tmf/org.eclipse.tracecompass.tmf.core/src/org/eclipse/tracecompass/internal/tmf/core/synchronization/SyncAlgorithmFullyIncremental.java

   1 /*******************************************************************************
   2  * Copyright (c) 2013, 2014 École Polytechnique de Montréal
   3  *
   4  * All rights reserved. This program and the accompanying materials are made
   5  * available under the terms of the Eclipse Public License v1.0 which
   6  * accompanies this distribution, and is available at
   7  * http://www.eclipse.org/legal/epl-v10.html
   8  *
   9  * Contributors:
  10  *   Geneviève Bastien - Initial implementation and API
  11  *   Francis Giraldeau - Transform computation using synchronization graph
  12  *******************************************************************************/
  13
  14 package org.eclipse.tracecompass.internal.tmf.core.synchronization;
  15
  16 import java.io.IOException;
  17 import java.io.ObjectInputStream;
  18 import java.io.Serializable;
  19 import java.math.BigDecimal;
  20 import java.math.MathContext;
  21 import java.util.Collection;
  22 import java.util.LinkedHashMap;
  23 import java.util.LinkedList;
  24 import java.util.List;
  25 import java.util.Map;
  26
  27 import org.eclipse.tracecompass.common.core.NonNullUtils;
  28 import org.eclipse.tracecompass.internal.tmf.core.synchronization.graph.SyncSpanningTree;
  29 import org.eclipse.tracecompass.tmf.core.event.ITmfEvent;
  30 import org.eclipse.tracecompass.tmf.core.event.matching.TmfEventDependency;
  31 import org.eclipse.tracecompass.tmf.core.synchronization.ITmfTimestampTransform;
  32 import org.eclipse.tracecompass.tmf.core.synchronization.Messages;
  33 import org.eclipse.tracecompass.tmf.core.synchronization.SynchronizationAlgorithm;
  34 import org.eclipse.tracecompass.tmf.core.synchronization.TimestampTransformFactory;
  35 import org.eclipse.tracecompass.tmf.core.timestamp.ITmfTimestamp;
  36 import org.eclipse.tracecompass.tmf.core.trace.ITmfTrace;
  37
  38 /**
  39  * Class implementing fully incremental trace synchronization approach as
  40  * described in
  41  *
  42  * Masoume Jabbarifar, Michel Dagenais and Alireza Shameli-Sendi,
  43  * "Streaming Mode Incremental Clock Synchronization"
  44  *
  45  * Since the algorithm itself applies to two traces, it is implemented in a
  46  * private class, while this public class manages the synchronization between
  47  * all traces.
  48  *
  49  * @author Geneviève Bastien
  50  */
  51 public class SyncAlgorithmFullyIncremental extends SynchronizationAlgorithm {
  52
  53     /**
  54      * Auto-generated serial UID
  55      */
  56     private static final long serialVersionUID = -1782788842774838830L;
  57
  58     private static final MathContext fMc = MathContext.DECIMAL128;
  59
  60     /** @Serial */
  61     private final List<ConvexHull> fSyncs;
  62
  63     private transient SyncSpanningTree fTree = null;
  64
  65     /**
  66      * Initialization of the attributes
  67      */
  68     public SyncAlgorithmFullyIncremental() {
  69         fSyncs = new LinkedList<>();
  70     }
  71
  72     /**
  73      * Function called after all matching has been done, to do any post-match
  74      * treatment. For this class, it calculates stats, while the data is
  75      * available
  76      */
  77     @Override
  78     public void matchingEnded() {
  79         getStats();
  80     }
  81
  82     @Override
  83     public void init(Collection<ITmfTrace> traces) {
  84         ITmfTrace[] traceArr = traces.toArray(new ITmfTrace[traces.size()]);
  85         fSyncs.clear();
  86         /* Create a convex hull for all trace pairs */
  87         // FIXME: is it necessary to make ConvexHull for every pairs up-front?
  88         // The ConvexHull seems to be created on the fly in processMatch().
  89         for (int i = 0; i < traceArr.length; i++) {
  90             for (int j = i + 1; j < traceArr.length; j++) {
  91                 if (!traceArr[i].getHostId().equals(traceArr[j].getHostId())) {
  92                     ConvexHull algo = new ConvexHull(traceArr[i].getHostId(), traceArr[j].getHostId());
  93                     fSyncs.add(algo);
  94                 }
  95             }
  96         }
  97     }
  98
  99     @Override
 100     protected void processMatch(TmfEventDependency match) {
 101         String host1 = match.getSourceEvent().getTrace().getHostId();
 102         String host2 = match.getDestinationEvent().getTrace().getHostId();
 103
 104         /* Process only if source and destination are different */
 105         if (host1.equals(host2)) {
 106             return;
 107         }
 108
 109         /* Check if a convex hull algorithm already exists for these 2 hosts */
 110         ConvexHull algo = null;
 111         for (ConvexHull traceSync : fSyncs) {
 112             if (traceSync.isForHosts(host1, host2)) {
 113                 algo = traceSync;
 114             }
 115         }
 116         if (algo == null) {
 117             algo = new ConvexHull(host1, host2);
 118             fSyncs.add(algo);
 119         }
 120         algo.processMatch(match);
 121         invalidateSyncGraph();
 122     }
 123
 124     private void invalidateSyncGraph() {
 125         fTree = null;
 126     }
 127
 128     @Override
 129     public ITmfTimestampTransform getTimestampTransform(ITmfTrace trace) {
 130         return getTimestampTransform(trace.getHostId());
 131     }
 132
 133     @Override
 134     public ITmfTimestampTransform getTimestampTransform(String hostId) {
 135         SyncSpanningTree tree = getSyncTree();
 136         return tree.getTimestampTransform(hostId);
 137     }
 138
 139     /**
 140      * Each convex hull computes the synchronization between 2 given hosts. A
 141      * synchronization can be done on multiple hosts that may not all
 142      * communicate with each other. We must use another algorithm to determine
 143      * which host will be the reference node and what synchronization formula
 144      * will be used between each host and this reference node.
 145      *
 146      * For example, take traces a, b and c where a and c talk to b but do not
 147      * know each other ({@literal a <-> b <-> c}). The convex hulls will contain
 148      * the formulae between their 2 traces, but if a is the reference node, then
 149      * the resulting formula of c would be the composition of {@literal a <-> b}
 150      * and {@literal b <-> c}
 151      *
 152      * @return The synchronization spanning tree for this synchronization
 153      */
 154     private SyncSpanningTree getSyncTree() {
 155         if (fTree == null) {
 156             fTree = new SyncSpanningTree(getRootNode());
 157             for (ConvexHull traceSync : fSyncs) {
 158                 SyncQuality q = traceSync.getQuality();
 159                 if (q == SyncQuality.ACCURATE || q == SyncQuality.APPROXIMATE) {
 160                     String from = traceSync.getReferenceHost();
 161                     String to = traceSync.getOtherHost();
 162                     fTree.addSynchronization(from, to, traceSync.getTimestampTransform(to), traceSync.getAccuracy());
 163                 }
 164             }
 165         }
 166         return fTree;
 167     }
 168
 169     @Override
 170     public SyncQuality getSynchronizationQuality(ITmfTrace trace1, ITmfTrace trace2) {
 171         for (ConvexHull traceSync : fSyncs) {
 172             if (traceSync.isForHosts(trace1.getHostId(), trace2.getHostId())) {
 173                 return traceSync.getQuality();
 174             }
 175         }
 176         return SyncQuality.ABSENT;
 177     }
 178
 179     @Override
 180     public boolean isTraceSynced(String hostId) {
 181         ITmfTimestampTransform t = getTimestampTransform(hostId);
 182         return !t.equals(TimestampTransformFactory.getDefaultTransform());
 183     }
 184
 185     @Override
 186     public Map<String, Map<String, Object>> getStats() {
 187         /*
 188          * TODO: Stats, while still accurate, may be misleading now that the
 189          * sync tree changes synchronization formula. The stats should use the
 190          * tree instead
 191          */
 192         Map<String, Map<String, Object>> statmap = new LinkedHashMap<>();
 193         for (ConvexHull traceSync : fSyncs) {
 194             statmap.put(traceSync.getReferenceHost() + " <==> " + traceSync.getOtherHost(), traceSync.getStats()); //$NON-NLS-1$
 195         }
 196         return statmap;
 197     }
 198
 199     @Override
 200     public String toString() {
 201         return getClass().getSimpleName() + ' ' + fSyncs.toString();
 202     }
 203
 204     /**
 205      * This is the actual synchronization algorithm between two traces using
 206      * convex hull
 207      */
 208     private class ConvexHull implements Serializable {
 209
 210         private static final long serialVersionUID = 8309351175030935291L;
 211
 212         private final String fReferenceHost;
 213         private final String fOtherHost;
 214
 215         /**
 216          * Slopes and ordinate at origin of respectively fLmin, fLmax and the
 217          * bisector
 218          */
 219         private BigDecimal fAlphamin, fBetamax, fAlphamax, fBetamin, fAlpha, fBeta;
 220         private int fNbMatches, fNbAccurateMatches;
 221         private SyncQuality fQuality;
 222
 223         /**
 224          * The list of meaningful points on the upper hull (received by the
 225          * reference trace, below in a graph)
 226          */
 227         private transient LinkedList<SyncPoint> fUpperBoundList = new LinkedList<>();
 228         /**
 229          * The list of meaninful points on the lower hull (sent by the reference
 230          * trace, above in a graph)
 231          */
 232         private transient LinkedList<SyncPoint> fLowerBoundList = new LinkedList<>();
 233
 234         /** Points forming the line with maximum slope */
 235         private transient SyncPoint[] fLmax = new SyncPoint[2];
 236         /** Points forming the line with minimum slope */
 237         private transient SyncPoint[] fLmin = new SyncPoint[2];
 238
 239         private transient Map<String, Object> fStats = new LinkedHashMap<>();
 240
 241         /**
 242          * Initialization of the attributes
 243          *
 244          * @param host1
 245          *            ID of the first host
 246          * @param host2
 247          *            ID of the second host
 248          */
 249         public ConvexHull(String host1, String host2) {
 250             if (host1.compareTo(host2) > 0) {
 251                 fReferenceHost = host2;
 252                 fOtherHost = host1;
 253             } else {
 254                 fReferenceHost = host1;
 255                 fOtherHost = host2;
 256             }
 257             fAlpha = BigDecimal.ONE;
 258             fAlphamax = BigDecimal.ONE;
 259             fAlphamin = BigDecimal.ONE;
 260             fBeta = BigDecimal.ZERO;
 261             fBetamax = BigDecimal.ZERO;
 262             fBetamin = BigDecimal.ZERO;
 263             fNbMatches = 0;
 264             fNbAccurateMatches = 0;
 265             fQuality = SyncQuality.ABSENT; // default quality
 266         }
 267
 268         protected void processMatch(TmfEventDependency match) {
 269
 270             LinkedList<SyncPoint> boundList, otherBoundList;
 271
 272             SyncPoint[] line, otherLine;
 273             SyncPoint p;
 274             int inversionFactor = 1;
 275             boolean qualify = false;
 276             fNbMatches++;
 277
 278             /* Initialize data depending on the which hull the match is part of */
 279             if (match.getSourceEvent().getTrace().getHostId().compareTo(match.getDestinationEvent().getTrace().getHostId()) > 0) {
 280                 boundList = fUpperBoundList;
 281                 otherBoundList = fLowerBoundList;
 282                 line = fLmin;
 283                 otherLine = fLmax;
 284                 p = new SyncPoint(match.getDestinationEvent(), match.getSourceEvent());
 285                 inversionFactor = 1;
 286             } else {
 287                 boundList = fLowerBoundList;
 288                 otherBoundList = fUpperBoundList;
 289                 line = fLmax;
 290                 otherLine = fLmin;
 291                 p = new SyncPoint(match.getSourceEvent(), match.getDestinationEvent());
 292                 inversionFactor = -1;
 293             }
 294
 295             /*
 296              * Does the message qualify for the hull, or is in on the wrong side
 297              * of the reference line
 298              */
 299             if ((line[0] == null) || (line[1] == null) || (p.crossProduct(line[0], line[1]) * inversionFactor > 0)) {
 300                 /*
 301                  * If message qualifies, verify if points need to be removed
 302                  * from the hull and add the new point as the maximum reference
 303                  * point for the line. Also clear the stats that are not good
 304                  * anymore
 305                  */
 306                 fNbAccurateMatches++;
 307                 qualify = true;
 308                 removeUselessPoints(p, boundList, inversionFactor);
 309                 line[1] = p;
 310                 fStats.clear();
 311             }
 312
 313             /*
 314              * Adjust the boundary of the reference line and if one of the
 315              * reference point of the other line was removed from the hull, also
 316              * adjust the other line
 317              */
 318             adjustBound(line, otherBoundList, inversionFactor);
 319             if ((otherLine[1] != null) && !boundList.contains(otherLine[0])) {
 320                 adjustBound(otherLine, boundList, inversionFactor * -1);
 321             }
 322
 323             if (qualify) {
 324                 approximateSync();
 325             }
 326
 327         }
 328
 329         /**
 330          * Calculates slopes and ordinate at origin of fLmax and fLmin to obtain
 331          * and approximation of the synchronization at this time
 332          */
 333         private void approximateSync() {
 334
 335             /**
 336              * Line slopes functions
 337              *
 338              * Lmax = alpha_max T + beta_min
 339              *
 340              * Lmin = alpha_min T + beta_max
 341              */
 342             if ((fLmax[0] != null) || (fLmin[0] != null)) {
 343                 /**
 344                  * Do not recalculate synchronization after it is failed. We
 345                  * keep the last not failed result.
 346                  */
 347                 if (getQuality() != SyncQuality.FAIL) {
 348                     BigDecimal alphamax = fLmax[1].getAlpha(fLmax[0]);
 349                     BigDecimal alphamin = fLmin[1].getAlpha(fLmin[0]);
 350                     SyncQuality quality = null;
 351
 352                     if ((fLmax[0] == null) || (fLmin[0] == null)) {
 353                         quality = SyncQuality.APPROXIMATE;
 354                     }
 355                     else if (alphamax.compareTo(alphamin) > 0) {
 356                         quality = SyncQuality.ACCURATE;
 357                     } else {
 358                         /* Lines intersect, not good */
 359                         quality = SyncQuality.FAIL;
 360                     }
 361                     /*
 362                      * Only calculate sync if this match does not cause failure
 363                      * of synchronization
 364                      */
 365                     if (quality != SyncQuality.FAIL) {
 366                         fAlphamax = alphamax;
 367                         fBetamin = fLmax[1].getBeta(fAlphamax);
 368                         fAlphamin = alphamin;
 369                         fBetamax = fLmin[1].getBeta(fAlphamin);
 370                         fAlpha = fAlphamax.add(fAlphamin).divide(BigDecimal.valueOf(2), fMc);
 371                         fBeta = fBetamin.add(fBetamax).divide(BigDecimal.valueOf(2), fMc);
 372                     }
 373                     setQuality(quality);
 374                 }
 375             } else if (((fLmax[0] == null) && (fLmin[1] == null))
 376                     || ((fLmax[1] == null) && (fLmin[0] == null))) {
 377                 /* Either there is no upper hull point or no lower hull */
 378                 setQuality(SyncQuality.INCOMPLETE);
 379             }
 380         }
 381
 382         /*
 383          * Verify if the line should be adjusted to be more accurate give the
 384          * hull
 385          */
 386         private void adjustBound(SyncPoint[] line, LinkedList<SyncPoint> otherBoundList, int inversionFactor) {
 387             SyncPoint minPoint = null, nextPoint;
 388             boolean finishedSearch = false;
 389
 390             /*
 391              * Find in the other bound, the origin point of the line, start from
 392              * the beginning if the point was lost
 393              */
 394             int i = Math.max(0, otherBoundList.indexOf(line[0]));
 395
 396             while ((i < otherBoundList.size() - 1) && !finishedSearch) {
 397                 minPoint = otherBoundList.get(i);
 398                 nextPoint = otherBoundList.get(i + 1);
 399
 400                 /*
 401                  * If the rotation (cross-product) is not optimal, move to next
 402                  * point as reference for the line (if available)
 403                  *
 404                  * Otherwise, the current minPoint is the minPoint of the line
 405                  */
 406                 if (minPoint.crossProduct(nextPoint, line[1]) * inversionFactor > 0) {
 407                     if (nextPoint.getTimeX() < line[1].getTimeX()) {
 408                         i++;
 409                     } else {
 410                         line[0] = null;
 411                         finishedSearch = true;
 412                     }
 413                 } else {
 414                     line[0] = minPoint;
 415                     finishedSearch = true;
 416                 }
 417             }
 418
 419             if (line[0] == null) {
 420                 line[0] = minPoint;
 421             }
 422
 423             /* Make sure point 0 is before point 1 */
 424             if ((line[0] != null) && (line[0].getTimeX() > line[1].getTimeX())) {
 425                 line[0] = null;
 426             }
 427         }
 428
 429         /*
 430          * When a point qualifies to be in a hull, we verify if any of the
 431          * existing points need to be removed from the hull
 432          */
 433         private void removeUselessPoints(final SyncPoint p, final LinkedList<SyncPoint> boundList, final int inversionFactor) {
 434
 435             boolean checkRemove = true;
 436
 437             while (checkRemove && boundList.size() >= 2) {
 438                 if (p.crossProduct(boundList.get(boundList.size() - 2), boundList.getLast()) * inversionFactor > 0) {
 439                     boundList.removeLast();
 440                 } else {
 441                     checkRemove = false;
 442                 }
 443             }
 444             boundList.addLast(p);
 445         }
 446
 447         public ITmfTimestampTransform getTimestampTransform(String hostId) {
 448             if (hostId.equals(fOtherHost) && (getQuality() == SyncQuality.ACCURATE || getQuality() == SyncQuality.APPROXIMATE || getQuality() == SyncQuality.FAIL)) {
 449                 /* alpha: beta => 1 / fAlpha, -1 * fBeta / fAlpha); */
 450                 return TimestampTransformFactory.createLinear(NonNullUtils.checkNotNull(BigDecimal.ONE.divide(fAlpha, fMc)), NonNullUtils.checkNotNull(BigDecimal.valueOf(-1).multiply(fBeta).divide(fAlpha, fMc)));
 451             }
 452             return TimestampTransformFactory.getDefaultTransform();
 453         }
 454
 455         public SyncQuality getQuality() {
 456             return fQuality;
 457         }
 458
 459         public BigDecimal getAccuracy() {
 460             return fAlphamax.subtract(fAlphamin);
 461         }
 462
 463         public Map<String, Object> getStats() {
 464             if (fStats.size() == 0) {
 465                 String syncQuality;
 466                 switch (getQuality()) {
 467                 case ABSENT:
 468                     syncQuality = Messages.SyncAlgorithmFullyIncremental_absent;
 469                     break;
 470                 case ACCURATE:
 471                     syncQuality = Messages.SyncAlgorithmFullyIncremental_accurate;
 472                     break;
 473                 case APPROXIMATE:
 474                     syncQuality = Messages.SyncAlgorithmFullyIncremental_approx;
 475                     break;
 476                 case INCOMPLETE:
 477                     syncQuality = Messages.SyncAlgorithmFullyIncremental_incomplete;
 478                     break;
 479                 case FAIL:
 480                 default:
 481                     syncQuality = Messages.SyncAlgorithmFullyIncremental_fail;
 482                     break;
 483                 }
 484
 485                 fStats.put(Messages.SyncAlgorithmFullyIncremental_refhost, fReferenceHost);
 486                 fStats.put(Messages.SyncAlgorithmFullyIncremental_otherhost, fOtherHost);
 487                 fStats.put(Messages.SyncAlgorithmFullyIncremental_quality, syncQuality);
 488                 fStats.put(Messages.SyncAlgorithmFullyIncremental_alpha, fAlpha);
 489                 fStats.put(Messages.SyncAlgorithmFullyIncremental_beta, fBeta);
 490                 fStats.put(Messages.SyncAlgorithmFullyIncremental_ub, (fUpperBoundList.size() == 0) ? Messages.SyncAlgorithmFullyIncremental_NA : fUpperBoundList.size());
 491                 fStats.put(Messages.SyncAlgorithmFullyIncremental_lb, (fLowerBoundList.size() == 0) ? Messages.SyncAlgorithmFullyIncremental_NA : fLowerBoundList.size());
 492                 fStats.put(Messages.SyncAlgorithmFullyIncremental_accuracy, getAccuracy().doubleValue());
 493                 fStats.put(Messages.SyncAlgorithmFullyIncremental_nbmatch, (fNbMatches == 0) ? Messages.SyncAlgorithmFullyIncremental_NA : fNbMatches);
 494                 fStats.put(Messages.SyncAlgorithmFullyIncremental_nbacc, (fNbAccurateMatches == 0) ? Messages.SyncAlgorithmFullyIncremental_NA : fNbAccurateMatches);
 495                 fStats.put(Messages.SyncAlgorithmFullyIncremental_refformula, Messages.SyncAlgorithmFullyIncremental_T_ + fReferenceHost);
 496                 fStats.put(Messages.SyncAlgorithmFullyIncremental_otherformula, fAlpha + Messages.SyncAlgorithmFullyIncremental_mult + Messages.SyncAlgorithmFullyIncremental_T_ + fReferenceHost + Messages.SyncAlgorithmFullyIncremental_add + fBeta);
 497             }
 498             return fStats;
 499
 500         }
 501
 502         public String getReferenceHost() {
 503             return fReferenceHost;
 504         }
 505
 506         public String getOtherHost() {
 507             return fOtherHost;
 508         }
 509
 510         public boolean isForHosts(String hostId1, String hostId2) {
 511             return ((fReferenceHost.equals(hostId1) && fOtherHost.equals(hostId2)) || (fReferenceHost.equals(hostId2) && fOtherHost.equals(hostId1)));
 512         }
 513
 514         private void readObject(ObjectInputStream stream)
 515                 throws IOException, ClassNotFoundException {
 516             stream.defaultReadObject();
 517
 518             /* Initialize transient fields */
 519             fUpperBoundList = new LinkedList<>();
 520             fLowerBoundList = new LinkedList<>();
 521             fLmax = new SyncPoint[2];
 522             fLmin = new SyncPoint[2];
 523             fStats = new LinkedHashMap<>();
 524         }
 525
 526         @SuppressWarnings("nls")
 527         @Override
 528         public String toString() {
 529             StringBuilder b = new StringBuilder();
 530             b.append("Between " + fReferenceHost + " and " + fOtherHost + " [");
 531             b.append(" alpha " + fAlpha + " beta " + fBeta + " ]");
 532             return b.toString();
 533         }
 534
 535         private void setQuality(SyncQuality fQuality) {
 536             this.fQuality = fQuality;
 537         }
 538
 539     }
 540
 541     /**
 542      * Private class representing a point to synchronize on a graph. The x axis
 543      * is the timestamp of the event from the reference trace while the y axis
 544      * is the timestamp of the event on the other trace
 545      */
 546     private class SyncPoint {
 547         private final ITmfTimestamp x, y;
 548
 549         public SyncPoint(ITmfEvent ex, ITmfEvent ey) {
 550             x = ex.getTimestamp();
 551             y = ey.getTimestamp();
 552         }
 553
 554         public long getTimeX() {
 555             return x.getValue();
 556         }
 557
 558         /**
 559          * Calculate a cross product of 3 points:
 560          *
 561          * If the cross-product < 0, then p, pa, pb are clockwise
 562          *
 563          * If the cross-product > 0, then p, pa, pb are counter-clockwise
 564          *
 565          * If cross-product == 0, then they are in a line
 566          *
 567          * @param pa
 568          *            First point
 569          * @param pb
 570          *            Second point
 571          * @return The cross product
 572          */
 573         public long crossProduct(SyncPoint pa, SyncPoint pb) {
 574             long cp = ((pa.x.getValue() - x.getValue()) * (pb.y.getValue() - y.getValue()) - (pa.y.getValue() - y.getValue()) * (pb.x.getValue() - x.getValue()));
 575             return cp;
 576         }
 577
 578         /*
 579          * Gets the alpha (slope) between two points
 580          */
 581         public BigDecimal getAlpha(SyncPoint p1) {
 582             if (p1 == null) {
 583                 return BigDecimal.ONE;
 584             }
 585             BigDecimal deltay = BigDecimal.valueOf(y.getValue() - p1.y.getValue());
 586             BigDecimal deltax = BigDecimal.valueOf(x.getValue() - p1.x.getValue());
 587             if (deltax.equals(BigDecimal.ZERO)) {
 588                 return BigDecimal.ONE;
 589             }
 590             return deltay.divide(deltax, fMc);
 591         }
 592
 593         /*
 594          * Get the beta value (when x = 0) of the line given alpha
 595          */
 596         public BigDecimal getBeta(BigDecimal alpha) {
 597             return BigDecimal.valueOf(y.getValue()).subtract(alpha.multiply(BigDecimal.valueOf(x.getValue()), fMc));
 598         }
 599
 600         @Override
 601         public String toString() {
 602             return String.format("%s (%s,  %s)", this.getClass().getCanonicalName(), x, y); //$NON-NLS-1$
 603         }
 604     }
 605
 606 }