | Factors* const factors) | |
1493 | { | |
1494 | unsigned int reference; | |
1495 | ||
1496 | reference= references[traceNum]; | |
1497 | ||
1498 | if (reference == traceNum) | |
1499 | { | |
1500 | factors->offset= 0.; | |
1501 | factors->drift= 1.; | |
1502 | } | |
1503 | else | |
1504 | { | |
1505 | Factors previousVertexFactors; | |
1506 | ||
1507 | getFactors(allFactors, predecessors, references, | |
1508 | predecessors[reference][traceNum], &previousVertexFactors); | |
1509 | ||
1510 | // convertir de traceNum à reference | |
1511 | ||
1512 | // allFactors convertit de col à row | |
1513 | ||
1514 | if (reference > traceNum) | |
1515 | { | |
1516 | factors->offset= previousVertexFactors.drift * | |
1517 | allFactors[reference][traceNum].approx->offset + | |
1518 | previousVertexFactors.offset; | |
1519 | factors->drift= previousVertexFactors.drift * | |
1520 | allFactors[reference][traceNum].approx->drift; | |
1521 | } | |
1522 | else | |
1523 | { | |
1524 | factors->offset= previousVertexFactors.drift * (-1. * | |
1525 | allFactors[traceNum][reference].approx->offset / | |
1526 | allFactors[traceNum][reference].approx->drift) + | |
1527 | previousVertexFactors.offset; | |
1528 | factors->drift= previousVertexFactors.drift * (1. / | |
1529 | allFactors[traceNum][reference].approx->drift); | |
1530 | } | |
1531 | } | |
1532 | } | |
1533 | ||
1534 | ||
1535 | /* | |
1536 | * Write the analysis-specific graph lines in the gnuplot script. | |
1537 | * | |
1538 | * Args: | |
08365995 BP |
1539 | * syncState: container for synchronization data |
1540 | * i: first trace number | |
1541 | * j: second trace number, garanteed to be larger than i | |
1542 | */ | |
8d7d16dd BP |
1543 | void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned |
1544 | int i, const unsigned int j) | |
08365995 BP |
1545 | { |
1546 | AnalysisDataCHull* analysisData; | |
1547 | FactorsCHull* factorsCHull; | |
1548 | ||
1549 | analysisData= (AnalysisDataCHull*) syncState->analysisData; | |
1550 | ||
8d7d16dd | 1551 | fprintf(syncState->graphsStream, |
08365995 BP |
1552 | "\t\"analysis_chull-%1$03d_to_%2$03d.data\" " |
1553 | "title \"Lower half-hull\" with linespoints " | |
1554 | "linecolor rgb \"#015a01\" linetype 4 pointtype 8 pointsize 0.8, \\\n" | |
1555 | "\t\"analysis_chull-%2$03d_to_%1$03d.data\" " | |
1556 | "title \"Upper half-hull\" with linespoints " | |
1557 | "linecolor rgb \"#003366\" linetype 4 pointtype 10 pointsize 0.8, \\\n", | |
1558 | i, j); | |
1559 | ||
1560 | factorsCHull= &analysisData->graphsData->allFactors[j][i]; | |
1561 | if (factorsCHull->type == EXACT) | |
1562 | { | |
8d7d16dd | 1563 | fprintf(syncState->graphsStream, |
08365995 BP |
1564 | "\t%7g + %7g * x " |
1565 | "title \"Exact conversion\" with lines " | |
1566 | "linecolor rgb \"black\" linetype 1, \\\n", | |
1567 | factorsCHull->approx->offset, factorsCHull->approx->drift); | |
1568 | } | |
1569 | else if (factorsCHull->type == MIDDLE) | |
1570 | { | |
8d7d16dd | 1571 | fprintf(syncState->graphsStream, |
08365995 BP |
1572 | "\t%.2f + %.10f * x " |
1573 | "title \"Min conversion\" with lines " | |
1574 | "linecolor rgb \"black\" linetype 5, \\\n", | |
1575 | factorsCHull->min->offset, factorsCHull->min->drift); | |
8d7d16dd | 1576 | fprintf(syncState->graphsStream, |
08365995 BP |
1577 | "\t%.2f + %.10f * x " |
1578 | "title \"Max conversion\" with lines " | |
1579 | "linecolor rgb \"black\" linetype 8, \\\n", | |
1580 | factorsCHull->max->offset, factorsCHull->max->drift); | |
8d7d16dd | 1581 | fprintf(syncState->graphsStream, |
08365995 BP |
1582 | "\t%.2f + %.10f * x " |
1583 | "title \"Middle conversion\" with lines " | |
66eaf2eb | 1584 | "linecolor rgb \"black\" linetype 1, \\\n", |
08365995 BP |
1585 | factorsCHull->approx->offset, factorsCHull->approx->drift); |
1586 | } | |
1587 | else if (factorsCHull->type == FALLBACK) | |
1588 | { | |
8d7d16dd | 1589 | fprintf(syncState->graphsStream, |
08365995 BP |
1590 | "\t%.2f + %.10f * x " |
1591 | "title \"Fallback conversion\" with lines " | |
1592 | "linecolor rgb \"gray60\" linetype 1, \\\n", | |
1593 | factorsCHull->approx->offset, factorsCHull->approx->drift); | |
1594 | } | |
1595 | else if (factorsCHull->type == INCOMPLETE) | |
1596 | { | |
1597 | if (factorsCHull->min->drift != -INFINITY) | |
1598 | { | |
8d7d16dd | 1599 | fprintf(syncState->graphsStream, |
08365995 BP |
1600 | "\t%.2f + %.10f * x " |
1601 | "title \"Min conversion\" with lines " | |
1602 | "linecolor rgb \"black\" linetype 5, \\\n", | |
1603 | factorsCHull->min->offset, factorsCHull->min->drift); | |
1604 | } | |
1605 | ||
1606 | if (factorsCHull->max->drift != INFINITY) | |
1607 | { | |
8d7d16dd | 1608 | fprintf(syncState->graphsStream, |
08365995 BP |
1609 | "\t%.2f + %.10f * x " |
1610 | "title \"Max conversion\" with lines " | |
1611 | "linecolor rgb \"black\" linetype 8, \\\n", | |
1612 | factorsCHull->max->offset, factorsCHull->max->drift); | |
1613 | } | |
1614 | } | |
1615 | else if (factorsCHull->type == SCREWED) | |
1616 | { | |
1617 | if (factorsCHull->min != NULL && factorsCHull->min->drift != -INFINITY) | |
1618 | { | |
8d7d16dd | 1619 | fprintf(syncState->graphsStream, |
08365995 BP |
1620 | "\t%.2f + %.10f * x " |
1621 | "title \"Min conversion\" with lines " | |
1622 | "linecolor rgb \"black\" linetype 5, \\\n", | |
1623 | factorsCHull->min->offset, factorsCHull->min->drift); | |
1624 | } | |
1625 | ||
1626 | if (factorsCHull->max != NULL && factorsCHull->max->drift != INFINITY) | |
1627 | { | |
8d7d16dd | 1628 | fprintf(syncState->graphsStream, |
08365995 BP |
1629 | "\t%.2f + %.10f * x " |
1630 | "title \"Max conversion\" with lines " | |
1631 | "linecolor rgb \"black\" linetype 8, \\\n", | |
1632 | factorsCHull->max->offset, factorsCHull->max->drift); | |
1633 | } | |
1634 | } | |
1635 | else if (factorsCHull->type == ABSENT) | |
1636 | { | |
1637 | } | |
1638 | else | |
1639 | { | |
1640 | g_assert_not_reached(); | |
1641 | } | |
1642 | } |