Calculate synchronization accuracy within the chull module
[lttv.git] / lttv / lttv / sync / event_analysis_chull.c
index 1dc995b17da63a406b850cb317ce06d034837dac..154258e00effc5af9369dc13c1c036e2d999125a 100644 (file)
@@ -1,19 +1,18 @@
 /* This file is part of the Linux Trace Toolkit viewer
- * Copyright (C) 2009 Benjamin Poirier <benjamin.poirier@polymtl.ca>
+ * Copyright (C) 2009, 2010 Benjamin Poirier <benjamin.poirier@polymtl.ca>
  *
- * This program is free software; you can redistribute it and/or modify
- * it under the terms of the GNU General Public License Version 2 as
- * published by the Free Software Foundation;
+ * This program is free software: you can redistribute it and/or modify it
+ * under the terms of the GNU Lesser General Public License as published by
+ * the Free Software Foundation, either version 2.1 of the License, or (at
+ * your option) any later version.
  *
- * This program is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
- * GNU General Public License for more details.
+ * This program is distributed in the hope that it will be useful, but WITHOUT
+ * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
+ * FITNESS FOR A PARTICULAR PURPOSE.  See the GNU Lesser General Public
+ * License for more details.
  *
- * You should have received a copy of the GNU General Public License
- * along with this program; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
+ * You should have received a copy of the GNU Lesser General Public License
+ * along with this program.  If not, see <http://www.gnu.org/licenses/>.
  */
 #define _ISOC99_SOURCE
 
 #endif
 
 #include <errno.h>
+#include <inttypes.h>
 #include <math.h>
 #include <float.h>
 #include <stdlib.h>
 #include <stdio.h>
+#include <string.h>
 #include <unistd.h>
 
 #include "sync_chain.h"
 #include "event_analysis_chull.h"
 
 
-#ifndef g_info
-#define g_info(format...) g_log (G_LOG_DOMAIN, G_LOG_LEVEL_INFO, format)
-#endif
-
-
 typedef enum
 {
        LOWER,
        UPPER
 } HullType;
 
-
 typedef enum
 {
        MINIMUM,
        MAXIMUM
 } LineType;
 
+#ifdef HAVE_LIBGLPK
+struct LPAddRowInfo
+{
+       glp_prob* lp;
+       int boundType;
+       GArray* iArray, * jArray, * aArray;
+};
+#endif
+
 
 // Functions common to all analysis modules
 static void initAnalysisCHull(SyncState* const syncState);
@@ -58,69 +62,91 @@ static void destroyAnalysisCHull(SyncState* const syncState);
 
 static void analyzeMessageCHull(SyncState* const syncState, Message* const
        message);
-static GArray* finalizeAnalysisCHull(SyncState* const syncState);
+static AllFactors* finalizeAnalysisCHull(SyncState* const syncState);
 static void printAnalysisStatsCHull(SyncState* const syncState);
-static void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const
-       unsigned int i, const unsigned int j);
+static void writeAnalysisTraceTraceForePlotsCHull(SyncState* const syncState,
+       const unsigned int i, const unsigned int j);
 
 // Functions specific to this module
-static void registerAnalysisCHull() __attribute__((constructor (101)));
-
 static void openGraphFiles(SyncState* const syncState);
 static void closeGraphFiles(SyncState* const syncState);
 static void writeGraphFiles(SyncState* const syncState);
 static void gfDumpHullToFile(gpointer data, gpointer userData);
 
+AllFactors* calculateAllFactors(struct _SyncState* const syncState);
+void calculateFactorsMiddle(PairFactors* const factors);
+static Factors* calculateFactorsExact(GQueue* const cu, GQueue* const cl, const
+       LineType lineType) __attribute__((pure));
+static void calculateFactorsFallback(GQueue* const cr, GQueue* const cs,
+       PairFactors* const result);
 static void grahamScan(GQueue* const hull, Point* const newPoint, const
        HullType type);
 static int jointCmp(const Point* const p1, const Point* const p2, const Point*
        const p3) __attribute__((pure));
 static double crossProductK(const Point const* p1, const Point const* p2,
        const Point const* p3, const Point const* p4) __attribute__((pure));
-static FactorsCHull** calculateAllFactors(SyncState* const syncState);
-static Factors* calculateFactorsExact(GQueue* const cu, GQueue* const cl, const
-       LineType lineType) __attribute__((pure));
-static void calculateFactorsMiddle(FactorsCHull* factors);
-static void calculateFactorsFallback(GQueue* const cr, GQueue* const cs,
-       FactorsCHull* const result);
 static double slope(const Point* const p1, const Point* const p2)
        __attribute__((pure));
 static double intercept(const Point* const p1, const Point* const p2)
        __attribute__((pure));
-static GArray* reduceFactors(SyncState* const syncState, FactorsCHull**
-       allFactors);
-static void freeAllFactors(const SyncState* const syncState, FactorsCHull**
-       const allFactors);
 static double verticalDistance(Point* p1, Point* p2, Point* const point)
        __attribute__((pure));
-static void floydWarshall(SyncState* const syncState, FactorsCHull** const
-       allFactors, double*** const distances, unsigned int*** const
-       predecessors);
-static void getFactors(FactorsCHull** const allFactors, unsigned int** const
-       predecessors, unsigned int* const references, const unsigned int traceNum,
-       Factors* const factors);
 
 static void gfPointDestroy(gpointer data, gpointer userData);
 
+// The next group of functions is only needed when computing synchronization
+// accuracy.
+#ifdef HAVE_LIBGLPK
+static AllFactors* finalizeAnalysisCHullLP(SyncState* const syncState);
+static void writeAnalysisTraceTimeBackPlotsCHull(SyncState* const syncState,
+       const unsigned int i, const unsigned int j);
+static void writeAnalysisTraceTimeForePlotsCHull(SyncState* const syncState,
+       const unsigned int i, const unsigned int j);
+static void writeAnalysisTraceTraceBackPlotsCHull(SyncState* const syncState,
+       const unsigned int i, const unsigned int j);
+
+static glp_prob* lpCreateProblem(GQueue* const lowerHull, GQueue* const
+       upperHull);
+static void gfLPAddRow(gpointer data, gpointer user_data);
+static Factors* calculateFactorsLP(glp_prob* const lp, const int direction);
+static void calculateCompleteFactorsLP(glp_prob* const lp, PairFactors*
+       factors);
+void timeCorrectionLP(glp_prob* const lp, const PairFactors* const lpFactors,
+       const uint64_t time, CorrectedTime* const correctedTime);
+
+static void gfAddAbsiscaToArray(gpointer data, gpointer user_data);
+static gint gcfCompareUint64(gconstpointer a, gconstpointer b);
+#else
+static inline AllFactors* finalizeAnalysisCHullLP(SyncState* const syncState)
+{
+       return NULL;
+}
+#endif
+
+
 
 static AnalysisModule analysisModuleCHull= {
        .name= "chull",
        .initAnalysis= &initAnalysisCHull,
        .destroyAnalysis= &destroyAnalysisCHull,
        .analyzeMessage= &analyzeMessageCHull,
-       .analyzeExchange= NULL,
-       .analyzeBroadcast= NULL,
        .finalizeAnalysis= &finalizeAnalysisCHull,
        .printAnalysisStats= &printAnalysisStatsCHull,
-       .writeAnalysisGraphsPlots= &writeAnalysisGraphsPlotsCHull,
-       .writeAnalysisGraphsOptions= NULL,
+       .graphFunctions= {
+#ifdef HAVE_LIBGLPK
+               .writeTraceTimeBackPlots= &writeAnalysisTraceTimeBackPlotsCHull,
+               .writeTraceTimeForePlots= &writeAnalysisTraceTimeForePlotsCHull,
+               .writeTraceTraceBackPlots= &writeAnalysisTraceTraceBackPlotsCHull,
+#endif
+               .writeTraceTraceForePlots= &writeAnalysisTraceTraceForePlotsCHull,
+       }
 };
 
 
 /*
  * Analysis module registering function
  */
-static void registerAnalysisCHull()
+void registerAnalysisCHull()
 {
        g_queue_push_tail(&analysisModules, &analysisModuleCHull);
 }
@@ -159,19 +185,19 @@ static void initAnalysisCHull(SyncState* const syncState)
                        analysisData->hullArray[i][j]= g_queue_new();
                }
        }
+#ifdef HAVE_LIBGLPK
+       analysisData->lps= NULL;
+#endif
 
        if (syncState->stats)
        {
-               analysisData->stats= malloc(sizeof(AnalysisStatsCHull));
-               analysisData->stats->dropped= 0;
-               analysisData->stats->allFactors= NULL;
+               analysisData->stats= calloc(1, sizeof(AnalysisStatsCHull));
        }
 
        if (syncState->graphsStream)
        {
-               analysisData->graphsData= malloc(sizeof(AnalysisGraphsDataCHull));
+               analysisData->graphsData= calloc(1, sizeof(AnalysisGraphsDataCHull));
                openGraphFiles(syncState);
-               analysisData->graphsData->allFactors= NULL;
        }
 }
 
@@ -193,7 +219,7 @@ static void openGraphFiles(SyncState* const syncState)
 
        analysisData= (AnalysisDataCHull*) syncState->analysisData;
 
-       cwd= changeToGraphDir(syncState->graphsDir);
+       cwd= changeToGraphsDir(syncState->graphsDir);
 
        analysisData->graphsData->hullPoints= malloc(syncState->traceNb *
                sizeof(FILE**));
@@ -270,7 +296,7 @@ static void gfDumpHullToFile(gpointer data, gpointer userData)
        Point* point;
 
        point= (Point*) data;
-       fprintf((FILE*) userData, "%20llu %20llu\n", point->x, point->y);
+       fprintf((FILE*) userData, "%20" PRIu64 " %20" PRIu64 "\n", point->x, point->y);
 }
 
 
@@ -341,33 +367,59 @@ static void destroyAnalysisCHull(SyncState* const syncState)
        {
                for (j= 0; j < syncState->traceNb; j++)
                {
-                       g_queue_foreach(analysisData->hullArray[i][j], gfPointDestroy, NULL);
+                       g_queue_foreach(analysisData->hullArray[i][j], gfPointDestroy,
+                               NULL);
+                       g_queue_free(analysisData->hullArray[i][j]);
                }
                free(analysisData->hullArray[i]);
        }
        free(analysisData->hullArray);
 
-       if (syncState->stats)
+#ifdef HAVE_LIBGLPK
+       if (analysisData->lps != NULL)
        {
-               if (analysisData->stats->allFactors != NULL)
+               for (i= 0; i < syncState->traceNb; i++)
                {
-                       freeAllFactors(syncState, analysisData->stats->allFactors);
+                       unsigned int j;
+
+                       for (j= 0; j < i; j++)
+                       {
+                               // There seems to be a memory leak in glpk, valgrind reports a
+                               // loss (reachable) even if the problem is deleted
+                               glp_delete_prob(analysisData->lps[i][j]);
+                       }
+                       free(analysisData->lps[i]);
                }
+               free(analysisData->lps);
+       }
+#endif
+
+       if (syncState->stats)
+       {
+               freeAllFactors(analysisData->stats->allFactors, syncState->traceNb);
+               freeAllFactors(analysisData->stats->geoFactors, syncState->traceNb);
+
+#ifdef HAVE_LIBGLPK
+               freeAllFactors(analysisData->stats->lpFactors, syncState->traceNb);
+#endif
 
                free(analysisData->stats);
        }
 
        if (syncState->graphsStream)
        {
-               if (analysisData->graphsData->hullPoints != NULL)
+               AnalysisGraphsDataCHull* graphs= analysisData->graphsData;
+
+               if (graphs->hullPoints != NULL)
                {
                        closeGraphFiles(syncState);
                }
 
-               if (!syncState->stats && analysisData->graphsData->allFactors != NULL)
-               {
-                       freeAllFactors(syncState, analysisData->graphsData->allFactors);
-               }
+               freeAllFactors(graphs->allFactors, syncState->traceNb);
+
+#ifdef HAVE_LIBGLPK
+               freeAllFactors(graphs->lpFactors, syncState->traceNb);
+#endif
 
                free(analysisData->graphsData);
        }
@@ -400,7 +452,8 @@ static void analyzeMessageCHull(SyncState* const syncState, Message* const messa
                newPoint->x= message->inE->cpuTime;
                newPoint->y= message->outE->cpuTime;
                hullType= UPPER;
-               g_debug("Reception point hullArray[%lu][%lu] x= inE->time= %llu y= outE->time= %llu",
+               g_debug("Reception point hullArray[%lu][%lu] "
+                       "x= inE->time= %" PRIu64 " y= outE->time= %" PRIu64,
                        message->inE->traceNum, message->outE->traceNum, newPoint->x,
                        newPoint->y);
        }
@@ -410,7 +463,8 @@ static void analyzeMessageCHull(SyncState* const syncState, Message* const messa
                newPoint->x= message->outE->cpuTime;
                newPoint->y= message->inE->cpuTime;
                hullType= LOWER;
-               g_debug("Send point hullArray[%lu][%lu] x= inE->time= %llu y= outE->time= %llu",
+               g_debug("Send point hullArray[%lu][%lu] "
+                       "x= inE->time= %" PRIu64 " y= outE->time= %" PRIu64,
                        message->inE->traceNum, message->outE->traceNum, newPoint->x,
                        newPoint->y);
        }
@@ -500,13 +554,13 @@ static void grahamScan(GQueue* const hull, Point* const newPoint, const
  *   syncState     container for synchronization data.
  *
  * Returns:
- *   Factors[traceNb] synchronization factors for each trace
+ *   AllFactors*   synchronization factors for each trace pair, the caller is
+ *   responsible for freeing the structure
  */
-static GArray* finalizeAnalysisCHull(SyncState* const syncState)
+static AllFactors* finalizeAnalysisCHull(SyncState* const syncState)
 {
        AnalysisDataCHull* analysisData;
-       GArray* factors;
-       FactorsCHull** allFactors;
+       AllFactors* geoFactors, * lpFactors;
 
        analysisData= (AnalysisDataCHull*) syncState->analysisData;
 
@@ -516,28 +570,50 @@ static GArray* finalizeAnalysisCHull(SyncState* const syncState)
                closeGraphFiles(syncState);
        }
 
-       allFactors= calculateAllFactors(syncState);
+       geoFactors= calculateAllFactors(syncState);
+       lpFactors= finalizeAnalysisCHullLP(syncState);
 
-       factors= reduceFactors(syncState, allFactors);
-
-       if (syncState->stats || syncState->graphsStream)
+       if (syncState->stats)
        {
-               if (syncState->stats)
+               geoFactors->refCount++;
+               analysisData->stats->geoFactors= geoFactors;
+
+               if (lpFactors != NULL)
                {
-                       analysisData->stats->allFactors= allFactors;
+                       lpFactors->refCount++;
+                       analysisData->stats->allFactors= lpFactors;
                }
+               else
+               {
+                       geoFactors->refCount++;
+                       analysisData->stats->allFactors= geoFactors;
+               }
+       }
 
-               if (syncState->graphsStream)
+       if (syncState->graphsStream)
+       {
+               if (lpFactors != NULL)
+               {
+                       lpFactors->refCount++;
+                       analysisData->graphsData->allFactors= lpFactors;
+               }
+               else
                {
-                       analysisData->graphsData->allFactors= allFactors;
+                       geoFactors->refCount++;
+                       analysisData->graphsData->allFactors= geoFactors;
                }
        }
+
+       if (lpFactors != NULL)
+       {
+               freeAllFactors(geoFactors, syncState->traceNb);
+               return lpFactors;
+       }
        else
        {
-               freeAllFactors(syncState, allFactors);
+               freeAllFactors(lpFactors, syncState->traceNb);
+               return geoFactors;
        }
-
-       return factors;
 }
 
 
@@ -582,41 +658,38 @@ static void printAnalysisStatsCHull(SyncState* const syncState)
        {
                for (j= i + 1; j < syncState->traceNb; j++)
                {
-                       FactorsCHull* factorsCHull;
+                       PairFactors* factorsCHull;
 
-                       factorsCHull= &analysisData->stats->allFactors[j][i];
-                       printf("\t\t%3d - %-3d: ", i, j);
+                       factorsCHull= &analysisData->stats->allFactors->pairFactors[j][i];
+                       printf("\t\t%3d - %-3d: %s", i, j,
+                               approxNames[factorsCHull->type]);
 
                        if (factorsCHull->type == EXACT)
                        {
-                               printf("Exact      a0= % 7g a1= 1 %c %7g\n",
+                               printf("      a0= % 7g a1= 1 %c %7g\n",
                                        factorsCHull->approx->offset,
                                        factorsCHull->approx->drift < 0. ? '-' : '+',
                                        fabs(factorsCHull->approx->drift));
                        }
-                       else if (factorsCHull->type == MIDDLE)
+                       else if (factorsCHull->type == ACCURATE)
                        {
-                               printf("Middle     a0= % 7g a1= 1 %c %7g accuracy %7g\n",
-                                       factorsCHull->approx->offset, factorsCHull->approx->drift
-                                       - 1. < 0. ? '-' : '+', fabs(factorsCHull->approx->drift -
-                                               1.), factorsCHull->accuracy);
-                               printf("\t\t                      a0: % 7g to % 7g (delta= %7g)\n",
+                               printf("\n\t\t                      a0: % 7g to % 7g (delta= %7g)\n",
                                        factorsCHull->max->offset, factorsCHull->min->offset,
                                        factorsCHull->min->offset - factorsCHull->max->offset);
                                printf("\t\t                      a1: 1 %+7g to %+7g (delta= %7g)\n",
                                        factorsCHull->min->drift - 1., factorsCHull->max->drift -
                                        1., factorsCHull->max->drift - factorsCHull->min->drift);
                        }
-                       else if (factorsCHull->type == FALLBACK)
+                       else if (factorsCHull->type == APPROXIMATE)
                        {
-                               printf("Fallback   a0= % 7g a1= 1 %c %7g error= %7g\n",
+                               printf("   a0= % 7g a1= 1 %c %7g error= %7g\n",
                                        factorsCHull->approx->offset, factorsCHull->approx->drift
                                        - 1. < 0. ? '-' : '+', fabs(factorsCHull->approx->drift -
                                                1.), factorsCHull->accuracy);
                        }
                        else if (factorsCHull->type == INCOMPLETE)
                        {
-                               printf("Incomplete\n");
+                               printf("\n");
 
                                if (factorsCHull->min->drift != -INFINITY)
                                {
@@ -633,9 +706,9 @@ static void printAnalysisStatsCHull(SyncState* const syncState)
                                                        1.));
                                }
                        }
-                       else if (factorsCHull->type == SCREWED)
+                       else if (factorsCHull->type == FAIL)
                        {
-                               printf("Screwed\n");
+                               printf("\n");
 
                                if (factorsCHull->min != NULL && factorsCHull->min->drift != -INFINITY)
                                {
@@ -654,7 +727,7 @@ static void printAnalysisStatsCHull(SyncState* const syncState)
                        }
                        else if (factorsCHull->type == ABSENT)
                        {
-                               printf("Absent\n");
+                               printf("\n");
                        }
                        else
                        {
@@ -662,6 +735,47 @@ static void printAnalysisStatsCHull(SyncState* const syncState)
                        }
                }
        }
+
+#ifdef HAVE_LIBGLPK
+       printf("\tFactor comparison:\n"
+               "\t\tTrace pair  Factors type  Differences (lp - chull)\n"
+               "\t\t                          a0                    a1\n"
+               "\t\t                          Min        Max        Min        Max\n");
+
+       for (i= 0; i < syncState->traceNb; i++)
+       {
+               for (j= 0; j < i; j++)
+               {
+                       PairFactors* geoFactors=
+                               &analysisData->stats->geoFactors->pairFactors[i][j];
+                       PairFactors* lpFactors=
+                               &analysisData->stats->lpFactors->pairFactors[i][j];
+
+                       printf("\t\t%3d - %-3d   ", i, j);
+                       if (lpFactors->type == geoFactors->type)
+                       {
+                               if (lpFactors->type == ACCURATE)
+                               {
+                                       printf("%-13s %-10.4g %-10.4g %-10.4g %.4g\n",
+                                               approxNames[lpFactors->type],
+                                               lpFactors->min->offset - geoFactors->min->offset,
+                                               lpFactors->max->offset - geoFactors->max->offset,
+                                               lpFactors->min->drift - geoFactors->min->drift,
+                                               lpFactors->max->drift - geoFactors->max->drift);
+                               }
+                               else if (lpFactors->type == ABSENT)
+                               {
+                                       printf("%s\n", approxNames[lpFactors->type]);
+                               }
+                       }
+                       else
+                       {
+                               printf("Different! %s and %s\n", approxNames[lpFactors->type],
+                                       approxNames[geoFactors->type]);
+                       }
+               }
+       }
+#endif
 }
 
 
@@ -701,7 +815,9 @@ static int jointCmp(const Point const* p1, const Point const* p2, const
        const double fuzzFactor= 0.;
 
        result= crossProductK(p1, p2, p1, p3);
-       g_debug("crossProductK(p1= (%llu, %llu), p2= (%llu, %llu), p1= (%llu, %llu), p3= (%llu, %llu))= %g",
+       g_debug("crossProductK(p1= (%" PRIu64 ", %" PRIu64 "), "
+               "p2= (%" PRIu64 ", %" PRIu64 "), p1= (%" PRIu64 ", %" PRIu64 "), "
+               "p3= (%" PRIu64 ", %" PRIu64 "))= %g",
                p1->x, p1->y, p2->x, p2->y, p1->x, p1->y, p3->x, p3->y, result);
        if (result < fuzzFactor)
        {
@@ -738,55 +854,6 @@ static double crossProductK(const Point const* p1, const Point const* p2,
 }
 
 
-/*
- * Free a container of FactorsCHull
- *
- * Args:
- *   syncState:     container for synchronization data.
- *   allFactors:   container of Factors
- */
-static void freeAllFactors(const SyncState* const syncState, FactorsCHull**
-       const allFactors)
-{
-       unsigned int i, j;
-
-       for (i= 0; i < syncState->traceNb; i++)
-       {
-               for (j= 0; j <= i; j++)
-               {
-                       FactorsCHull* factorsCHull;
-
-                       factorsCHull= &allFactors[i][j];
-                       if (factorsCHull->type == MIDDLE || factorsCHull->type ==
-                               INCOMPLETE || factorsCHull->type == ABSENT)
-                       {
-                               free(factorsCHull->min);
-                               free(factorsCHull->max);
-                       }
-                       else if (factorsCHull->type == SCREWED)
-                       {
-                               if (factorsCHull->min != NULL)
-                               {
-                                       free(factorsCHull->min);
-                               }
-                               if (factorsCHull->max != NULL)
-                               {
-                                       free(factorsCHull->max);
-                               }
-                       }
-
-                       if (factorsCHull->type == EXACT || factorsCHull->type == MIDDLE ||
-                               factorsCHull->type == FALLBACK)
-                       {
-                               free(factorsCHull->approx);
-                       }
-               }
-               free(allFactors[i]);
-       }
-       free(allFactors);
-}
-
-
 /*
  * Analyze the convex hulls to determine the synchronization factors between
  * each pair of trace.
@@ -795,28 +862,21 @@ static void freeAllFactors(const SyncState* const syncState, FactorsCHull**
  *   syncState     container for synchronization data.
  *
  * Returns:
- *   FactorsCHull*[TraceNum][TraceNum] array. See the documentation for the
- *   member allFactors of AnalysisStatsCHull.
+ *   AllFactors*, see the documentation for the member geoFactors of
+ *   AnalysisStatsCHull.
  */
-static FactorsCHull** calculateAllFactors(SyncState* const syncState)
+AllFactors* calculateAllFactors(SyncState* const syncState)
 {
        unsigned int traceNumA, traceNumB;
-       FactorsCHull** allFactors;
+       AllFactors* geoFactors;
        AnalysisDataCHull* analysisData;
 
        analysisData= (AnalysisDataCHull*) syncState->analysisData;
 
-       // Allocate allFactors and calculate min and max
-       allFactors= malloc(syncState->traceNb * sizeof(FactorsCHull*));
+       // Allocate geoFactors and calculate min and max
+       geoFactors= createAllFactors(syncState->traceNb);
        for (traceNumA= 0; traceNumA < syncState->traceNb; traceNumA++)
        {
-               allFactors[traceNumA]= malloc((traceNumA + 1) * sizeof(FactorsCHull));
-
-               allFactors[traceNumA][traceNumA].type= EXACT;
-               allFactors[traceNumA][traceNumA].approx= malloc(sizeof(Factors));
-               allFactors[traceNumA][traceNumA].approx->drift= 1.;
-               allFactors[traceNumA][traceNumA].approx->offset= 0.;
-
                for (traceNumB= 0; traceNumB < traceNumA; traceNumB++)
                {
                        unsigned int i;
@@ -826,8 +886,8 @@ static FactorsCHull** calculateAllFactors(SyncState* const syncState)
                                LineType lineType;
                                size_t factorsOffset;
                        } loopValues[]= {
-                               {MINIMUM, offsetof(FactorsCHull, min)},
-                               {MAXIMUM, offsetof(FactorsCHull, max)}
+                               {MINIMUM, offsetof(PairFactors, min)},
+                               {MAXIMUM, offsetof(PairFactors, max)}
                        };
 
                        cr= analysisData->hullArray[traceNumB][traceNumA];
@@ -835,12 +895,14 @@ static FactorsCHull** calculateAllFactors(SyncState* const syncState)
 
                        for (i= 0; i < sizeof(loopValues) / sizeof(*loopValues); i++)
                        {
-                               g_debug("allFactors[%u][%u].%s = calculateFactorsExact(cr= hullArray[%u][%u], cs= hullArray[%u][%u], %s)",
+                               g_debug("geoFactors[%u][%u].%s = calculateFactorsExact(cr= "
+                                       "hullArray[%u][%u], cs= hullArray[%u][%u], %s)",
                                        traceNumA, traceNumB, loopValues[i].factorsOffset ==
-                                       offsetof(FactorsCHull, min) ? "min" : "max", traceNumB,
+                                       offsetof(PairFactors, min) ? "min" : "max", traceNumB,
                                        traceNumA, traceNumA, traceNumB, loopValues[i].lineType ==
                                        MINIMUM ? "MINIMUM" : "MAXIMUM");
-                               *((Factors**) ((void*) &allFactors[traceNumA][traceNumB] +
+                               *((Factors**) ((void*)
+                                               &geoFactors->pairFactors[traceNumA][traceNumB] +
                                                loopValues[i].factorsOffset))=
                                        calculateFactorsExact(cr, cs, loopValues[i].lineType);
                        }
@@ -852,22 +914,22 @@ static FactorsCHull** calculateAllFactors(SyncState* const syncState)
        {
                for (traceNumB= 0; traceNumB < traceNumA; traceNumB++)
                {
-                       FactorsCHull* factorsCHull;
+                       PairFactors* factorsCHull;
 
-                       factorsCHull= &allFactors[traceNumA][traceNumB];
+                       factorsCHull= &geoFactors->pairFactors[traceNumA][traceNumB];
                        if (factorsCHull->min == NULL && factorsCHull->max == NULL)
                        {
-                               factorsCHull->type= FALLBACK;
+                               factorsCHull->type= APPROXIMATE;
                                calculateFactorsFallback(analysisData->hullArray[traceNumB][traceNumA],
                                        analysisData->hullArray[traceNumA][traceNumB],
-                                       &allFactors[traceNumA][traceNumB]);
+                                       &geoFactors->pairFactors[traceNumA][traceNumB]);
                        }
                        else if (factorsCHull->min != NULL && factorsCHull->max != NULL)
                        {
                                if (factorsCHull->min->drift != -INFINITY &&
                                        factorsCHull->max->drift != INFINITY)
                                {
-                                       factorsCHull->type= MIDDLE;
+                                       factorsCHull->type= ACCURATE;
                                        calculateFactorsMiddle(factorsCHull);
                                }
                                else if (factorsCHull->min->drift != -INFINITY ||
@@ -883,12 +945,12 @@ static FactorsCHull** calculateAllFactors(SyncState* const syncState)
                        else
                        {
                                //g_assert_not_reached();
-                               factorsCHull->type= SCREWED;
+                               factorsCHull->type= FAIL;
                        }
                }
        }
 
-       return allFactors;
+       return geoFactors;
 }
 
 
@@ -908,7 +970,7 @@ static FactorsCHull** calculateAllFactors(SyncState* const syncState)
  * Args:
  *   factors:      contains the min and max limits, used to store the result
  */
-static void calculateFactorsMiddle(FactorsCHull* factors)
+void calculateFactorsMiddle(PairFactors* const factors)
 {
        double amin, amax, bmin, bmax, bhat;
 
@@ -917,7 +979,7 @@ static void calculateFactorsMiddle(FactorsCHull* factors)
        bmin= factors->min->drift;
        bmax= factors->max->drift;
 
-       g_assert_cmpfloat(bmax, >, bmin);
+       g_assert_cmpfloat(bmax, >=, bmin);
 
        factors->approx= malloc(sizeof(Factors));
        bhat= (bmax * bmin - 1. + sqrt(1. + pow(bmax, 2.) * pow(bmin, 2.) +
@@ -1064,14 +1126,15 @@ static Factors* calculateFactorsExact(GQueue* const cu, GQueue* const cl, const
        p1= g_queue_peek_nth(c1, i1);
        p2= g_queue_peek_nth(c2, i2);
 
-       g_debug("Resulting points are: c1[i1]: x= %llu y= %llu c2[i2]: x= %llu y= %llu",
-               p1->x, p1->y, p2->x, p2->y);
+       g_debug("Resulting points are: c1[i1]: x= %" PRIu64 " y= %" PRIu64
+               " c2[i2]: x= %" PRIu64 " y= %" PRIu64 "", p1->x, p1->y, p2->x, p2->y);
 
        result= malloc(sizeof(Factors));
        result->drift= slope(p1, p2);
        result->offset= intercept(p1, p2);
 
-       g_debug("Resulting factors are: drift= %g offset= %g", result->drift, result->offset);
+       g_debug("Resulting factors are: drift= %g offset= %g", result->drift,
+               result->offset);
 
        return result;
 }
@@ -1103,7 +1166,7 @@ static Factors* calculateFactorsExact(GQueue* const cu, GQueue* const cl, const
  *                 will be stored
  */
 static void calculateFactorsFallback(GQueue* const cr, GQueue* const cs,
-       FactorsCHull* const result)
+       PairFactors* const result)
 {
        unsigned int i, j, k;
        double errorMin;
@@ -1210,314 +1273,6 @@ static double intercept(const Point* const p1, const Point* const p2)
 }
 
 
-/*
- * Calculate a resulting offset and drift for each trace.
- *
- * Traces are assembled in groups. A group is an "island" of nodes/traces that
- * exchanged messages. A reference is determined for each group by using a
- * shortest path search based on the accuracy of the approximation. This also
- * forms a tree of the best way to relate each node's clock to the reference's
- * based on the accuracy. Sometimes it may be necessary or advantageous to
- * propagate the factors through intermediary clocks. Resulting factors for
- * each trace are determined based on this tree.
- *
- * This part was not the focus of my research. The algorithm used here is
- * inexact in some ways:
- * 1) The reference used may not actually be the best one to use. This is
- *    because the accuracy is not corrected based on the drift during the
- *    shortest path search.
- * 2) The min and max factors are not propagated and are no longer valid.
- * 3) Approximations of different types (MIDDLE and FALLBACK) are compared
- *    together. The "accuracy" parameters of these have different meanings and
- *    are not readily comparable.
- *
- * Nevertheless, the result is satisfactory. You just can't tell "how much" it
- * is.
- *
- * Two alternative (and subtly different) ways of propagating factors to
- * preserve min and max bondaries have been proposed, see:
- * [Duda, A., Harrus, G., Haddad, Y., and Bernard, G.: Estimating global time
- * in distributed systems, Proc. 7th Int. Conf. on Distributed Computing
- * Systems, Berlin, volume 18, 1987] p.304
- *
- * [Jezequel, J.M., and Jard, C.: Building a global clock for observing
- * computations in distributed memory parallel computers, Concurrency:
- * Practice and Experience 8(1), volume 8, John Wiley & Sons, Ltd Chichester,
- * 1996, 32] Section 5; which is mostly the same as
- * [Jezequel, J.M.: Building a global time on parallel machines, Proceedings
- * of the 3rd International Workshop on Distributed Algorithms, LNCS, volume
- * 392, 136–147, 1989] Section 5
- *
- * Args:
- *   syncState:    container for synchronization data.
- *   allFactors:   offset and drift between each pair of traces
- *
- * Returns:
- *   Factors[traceNb] synchronization factors for each trace
- */
-static GArray* reduceFactors(SyncState* const syncState, FactorsCHull** const
-       allFactors)
-{
-       GArray* factors;
-       double** distances;
-       unsigned int** predecessors;
-       double* distanceSums;
-       unsigned int* references;
-       unsigned int i, j;
-
-       // Solve the all-pairs shortest path problem using the Floyd-Warshall
-       // algorithm
-       floydWarshall(syncState, allFactors, &distances, &predecessors);
-
-       /* Find the reference for each node
-        *
-        * First calculate, for each node, the sum of the distances to each other
-        * node it can reach.
-        *
-        * Then, go through each "island" of traces to find the trace that has the
-        * lowest distance sum. Assign this trace as the reference to each trace
-        * of the island.
-        */
-       distanceSums= malloc(syncState->traceNb * sizeof(double));
-       for (i= 0; i < syncState->traceNb; i++)
-       {
-               distanceSums[i]= 0.;
-               for (j= 0; j < syncState->traceNb; j++)
-               {
-                       distanceSums[i]+= distances[i][j];
-               }
-       }
-
-       references= malloc(syncState->traceNb * sizeof(unsigned int));
-       for (i= 0; i < syncState->traceNb; i++)
-       {
-               references[i]= UINT_MAX;
-       }
-       for (i= 0; i < syncState->traceNb; i++)
-       {
-               if (references[i] == UINT_MAX)
-               {
-                       unsigned int reference;
-                       double distanceSumMin;
-
-                       // A node is its own reference by default
-                       reference= i;
-                       distanceSumMin= INFINITY;
-                       for (j= 0; j < syncState->traceNb; j++)
-                       {
-                               if (distances[i][j] != INFINITY && distanceSums[j] <
-                                       distanceSumMin)
-                               {
-                                       reference= j;
-                                       distanceSumMin= distanceSums[j];
-                               }
-                       }
-                       for (j= 0; j < syncState->traceNb; j++)
-                       {
-                               if (distances[i][j] != INFINITY)
-                               {
-                                       references[j]= reference;
-                               }
-                       }
-               }
-       }
-
-       for (i= 0; i < syncState->traceNb; i++)
-       {
-               free(distances[i]);
-       }
-       free(distances);
-       free(distanceSums);
-
-       /* For each trace, calculate the factors based on their corresponding
-        * tree. The tree is rooted at the reference and the shortest path to each
-        * other nodes are the branches.
-        */
-       factors= g_array_sized_new(FALSE, FALSE, sizeof(Factors),
-               syncState->traceNb);
-       g_array_set_size(factors, syncState->traceNb);
-       for (i= 0; i < syncState->traceNb; i++)
-       {
-               getFactors(allFactors, predecessors, references, i, &g_array_index(factors,
-                               Factors, i));
-       }
-
-       for (i= 0; i < syncState->traceNb; i++)
-       {
-               free(predecessors[i]);
-       }
-       free(predecessors);
-       free(references);
-
-       return factors;
-}
-
-
-/*
- * Perform an all-source shortest path search using the Floyd-Warshall
- * algorithm.
- *
- * The algorithm is implemented accoding to the description here:
- * http://web.mit.edu/urban_or_book/www/book/chapter6/6.2.2.html
- *
- * Args:
- *   syncState:    container for synchronization data.
- *   allFactors:   offset and drift between each pair of traces
- *   distances:    resulting matrix of the length of the shortest path between
- *                 two nodes. If there is no path between two nodes, the
- *                 length is INFINITY
- *   predecessors: resulting matrix of each node's predecessor on the shortest
- *                 path between two nodes
- */
-static void floydWarshall(SyncState* const syncState, FactorsCHull** const
-       allFactors, double*** const distances, unsigned int*** const
-       predecessors)
-{
-       unsigned int i, j, k;
-
-       // Setup initial conditions
-       *distances= malloc(syncState->traceNb * sizeof(double*));
-       *predecessors= malloc(syncState->traceNb * sizeof(unsigned int*));
-       for (i= 0; i < syncState->traceNb; i++)
-       {
-               (*distances)[i]= malloc(syncState->traceNb * sizeof(double));
-               for (j= 0; j < syncState->traceNb; j++)
-               {
-                       if (i == j)
-                       {
-                               g_assert(allFactors[i][j].type == EXACT);
-
-                               (*distances)[i][j]= 0.;
-                       }
-                       else
-                       {
-                               unsigned int row, col;
-
-                               if (i > j)
-                               {
-                                       row= i;
-                                       col= j;
-                               }
-                               else if (i < j)
-                               {
-                                       row= j;
-                                       col= i;
-                               }
-
-                               if (allFactors[row][col].type == MIDDLE ||
-                                       allFactors[row][col].type == FALLBACK)
-                               {
-                                       (*distances)[i][j]= allFactors[row][col].accuracy;
-                               }
-                               else if (allFactors[row][col].type == INCOMPLETE ||
-                                       allFactors[row][col].type == SCREWED ||
-                                       allFactors[row][col].type == ABSENT)
-                               {
-                                       (*distances)[i][j]= INFINITY;
-                               }
-                               else
-                               {
-                                       g_assert_not_reached();
-                               }
-                       }
-               }
-
-               (*predecessors)[i]= malloc(syncState->traceNb * sizeof(unsigned int));
-               for (j= 0; j < syncState->traceNb; j++)
-               {
-                       if (i != j)
-                       {
-                               (*predecessors)[i][j]= i;
-                       }
-                       else
-                       {
-                               (*predecessors)[i][j]= UINT_MAX;
-                       }
-               }
-       }
-
-       // Run the iterations
-       for (k= 0; k < syncState->traceNb; k++)
-       {
-               for (i= 0; i < syncState->traceNb; i++)
-               {
-                       for (j= 0; j < syncState->traceNb; j++)
-                       {
-                               double distanceMin;
-
-                               distanceMin= MIN((*distances)[i][j], (*distances)[i][k] +
-                                       (*distances)[k][j]);
-
-                               if (distanceMin != (*distances)[i][j])
-                               {
-                                       (*predecessors)[i][j]= (*predecessors)[k][j];
-                               }
-
-                               (*distances)[i][j]= distanceMin;
-                       }
-               }
-       }
-}
-
-
-/*
- * Cummulate the time correction factors to convert a node's time to its
- * reference's time.
- * This function recursively calls itself until it reaches the reference node.
- *
- * Args:
- *   allFactors:   offset and drift between each pair of traces
- *   predecessors: matrix of each node's predecessor on the shortest
- *                 path between two nodes
- *   references:   reference node for each node
- *   traceNum:     node for which to find the factors
- *   factors:      resulting factors
- */
-static void getFactors(FactorsCHull** const allFactors, unsigned int** const
-       predecessors, unsigned int* const references, const unsigned int traceNum,
-       Factors* const factors)
-{
-       unsigned int reference;
-
-       reference= references[traceNum];
-
-       if (reference == traceNum)
-       {
-               factors->offset= 0.;
-               factors->drift= 1.;
-       }
-       else
-       {
-               Factors previousVertexFactors;
-
-               getFactors(allFactors, predecessors, references,
-                       predecessors[reference][traceNum], &previousVertexFactors);
-
-               // convertir de traceNum Ã  reference
-
-               // allFactors convertit de col Ã  row
-
-               if (reference > traceNum)
-               {
-                       factors->offset= previousVertexFactors.drift *
-                               allFactors[reference][traceNum].approx->offset +
-                               previousVertexFactors.offset;
-                       factors->drift= previousVertexFactors.drift *
-                               allFactors[reference][traceNum].approx->drift;
-               }
-               else
-               {
-                       factors->offset= previousVertexFactors.drift * (-1. *
-                               allFactors[traceNum][reference].approx->offset /
-                               allFactors[traceNum][reference].approx->drift) +
-                               previousVertexFactors.offset;
-                       factors->drift= previousVertexFactors.drift * (1. /
-                               allFactors[traceNum][reference].approx->drift);
-               }
-       }
-}
-
-
 /*
  * Write the analysis-specific graph lines in the gnuplot script.
  *
@@ -1526,11 +1281,11 @@ static void getFactors(FactorsCHull** const allFactors, unsigned int** const
  *   i:            first trace number
  *   j:            second trace number, garanteed to be larger than i
  */
-void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned
+void writeAnalysisTraceTraceForePlotsCHull(SyncState* const syncState, const unsigned
        int i, const unsigned int j)
 {
        AnalysisDataCHull* analysisData;
-       FactorsCHull* factorsCHull;
+       PairFactors* factorsCHull;
 
        analysisData= (AnalysisDataCHull*) syncState->analysisData;
 
@@ -1543,7 +1298,7 @@ void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned
                        "linecolor rgb \"#003366\" linetype 4 pointtype 10 pointsize 0.8, \\\n",
                i, j);
 
-       factorsCHull= &analysisData->graphsData->allFactors[j][i];
+       factorsCHull= &analysisData->graphsData->allFactors->pairFactors[j][i];
        if (factorsCHull->type == EXACT)
        {
                fprintf(syncState->graphsStream,
@@ -1552,7 +1307,7 @@ void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned
                                "linecolor rgb \"black\" linetype 1, \\\n",
                                factorsCHull->approx->offset, factorsCHull->approx->drift);
        }
-       else if (factorsCHull->type == MIDDLE)
+       else if (factorsCHull->type == ACCURATE)
        {
                fprintf(syncState->graphsStream,
                        "\t%.2f + %.10f * x "
@@ -1567,10 +1322,10 @@ void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned
                fprintf(syncState->graphsStream,
                        "\t%.2f + %.10f * x "
                                "title \"Middle conversion\" with lines "
-                               "linecolor rgb \"gray60\" linetype 1, \\\n",
+                               "linecolor rgb \"black\" linetype 1, \\\n",
                                factorsCHull->approx->offset, factorsCHull->approx->drift);
        }
-       else if (factorsCHull->type == FALLBACK)
+       else if (factorsCHull->type == APPROXIMATE)
        {
                fprintf(syncState->graphsStream,
                        "\t%.2f + %.10f * x "
@@ -1598,7 +1353,7 @@ void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned
                                        factorsCHull->max->offset, factorsCHull->max->drift);
                }
        }
-       else if (factorsCHull->type == SCREWED)
+       else if (factorsCHull->type == FAIL)
        {
                if (factorsCHull->min != NULL && factorsCHull->min->drift != -INFINITY)
                {
@@ -1626,3 +1381,480 @@ void writeAnalysisGraphsPlotsCHull(SyncState* const syncState, const unsigned
                g_assert_not_reached();
        }
 }
+
+
+#ifdef HAVE_LIBGLPK
+/*
+ * Create the linear programming problem containing the constraints defined by
+ * two half-hulls. The objective function and optimization directions are not
+ * written.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ *   i:            first trace number
+ *   j:            second trace number, garanteed to be larger than i
+ * Returns:
+ *   A new glp_prob*, this problem must be freed by the caller with
+ *   glp_delete_prob()
+ */
+static glp_prob* lpCreateProblem(GQueue* const lowerHull, GQueue* const
+       upperHull)
+{
+       unsigned int it;
+       const int zero= 0;
+       const double zeroD= 0.;
+       glp_prob* lp= glp_create_prob();
+       unsigned int hullPointNb= g_queue_get_length(lowerHull) +
+               g_queue_get_length(upperHull);
+       GArray* iArray= g_array_sized_new(FALSE, FALSE, sizeof(int), hullPointNb +
+               1);
+       GArray* jArray= g_array_sized_new(FALSE, FALSE, sizeof(int), hullPointNb +
+               1);
+       GArray* aArray= g_array_sized_new(FALSE, FALSE, sizeof(double),
+               hullPointNb + 1);
+       struct {
+               GQueue* hull;
+               struct LPAddRowInfo rowInfo;
+       } loopValues[2]= {
+               {lowerHull, {lp, GLP_UP, iArray, jArray, aArray}},
+               {upperHull, {lp, GLP_LO, iArray, jArray, aArray}},
+       };
+
+       // Create the LP problem
+       glp_term_out(GLP_OFF);
+       if (hullPointNb > 0)
+       {
+               glp_add_rows(lp, hullPointNb);
+       }
+       glp_add_cols(lp, 2);
+
+       glp_set_col_name(lp, 1, "a0");
+       glp_set_col_bnds(lp, 1, GLP_FR, 0., 0.);
+       glp_set_col_name(lp, 2, "a1");
+       glp_set_col_bnds(lp, 2, GLP_LO, 0., 0.);
+
+       // Add row constraints
+       g_array_append_val(iArray, zero);
+       g_array_append_val(jArray, zero);
+       g_array_append_val(aArray, zeroD);
+
+       for (it= 0; it < sizeof(loopValues) / sizeof(*loopValues); it++)
+       {
+               g_queue_foreach(loopValues[it].hull, &gfLPAddRow,
+                       &loopValues[it].rowInfo);
+       }
+
+       g_assert_cmpuint(iArray->len, ==, jArray->len);
+       g_assert_cmpuint(jArray->len, ==, aArray->len);
+       g_assert_cmpuint(aArray->len - 1, ==, hullPointNb * 2);
+
+       glp_load_matrix(lp, aArray->len - 1, &g_array_index(iArray, int, 0),
+               &g_array_index(jArray, int, 0), &g_array_index(aArray, double, 0));
+
+       glp_scale_prob(lp, GLP_SF_AUTO);
+
+       g_array_free(iArray, TRUE);
+       g_array_free(jArray, TRUE);
+       g_array_free(aArray, TRUE);
+
+       return lp;
+}
+
+
+/*
+ * A GFunc for g_queue_foreach(). Add constraints and bounds for one row.
+ *
+ * Args:
+ *   data          Point*, synchronization point for which to add an LP row
+ *                 (a constraint)
+ *   user_data     LPAddRowInfo*
+ */
+static void gfLPAddRow(gpointer data, gpointer user_data)
+{
+       Point* p= data;
+       struct LPAddRowInfo* rowInfo= user_data;
+       int indexes[2];
+       double constraints[2];
+
+       indexes[0]= g_array_index(rowInfo->iArray, int, rowInfo->iArray->len - 1) + 1;
+       indexes[1]= indexes[0];
+
+       if (rowInfo->boundType == GLP_UP)
+       {
+               glp_set_row_bnds(rowInfo->lp, indexes[0], GLP_UP, 0., p->y);
+       }
+       else if (rowInfo->boundType == GLP_LO)
+       {
+               glp_set_row_bnds(rowInfo->lp, indexes[0], GLP_LO, p->y, 0.);
+       }
+       else
+       {
+               g_assert_not_reached();
+       }
+
+       g_array_append_vals(rowInfo->iArray, indexes, 2);
+       indexes[0]= 1;
+       indexes[1]= 2;
+       g_array_append_vals(rowInfo->jArray, indexes, 2);
+       constraints[0]= 1.;
+       constraints[1]= p->x;
+       g_array_append_vals(rowInfo->aArray, constraints, 2);
+}
+
+
+/*
+ * Calculate min or max correction factors (as possible) using an LP problem.
+ *
+ * Args:
+ *   lp:           A linear programming problem with constraints and bounds
+ *                 initialized.
+ *   direction:    The type of factors desired. Use GLP_MAX for max
+ *                 approximation factors (a1, the drift or slope is the
+ *                 largest) and GLP_MIN in the other case.
+ *
+ * Returns:
+ *   If the calculation was successful, a new Factors struct. Otherwise, NULL.
+ *   The calculation will fail if the hull assumptions are not respected.
+ */
+static Factors* calculateFactorsLP(glp_prob* const lp, const int direction)
+{
+       int retval, status;
+       Factors* factors;
+
+       glp_set_obj_coef(lp, 1, 0.);
+       glp_set_obj_coef(lp, 2, 1.);
+
+       glp_set_obj_dir(lp, direction);
+       retval= glp_simplex(lp, NULL);
+       status= glp_get_status(lp);
+
+       if (retval == 0 && status == GLP_OPT)
+       {
+               factors= malloc(sizeof(Factors));
+               factors->offset= glp_get_col_prim(lp, 1);
+               factors->drift= glp_get_col_prim(lp, 2);
+       }
+       else
+       {
+               factors= NULL;
+       }
+
+       return factors;
+}
+
+
+/*
+ * Calculate min, max and approx correction factors (as possible) using an LP
+ * problem.
+ *
+ * Args:
+ *   lp            A linear programming problem with constraints and bounds
+ *                 initialized.
+ *   factors       Resulting factors, must be preallocated
+ */
+static void calculateCompleteFactorsLP(glp_prob* const lp, PairFactors* factors)
+{
+       factors->min= calculateFactorsLP(lp, GLP_MIN);
+       factors->max= calculateFactorsLP(lp, GLP_MAX);
+
+       if (factors->min && factors->max)
+       {
+               factors->type= ACCURATE;
+               calculateFactorsMiddle(factors);
+       }
+       else if (factors->min || factors->max)
+       {
+               factors->type= INCOMPLETE;
+       }
+       else
+       {
+               factors->type= ABSENT;
+       }
+}
+
+
+/*
+ * A GFunc for g_queue_foreach()
+ *
+ * Args:
+ *   data          Point*, a convex hull point
+ *   user_data     GArray*, an array of convex hull point absisca values, as
+ *                 uint64_t
+ */
+static void gfAddAbsiscaToArray(gpointer data, gpointer user_data)
+{
+       Point* p= data;
+       GArray* a= user_data;
+       uint64_t v= p->x;
+
+       g_array_append_val(a, v);
+}
+
+
+/*
+ * A GCompareFunc for g_array_sort()
+ *
+ * Args:
+ *   a, b          uint64_t*, absisca values
+ *
+ * Returns:
+ *   "returns less than zero for first arg is less than second arg, zero for
+ *   equal, greater zero if first arg is greater than second arg"
+ *   - the great glib documentation
+ */
+static gint gcfCompareUint64(gconstpointer a, gconstpointer b)
+{
+       if (*(uint64_t*) a < *(uint64_t*) b)
+       {
+               return -1;
+       }
+       else if (*(uint64_t*) a > *(uint64_t*) b)
+       {
+               return 1;
+       }
+       else
+       {
+               return 0;
+       }
+}
+
+
+/*
+ * Compute synchronization factors using a linear programming approach.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ */
+static AllFactors* finalizeAnalysisCHullLP(SyncState* const syncState)
+{
+       AnalysisDataCHull* analysisData= syncState->analysisData;
+       unsigned int i, j;
+       AllFactors* lpFactorsArray;
+
+       lpFactorsArray= createAllFactors(syncState->traceNb);
+       
+       analysisData->lps= malloc(syncState->traceNb * sizeof(glp_prob**));
+       for (i= 0; i < syncState->traceNb; i++)
+       {
+               analysisData->lps[i]= malloc(i * sizeof(glp_prob*));
+       }
+
+       for (i= 0; i < syncState->traceNb; i++)
+       {
+               for (j= 0; j < i; j++)
+               {
+                       glp_prob* lp;
+                       unsigned int it;
+                       GQueue*** hullArray= analysisData->hullArray;
+                       PairFactors* lpFactors= &lpFactorsArray->pairFactors[i][j];
+
+                       // Create the LP problem
+                       lp= lpCreateProblem(hullArray[i][j], hullArray[j][i]);
+                       analysisData->lps[i][j]= lp;
+
+                       // Use the LP problem to find the correction factors for this pair of
+                       // traces
+                       calculateCompleteFactorsLP(lp, lpFactors);
+
+                       // If possible, compute synchronization accuracy information for
+                       // graphs
+                       if (syncState->graphsStream && lpFactors->type == ACCURATE)
+                       {
+                               int retval;
+                               char* cwd;
+                               char fileName[43];
+                               FILE* fp;
+                               GArray* xValues;
+
+                               // Open the data file
+                               snprintf(fileName, sizeof(fileName),
+                                       "analysis_chull_accuracy-%03u_and_%03u.data", j, i);
+                               fileName[sizeof(fileName) - 1]= '\0';
+
+                               cwd= changeToGraphsDir(syncState->graphsDir);
+
+                               if ((fp= fopen(fileName, "w")) == NULL)
+                               {
+                                       g_error(strerror(errno));
+                               }
+                               fprintf(fp, "#%-24s %-25s %-25s %-25s\n", "x", "middle", "min", "max");
+
+                               retval= chdir(cwd);
+                               if (retval == -1)
+                               {
+                                       g_error(strerror(errno));
+                               }
+                               free(cwd);
+
+                               // Build the list of absisca values for the points in the accuracy graph
+                               xValues= g_array_sized_new(FALSE, FALSE, sizeof(uint64_t),
+                                       g_queue_get_length(hullArray[i][j]) +
+                                       g_queue_get_length(hullArray[j][i]));
+
+                               g_queue_foreach(hullArray[i][j], &gfAddAbsiscaToArray, xValues);
+                               g_queue_foreach(hullArray[j][i], &gfAddAbsiscaToArray, xValues);
+
+                               g_array_sort(xValues, &gcfCompareUint64);
+
+                               /* For each absisca value and each optimisation direction, solve the LP
+                                * and write a line in the data file */
+                               for (it= 0; it < xValues->len; it++)
+                               {
+                                       uint64_t time;
+                                       CorrectedTime correctedTime;
+
+                                       time= g_array_index(xValues, uint64_t, it);
+                                       timeCorrectionLP(lp, lpFactors, time, &correctedTime);
+                                       fprintf(fp, "%24" PRIu64 " %24" PRIu64 " %24" PRIu64
+                                               "%24" PRIu64 "\n", time, correctedTime.time,
+                                               correctedTime.min, correctedTime.max);
+                               }
+
+                               g_array_free(xValues, TRUE);
+                               fclose(fp);
+                       }
+               }
+       }
+
+       if (syncState->stats)
+       {
+               lpFactorsArray->refCount++;
+               analysisData->stats->lpFactors= lpFactorsArray;
+       }
+
+       if (syncState->graphsStream)
+       {
+               lpFactorsArray->refCount++;
+               analysisData->graphsData->lpFactors= lpFactorsArray;
+       }
+
+       return lpFactorsArray;
+}
+
+
+/*
+ * Perform correction on one time value and calculate accuracy bounds.
+ *
+ * Args:
+ *   lp:           Linear Programming problem containing the coefficients for
+ *                 the trace pair between which to perform time correction.
+ *   lpFactors:    Correction factors for this trace pair, the factors must be
+ *                 of type ACCURATE.
+ *   time:         Time value to correct.
+ *   correctedTime: Result of the time correction, preallocated.
+ */
+void timeCorrectionLP(glp_prob* const lp, const PairFactors* const lpFactors,
+       const uint64_t time, CorrectedTime* const correctedTime)
+{
+       unsigned int it;
+       const struct
+       {
+               int direction;
+               size_t offset;
+       } loopValues[]= {
+               {GLP_MIN, offsetof(CorrectedTime, min)},
+               {GLP_MAX, offsetof(CorrectedTime, max)}
+       };
+
+       glp_set_obj_coef(lp, 1, 1.);
+       glp_set_obj_coef(lp, 2, time);
+
+       g_assert(lpFactors->type == ACCURATE);
+
+       correctedTime->time= lpFactors->approx->offset + lpFactors->approx->drift
+               * time;
+
+       for (it= 0; it < ARRAY_SIZE(loopValues); it++)
+       {
+               int status;
+               int retval;
+
+               glp_set_obj_dir(lp, loopValues[it].direction);
+               retval= glp_simplex(lp, NULL);
+               status= glp_get_status(lp);
+
+               g_assert(retval == 0 && status == GLP_OPT);
+               *(uint64_t*) ((void*) correctedTime + loopValues[it].offset)=
+                       round(glp_get_obj_val(lp));
+       }
+}
+
+
+/*
+ * Write the analysis-specific graph lines in the gnuplot script.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ *   i:            first trace number
+ *   j:            second trace number, garanteed to be larger than i
+ */
+static void writeAnalysisTraceTimeBackPlotsCHull(SyncState* const syncState,
+       const unsigned int i, const unsigned int j)
+{
+       if (((AnalysisDataCHull*)
+                       syncState->analysisData)->graphsData->lpFactors->pairFactors[j][i].type
+               == ACCURATE)
+       {
+               fprintf(syncState->graphsStream,
+                       "\t\"analysis_chull_accuracy-%1$03u_and_%2$03u.data\" "
+                               "using 1:(($3 - $2) / clock_freq_%2$u):(($4 - $2) / clock_freq_%2$u) "
+                               "title \"Synchronization accuracy\" "
+                               "with filledcurves linewidth 2 linetype 1 "
+                               "linecolor rgb \"black\" fill solid 0.25 noborder, \\\n", i,
+                               j);
+       }
+}
+
+
+/*
+ * Write the analysis-specific graph lines in the gnuplot script.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ *   i:            first trace number
+ *   j:            second trace number, garanteed to be larger than i
+ */
+static void writeAnalysisTraceTimeForePlotsCHull(SyncState* const syncState,
+       const unsigned int i, const unsigned int j)
+{
+       if (((AnalysisDataCHull*)
+                       syncState->analysisData)->graphsData->lpFactors->pairFactors[j][i].type
+               == ACCURATE)
+       {
+               fprintf(syncState->graphsStream,
+                       "\t\"analysis_chull_accuracy-%1$03u_and_%2$03u.data\" "
+                               "using 1:(($3 - $2) / clock_freq_%2$u) notitle "
+                               "with lines linewidth 2 linetype 1 "
+                               "linecolor rgb \"gray60\", \\\n"
+                       "\t\"analysis_chull_accuracy-%1$03u_and_%2$03u.data\" "
+                               "using 1:(($4 - $2) / clock_freq_%2$u) notitle "
+                               "with lines linewidth 2 linetype 1 "
+                               "linecolor rgb \"gray60\", \\\n", i, j);
+       }
+}
+
+
+/*
+ * Write the analysis-specific graph lines in the gnuplot script.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ *   i:            first trace number
+ *   j:            second trace number, garanteed to be larger than i
+ */
+static void writeAnalysisTraceTraceBackPlotsCHull(SyncState* const syncState,
+       const unsigned int i, const unsigned int j)
+{
+       if (((AnalysisDataCHull*)
+                       syncState->analysisData)->graphsData->lpFactors->pairFactors[j][i].type
+               == ACCURATE)
+       {
+               fprintf(syncState->graphsStream,
+                       "\t\"analysis_chull_accuracy-%1$03u_and_%2$03u.data\" "
+                       "using 1:3:4 "
+                       "title \"Synchronization accuracy\" "
+                       "with filledcurves linewidth 2 linetype 1 "
+                       "linecolor rgb \"black\" fill solid 0.25 noborder, \\\n", i, j);
+       }
+}
+#endif
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