Make the accuracy area easier to see on the broadcast graphs
[lttv.git] / lttv / lttv / sync / event_analysis_eval.c
index 57ee73ec7a9fdead2f6312d12811a9bf9d32ff18..3c1b110aeeee1e7f766cd7805952b60694c90566 100644 (file)
 
 #include "lookup3.h"
 #include "sync_chain.h"
+#include "event_analysis_chull.h"
 
 #include "event_analysis_eval.h"
 
 
+struct WriteHistogramInfo
+{
+       GHashTable* rttInfo;
+       FILE* graphsStream;
+};
+
+#ifdef HAVE_LIBGLPK
+struct LPAddRowInfo
+{
+       glp_prob* lp;
+       int boundType;
+       GArray* iArray, * jArray, * aArray;
+};
+#endif
+
 // Functions common to all analysis modules
 static void initAnalysisEval(SyncState* const syncState);
 static void destroyAnalysisEval(SyncState* const syncState);
@@ -52,10 +68,14 @@ static void analyzeBroadcastEval(SyncState* const syncState, Broadcast* const
        broadcast);
 static GArray* finalizeAnalysisEval(SyncState* const syncState);
 static void printAnalysisStatsEval(SyncState* const syncState);
-static void writeAnalysisGraphsPlotsEval(SyncState* const syncState, const
-       unsigned int i, const unsigned int j);
-static void writeAnalysisGraphsOptionsEval(SyncState* const syncState, const
-       unsigned int i, const unsigned int j);
+static void writeAnalysisTraceTimeBackPlotsEval(SyncState* const syncState,
+       const unsigned int i, const unsigned int j);
+static void writeAnalysisTraceTimeForePlotsEval(SyncState* const syncState,
+       const unsigned int i, const unsigned int j);
+static void writeAnalysisTraceTraceBackPlotsEval(SyncState* const syncState,
+       const unsigned int i, const unsigned int j);
+static void writeAnalysisTraceTraceForePlotsEval(SyncState* const syncState,
+       const unsigned int i, const unsigned int j);
 
 // Functions specific to this module
 static void registerAnalysisEval() __attribute__((constructor (102)));
@@ -68,19 +88,46 @@ static void positionStream(FILE* stream);
 
 static void gfSum(gpointer data, gpointer userData);
 static void gfSumSquares(gpointer data, gpointer userData);
-static void ghfPrintExchangeRtt(gpointer key, gpointer value, gpointer user_data);
+static void ghfPrintExchangeRtt(gpointer key, gpointer value, gpointer
+       user_data);
 
-static void initGraphs(SyncState* const syncState);
-static void writeGraphFiles(SyncState* const syncState);
-static void dumpBinToFile(const uint32_t* const bin, const uint32_t total,
-       FILE* const file);
-static void destroyGraphs(SyncState* const syncState);
+static void hitBin(struct Bins* const bins, const double value);
 static unsigned int binNum(const double value) __attribute__((pure));
 static double binStart(const unsigned int binNum) __attribute__((pure));
 static double binEnd(const unsigned int binNum) __attribute__((pure));
+static uint32_t normalTotal(struct Bins* const bins) __attribute__((const));
+
+static AnalysisHistogramEval* constructAnalysisHistogramEval(const char* const
+       graphsDir, const struct RttKey* const rttKey);
+static void destroyAnalysisHistogramEval(AnalysisHistogramEval* const
+       histogram);
+static void gdnDestroyAnalysisHistogramEval(gpointer data);
+static void ghfWriteHistogram(gpointer key, gpointer value, gpointer
+       user_data);
+static void dumpBinToFile(const struct Bins* const bins, FILE* const file);
+static void writeHistogram(FILE* graphsStream, const struct RttKey* rttKey,
+       double* minRtt, AnalysisHistogramEval* const histogram);
+
+static void updateBounds(Bounds** const bounds, Event* const e1, Event* const
+       e2);
+
+// The next group of functions is only needed when computing synchronization
+// accuracy.
+#ifdef HAVE_LIBGLPK
+static glp_prob* lpCreateProblem(GQueue* const lowerHull, GQueue* const
+       upperHull);
+static void gfLPAddRow(gpointer data, gpointer user_data);
+static Factors* calculateFactors(glp_prob* const lp, const int direction);
+static void calculateCompleteFactors(glp_prob* const lp, FactorsCHull*
+       factors);
+static FactorsCHull** createAllFactors(const unsigned int traceNb);
+static inline void finalizeAnalysisEvalLP(SyncState* const syncState);
+#else
+static void finalizeAnalysisEvalLP(SyncState* const syncState);
+#endif
 
 
-const unsigned int binNb= 10000;
+// initialized in registerAnalysisEval()
 double binBase;
 
 static AnalysisModule analysisModuleEval= {
@@ -92,8 +139,12 @@ static AnalysisModule analysisModuleEval= {
        .analyzeBroadcast= &analyzeBroadcastEval,
        .finalizeAnalysis= &finalizeAnalysisEval,
        .printAnalysisStats= &printAnalysisStatsEval,
-       .writeAnalysisGraphsPlots= &writeAnalysisGraphsPlotsEval,
-       .writeAnalysisGraphsOptions= &writeAnalysisGraphsOptionsEval,
+       .graphFunctions= {
+               .writeTraceTimeBackPlots= &writeAnalysisTraceTimeBackPlotsEval,
+               .writeTraceTimeForePlots= &writeAnalysisTraceTimeForePlotsEval,
+               .writeTraceTraceBackPlots= &writeAnalysisTraceTraceBackPlotsEval,
+               .writeTraceTraceForePlots= &writeAnalysisTraceTraceForePlotsEval,
+       }
 };
 
 static ModuleOption optionEvalRttFile= {
@@ -110,6 +161,8 @@ static ModuleOption optionEvalRttFile= {
  */
 static void registerAnalysisEval()
 {
+       binBase= exp10(6. / (BIN_NB - 3));
+
        g_queue_push_tail(&analysisModules, &analysisModuleEval);
        g_queue_push_tail(&moduleOptions, &optionEvalRttFile);
 }
@@ -127,7 +180,7 @@ static void registerAnalysisEval()
 static void initAnalysisEval(SyncState* const syncState)
 {
        AnalysisDataEval* analysisData;
-       unsigned int i;
+       unsigned int i, j;
 
        analysisData= malloc(sizeof(AnalysisDataEval));
        syncState->analysisData= analysisData;
@@ -170,99 +223,106 @@ static void initAnalysisEval(SyncState* const syncState)
                analysisData->stats->exchangeRtt=
                        g_hash_table_new_full(&ghfRttKeyHash, &gefRttKeyEqual,
                                &gdnDestroyRttKey, &gdnDestroyDouble);
+
+#ifdef HAVE_LIBGLPK
+               analysisData->stats->chFactorsArray= NULL;
+               analysisData->stats->lpFactorsArray= NULL;
+#endif
        }
 
        if (syncState->graphsStream)
        {
-               binBase= exp10(6. / (binNb - 2));
-               analysisData->graphs= malloc(sizeof(AnalysisGraphsEval));
-               initGraphs(syncState);
+               AnalysisGraphsEval* graphs= malloc(sizeof(AnalysisGraphsEval));
+
+               analysisData->graphs= graphs;
+
+               graphs->histograms= g_hash_table_new_full(&ghfRttKeyHash,
+                       &gefRttKeyEqual, &gdnDestroyRttKey,
+                       &gdnDestroyAnalysisHistogramEval);
+
+               graphs->bounds= malloc(syncState->traceNb * sizeof(Bounds*));
+               for (i= 0; i < syncState->traceNb; i++)
+               {
+                       graphs->bounds[i]= malloc(i * sizeof(Bounds));
+                       for (j= 0; j < i; j++)
+                       {
+                               graphs->bounds[i][j].min= UINT64_MAX;
+                               graphs->bounds[i][j].max= 0;
+                       }
+               }
+
+#ifdef HAVE_LIBGLPK
+               graphs->lps= NULL;
+               graphs->lpFactorsArray= NULL;
+#endif
+       }
+
+       if (syncState->stats || syncState->graphsStream)
+       {
+               GList* result;
+
+               analysisData->chullSS= malloc(sizeof(SyncState));
+               memcpy(analysisData->chullSS, syncState, sizeof(SyncState));
+               analysisData->chullSS->stats= false;
+               analysisData->chullSS->analysisData= NULL;
+               result= g_queue_find_custom(&analysisModules, "chull",
+                       &gcfCompareAnalysis);
+               analysisData->chullSS->analysisModule= (AnalysisModule*) result->data;
+               analysisData->chullSS->analysisModule->initAnalysis(analysisData->chullSS);
        }
 }
 
 
 /*
- * Create and open files used to store histogram points to genereate
- * graphs. Allocate and populate array to store file pointers.
- *
- * Also create data structures to store histogram points during analysis.
+ * Create and open files used to store histogram points to generate graphs.
+ * Create data structures to store histogram points during analysis.
  *
  * Args:
- *   syncState:    container for synchronization data
+ *   graphsDir:    folder where to write files
+ *   rttKey:       host pair, make sure saddr < daddr
  */
-static void initGraphs(SyncState* const syncState)
+static AnalysisHistogramEval* constructAnalysisHistogramEval(const char* const
+       graphsDir, const struct RttKey* const rttKey)
 {
-       unsigned int i, j;
        int retval;
+       unsigned int i;
        char* cwd;
-       char name[36];
-       AnalysisDataEval* analysisData= syncState->analysisData;
-
-       cwd= changeToGraphDir(syncState->graphsDir);
-
-       analysisData->graphs->ttPoints= malloc(syncState->traceNb *
-               sizeof(FILE**));
-       analysisData->graphs->ttBinsArray= malloc(syncState->traceNb *
-               sizeof(uint32_t**));
-       analysisData->graphs->ttBinsTotal= malloc(syncState->traceNb *
-               sizeof(uint32_t*));
-       for (i= 0; i < syncState->traceNb; i++)
+       char name[60], saddr[16], daddr[16];
+       AnalysisHistogramEval* histogram= calloc(1, sizeof(*histogram));
+       const struct {
+               size_t pointsOffset;
+               const char* fileName;
+               const char* host1, *host2;
+       } loopValues[]= {
+               {offsetof(AnalysisHistogramEval, ttSendPoints),
+                       "analysis_eval_tt-%s_to_%s.data", saddr, daddr},
+               {offsetof(AnalysisHistogramEval, ttRecvPoints),
+                       "analysis_eval_tt-%s_to_%s.data", daddr, saddr},
+               {offsetof(AnalysisHistogramEval, hrttPoints),
+                       "analysis_eval_hrtt-%s_and_%s.data", saddr, daddr},
+       };
+
+       histogram->ttSendBins.min= BIN_NB - 1;
+       histogram->ttRecvBins.min= BIN_NB - 1;
+       histogram->hrttBins.min= BIN_NB - 1;
+
+       convertIP(saddr, rttKey->saddr);
+       convertIP(daddr, rttKey->daddr);
+
+       cwd= changeToGraphDir(graphsDir);
+
+       for (i= 0; i < sizeof(loopValues) / sizeof(*loopValues); i++)
        {
-               analysisData->graphs->ttPoints[i]= malloc(syncState->traceNb *
-                       sizeof(FILE*));
-               analysisData->graphs->ttBinsArray[i]= malloc(syncState->traceNb *
-                       sizeof(uint32_t*));
-               analysisData->graphs->ttBinsTotal[i]= calloc(syncState->traceNb,
-                       sizeof(uint32_t));
-               for (j= 0; j < syncState->traceNb; j++)
+               retval= snprintf(name, sizeof(name), loopValues[i].fileName,
+                       loopValues[i].host1, loopValues[i].host2);
+               if (retval > sizeof(name) - 1)
                {
-                       if (i != j)
-                       {
-                               retval= snprintf(name, sizeof(name),
-                                       "analysis_eval_tt-%03u_to_%03u.data", i, j);
-                               if (retval > sizeof(name) - 1)
-                               {
-                                       name[sizeof(name) - 1]= '\0';
-                               }
-                               if ((analysisData->graphs->ttPoints[i][j]= fopen(name, "w")) ==
-                                       NULL)
-                               {
-                                       g_error(strerror(errno));
-                               }
-
-                               analysisData->graphs->ttBinsArray[i][j]= calloc(binNb,
-                                       sizeof(uint32_t));
-                       }
+                       name[sizeof(name) - 1]= '\0';
                }
-       }
-
-       analysisData->graphs->hrttPoints= malloc(syncState->traceNb *
-               sizeof(FILE**));
-       analysisData->graphs->hrttBinsArray= malloc(syncState->traceNb *
-               sizeof(uint32_t**));
-       analysisData->graphs->hrttBinsTotal= malloc(syncState->traceNb *
-               sizeof(uint32_t*));
-       for (i= 0; i < syncState->traceNb; i++)
-       {
-               analysisData->graphs->hrttPoints[i]= malloc(i * sizeof(FILE*));
-               analysisData->graphs->hrttBinsArray[i]= malloc(i * sizeof(uint32_t*));
-               analysisData->graphs->hrttBinsTotal[i]= calloc(i, sizeof(uint32_t));
-               for (j= 0; j < i; j++)
+               if ((*(FILE**)((void*) histogram + loopValues[i].pointsOffset)=
+                               fopen(name, "w")) == NULL)
                {
-                       retval= snprintf(name, sizeof(name),
-                               "analysis_eval_hrtt-%03u_and_%03u.data", i, j);
-                       if (retval > sizeof(name) - 1)
-                       {
-                               name[sizeof(name) - 1]= '\0';
-                       }
-                       if ((analysisData->graphs->hrttPoints[i][j]= fopen(name, "w")) ==
-                               NULL)
-                       {
-                               g_error(strerror(errno));
-                       }
-
-                       analysisData->graphs->hrttBinsArray[i][j]= calloc(binNb,
-                               sizeof(uint32_t));
+                       g_error(strerror(errno));
                }
        }
 
@@ -272,41 +332,89 @@ static void initGraphs(SyncState* const syncState)
                g_error(strerror(errno));
        }
        free(cwd);
+
+       return histogram;
 }
 
 
 /*
- * Write histogram points to all files to generate graphs.
+ * Close files used to store histogram points to generate graphs.
  *
  * Args:
- *   syncState:    container for synchronization data
+ *   graphsDir:    folder where to write files
+ *   rttKey:       host pair, make sure saddr < daddr
  */
-static void writeGraphFiles(SyncState* const syncState)
+static void destroyAnalysisHistogramEval(AnalysisHistogramEval* const
+       histogram)
 {
-       unsigned int i, j;
-       AnalysisDataEval* analysisData= syncState->analysisData;
-
-       for (i= 0; i < syncState->traceNb; i++)
+       unsigned int i;
+       int retval;
+       const struct {
+               size_t pointsOffset;
+       } loopValues[]= {
+               {offsetof(AnalysisHistogramEval, ttSendPoints)},
+               {offsetof(AnalysisHistogramEval, ttRecvPoints)},
+               {offsetof(AnalysisHistogramEval, hrttPoints)},
+       };
+
+       for (i= 0; i < sizeof(loopValues) / sizeof(*loopValues); i++)
        {
-               for (j= 0; j < syncState->traceNb; j++)
+               retval= fclose(*(FILE**)((void*) histogram + loopValues[i].pointsOffset));
+               if (retval != 0)
                {
-                       if (i != j)
-                       {
-                               dumpBinToFile(analysisData->graphs->ttBinsArray[i][j],
-                                       analysisData->graphs->ttBinsTotal[i][j] -
-                                       analysisData->graphs->ttBinsArray[i][j][binNb - 1],
-                                       analysisData->graphs->ttPoints[i][j]);
-                       }
-
-                       if (i > j)
-                       {
-                               dumpBinToFile(analysisData->graphs->hrttBinsArray[i][j],
-                                       analysisData->graphs->hrttBinsTotal[i][j] -
-                                       analysisData->graphs->hrttBinsArray[i][j][binNb - 1],
-                                       analysisData->graphs->hrttPoints[i][j]);
-                       }
+                       g_error(strerror(errno));
                }
        }
+
+       free(histogram);
+}
+
+
+/*
+ * A GDestroyNotify function for g_hash_table_new_full()
+ *
+ * Args:
+ *   data:         AnalysisHistogramEval*
+ */
+static void gdnDestroyAnalysisHistogramEval(gpointer data)
+{
+       destroyAnalysisHistogramEval(data);
+}
+
+
+/*
+ * A GHFunc for g_hash_table_foreach()
+ *
+ * Args:
+ *   key:          RttKey* where saddr < daddr
+ *   value:        AnalysisHistogramEval*
+ *   user_data     struct WriteHistogramInfo*
+ */
+static void ghfWriteHistogram(gpointer key, gpointer value, gpointer user_data)
+{
+       double* rtt1, * rtt2;
+       struct RttKey* rttKey= key;
+       struct RttKey oppositeRttKey= {.saddr= rttKey->daddr, .daddr=
+               rttKey->saddr};
+       AnalysisHistogramEval* histogram= value;
+       struct WriteHistogramInfo* info= user_data;
+
+       rtt1= g_hash_table_lookup(info->rttInfo, rttKey);
+       rtt2= g_hash_table_lookup(info->rttInfo, &oppositeRttKey);
+
+       if (rtt1 == NULL)
+       {
+               rtt1= rtt2;
+       }
+       else if (rtt2 != NULL)
+       {
+               rtt1= MIN(rtt1, rtt2);
+       }
+
+       dumpBinToFile(&histogram->ttSendBins, histogram->ttSendPoints);
+       dumpBinToFile(&histogram->ttRecvBins, histogram->ttRecvPoints);
+       dumpBinToFile(&histogram->hrttBins, histogram->hrttPoints);
+       writeHistogram(info->graphsStream, rttKey, rtt1, histogram);
 }
 
 
@@ -315,90 +423,102 @@ static void writeGraphFiles(SyncState* const syncState)
  *
  * Args:
  *   bin:          array of values that make up a histogram
- *   total:        total number of messages in bins 0 to binNb - 2
- *   file:         FILE*
+ *   file:         FILE*, write to this file
  */
-static void dumpBinToFile(const uint32_t* const bin, const uint32_t total,
-       FILE* const file)
+static void dumpBinToFile(const struct Bins* const bins, FILE* const file)
 {
        unsigned int i;
 
-       // Last bin is skipped because is continues till infinity
-       for (i= 0; i < binNb - 1; i++)
+       // The first and last bins are skipped, see struct Bins
+       for (i= 1; i < BIN_NB - 1; i++)
        {
-               if (bin[i] > 0)
+               if (bins->bin[i] > 0)
                {
-                       fprintf(file, "%20.9f %20.9f %20.9f\n", (binStart(i) + binEnd(i)) / 2, (double) bin[i]
-                               / ((binEnd(i) - binStart(i)) * total), binEnd(i) - binStart(i));
+                       fprintf(file, "%20.9f %20.9f %20.9f\n", (binStart(i) + binEnd(i))
+                               / 2., (double) bins->bin[i] / ((binEnd(i) - binStart(i)) *
+                                       bins->total), binEnd(i) - binStart(i));
                }
        }
 }
 
 
 /*
- * Close files used to store histogram points to generate graphs. Deallocate
- * arrays of file pointers and arrays used to store histogram points during
- * analysis.
+ * Write the analysis-specific plot in the gnuplot script.
  *
  * Args:
- *   syncState:    container for synchronization data
+ *   graphsStream: write to this file
+ *   rttKey:       must be sorted such that saddr < daddr
+ *   minRtt:       if available, else NULL
+ *   histogram:    struct that contains the bins for the pair of traces
+ *                 identified by rttKey
  */
-static void destroyGraphs(SyncState* const syncState)
+static void writeHistogram(FILE* graphsStream, const struct RttKey* rttKey,
+       double* minRtt, AnalysisHistogramEval* const histogram)
 {
-       unsigned int i, j;
-       AnalysisDataEval* analysisData= syncState->analysisData;
-       int retval;
+       char saddr[16], daddr[16];
+
+       convertIP(saddr, rttKey->saddr);
+       convertIP(daddr, rttKey->daddr);
 
-       if (analysisData->graphs == NULL || analysisData->graphs->ttPoints ==
-               NULL)
+       fprintf(graphsStream,
+               "\nreset\n"
+               "set output \"histogram-%s-%s.eps\"\n"
+               "set title \"\"\n"
+               "set xlabel \"Message Latency (s)\"\n"
+               "set ylabel \"Proportion of messages per second\"\n", saddr, daddr);
+
+       if (minRtt != NULL)
        {
-               return;
+               fprintf(graphsStream,
+                       "set arrow from %.9f, 0 rto 0, graph 1 "
+                       "nohead linetype 3 linewidth 3 linecolor rgb \"black\"\n", *minRtt
+                       / 2);
        }
 
-       for (i= 0; i < syncState->traceNb; i++)
+       if (normalTotal(&histogram->ttSendBins) ||
+               normalTotal(&histogram->ttRecvBins) ||
+               normalTotal(&histogram->hrttBins))
        {
-               for (j= 0; j < syncState->traceNb; j++)
+               fprintf(graphsStream, "plot \\\n");
+
+               if (normalTotal(&histogram->hrttBins))
                {
-                       if (i != j)
-                       {
-                               retval= fclose(analysisData->graphs->ttPoints[i][j]);
-                               if (retval != 0)
-                               {
-                                       g_error(strerror(errno));
-                               }
+                       fprintf(graphsStream,
+                               "\t\"analysis_eval_hrtt-%s_and_%s.data\" "
+                                       "title \"RTT/2\" with linespoints linetype 1 linewidth 2 "
+                                       "linecolor rgb \"black\" pointtype 6 pointsize 1,\\\n",
+                                       saddr, daddr);
+               }
 
-                               free(analysisData->graphs->ttBinsArray[i][j]);
-                       }
+               if (normalTotal(&histogram->ttSendBins))
+               {
+                       fprintf(graphsStream,
+                               "\t\"analysis_eval_tt-%1$s_to_%2$s.data\" "
+                                       "title \"%1$s to %2$s\" with linespoints linetype 4 linewidth 2 "
+                                       "linecolor rgb \"gray60\" pointtype 6 pointsize 1,\\\n",
+                                       saddr, daddr);
                }
-               free(analysisData->graphs->ttPoints[i]);
-               free(analysisData->graphs->ttBinsArray[i]);
-               free(analysisData->graphs->ttBinsTotal[i]);
-       }
-       free(analysisData->graphs->ttPoints);
-       free(analysisData->graphs->ttBinsArray);
-       free(analysisData->graphs->ttBinsTotal);
 
-       for (i= 0; i < syncState->traceNb; i++)
-       {
-               for (j= 0; j < i; j++)
+               if (normalTotal(&histogram->ttRecvBins))
                {
-                       retval= fclose(analysisData->graphs->hrttPoints[i][j]);
-                       if (retval != 0)
-                       {
-                               g_error(strerror(errno));
-                       }
+                       fprintf(graphsStream,
+                               "\t\"analysis_eval_tt-%1$s_to_%2$s.data\" "
+                                       "title \"%1$s to %2$s\" with linespoints linetype 4 linewidth 2 "
+                                       "linecolor rgb \"gray30\" pointtype 6 pointsize 1,\\\n",
+                                       daddr, saddr);
+               }
 
-                       free(analysisData->graphs->hrttBinsArray[i][j]);
+               // Remove the ",\\\n" from the last graph plot line
+               if (ftruncate(fileno(graphsStream), ftell(graphsStream) - 3) == -1)
+               {
+                       g_error(strerror(errno));
+               }
+               if (fseek(graphsStream, 0, SEEK_END) == -1)
+               {
+                       g_error(strerror(errno));
                }
-               free(analysisData->graphs->hrttPoints[i]);
-               free(analysisData->graphs->hrttBinsArray[i]);
-               free(analysisData->graphs->hrttBinsTotal[i]);
+               fprintf(graphsStream, "\n");
        }
-       free(analysisData->graphs->hrttPoints);
-       free(analysisData->graphs->hrttBinsArray);
-       free(analysisData->graphs->hrttBinsTotal);
-
-       analysisData->graphs->ttPoints= NULL;
 }
 
 
@@ -412,36 +532,79 @@ static void destroyGraphs(SyncState* const syncState)
  */
 static void destroyAnalysisEval(SyncState* const syncState)
 {
-       unsigned int i;
+       unsigned int i, j;
        AnalysisDataEval* analysisData;
 
        analysisData= (AnalysisDataEval*) syncState->analysisData;
 
-       if (analysisData == NULL || analysisData->rttInfo == NULL)
+       if (analysisData == NULL)
        {
                return;
        }
 
        g_hash_table_destroy(analysisData->rttInfo);
-       analysisData->rttInfo= NULL;
 
        if (syncState->stats)
        {
+               AnalysisStatsEval* stats= analysisData->stats;
+
+               for (i= 0; i < syncState->traceNb; i++)
+               {
+                       free(stats->messageStats[i]);
+               }
+               free(stats->messageStats);
+
+               g_hash_table_destroy(stats->exchangeRtt);
+
+#ifdef HAVE_LIBGLPK
+               freeAllFactors(syncState->traceNb, stats->chFactorsArray);
+               freeAllFactors(syncState->traceNb, stats->lpFactorsArray);
+#endif
+
+               free(stats);
+       }
+
+       if (syncState->graphsStream)
+       {
+               AnalysisGraphsEval* graphs= analysisData->graphs;
+
+               if (graphs->histograms)
+               {
+                       g_hash_table_destroy(graphs->histograms);
+               }
+
+               for (i= 0; i < syncState->traceNb; i++)
+               {
+                       free(graphs->bounds[i]);
+               }
+               free(graphs->bounds);
+
+#ifdef HAVE_LIBGLPK
                for (i= 0; i < syncState->traceNb; i++)
                {
-                       free(analysisData->stats->messageStats[i]);
+                       for (j= 0; j < i; j++)
+                       {
+                               // There seems to be a memory leak in glpk, valgrind reports a
+                               // loss even if the problem is deleted
+                               glp_delete_prob(graphs->lps[i][j]);
+                       }
+                       free(graphs->lps[i]);
                }
-               free(analysisData->stats->messageStats);
+               free(graphs->lps);
 
-               g_hash_table_destroy(analysisData->stats->exchangeRtt);
+               if (!syncState->stats)
+               {
+                       freeAllFactors(syncState->traceNb, graphs->lpFactorsArray);
+               }
+#endif
 
-               free(analysisData->stats);
+               free(graphs);
        }
 
-       if (syncState->graphsStream && analysisData->graphs)
+       if (syncState->stats || syncState->graphsStream)
        {
-               destroyGraphs(syncState);
-               free(analysisData->graphs);
+               analysisData->chullSS->analysisModule->destroyAnalysis(analysisData->chullSS);
+               free(analysisData->chullSS);
        }
 
        free(syncState->analysisData);
@@ -458,56 +621,96 @@ static void destroyAnalysisEval(SyncState* const syncState)
  *   syncState     container for synchronization data
  *   message       structure containing the events
  */
-static void analyzeMessageEval(SyncState* const syncState, Message* const message)
+static void analyzeMessageEval(SyncState* const syncState, Message* const
+       message)
 {
-       AnalysisDataEval* analysisData;
-       MessageStats* messageStats;
+       AnalysisDataEval* analysisData= syncState->analysisData;
+       MessageStats* messageStats=
+               &analysisData->stats->messageStats[message->outE->traceNum][message->inE->traceNum];
        double* rtt;
        double tt;
        struct RttKey rttKey;
 
-       if (!syncState->stats)
+       g_assert(message->inE->type == TCP);
+
+       if (syncState->stats)
        {
-               return;
+               messageStats->total++;
        }
 
-       analysisData= (AnalysisDataEval*) syncState->analysisData;
-       messageStats=
-               &analysisData->stats->messageStats[message->outE->traceNum][message->inE->traceNum];
-
-       messageStats->total++;
-
        tt= wallTimeSub(&message->inE->wallTime, &message->outE->wallTime);
        if (tt <= 0)
        {
-               messageStats->inversionNb++;
+               if (syncState->stats)
+               {
+                       messageStats->inversionNb++;
+               }
        }
        else if (syncState->graphsStream)
        {
-               analysisData->graphs->ttBinsArray[message->outE->traceNum][message->inE->traceNum][binNum(tt)]++;
-               analysisData->graphs->ttBinsTotal[message->outE->traceNum][message->inE->traceNum]++;
+               struct RttKey rttKey= {
+                       .saddr=MIN(message->inE->event.tcpEvent->segmentKey->connectionKey.saddr,
+                               message->inE->event.tcpEvent->segmentKey->connectionKey.daddr),
+                       .daddr=MAX(message->inE->event.tcpEvent->segmentKey->connectionKey.saddr,
+                               message->inE->event.tcpEvent->segmentKey->connectionKey.daddr),
+               };
+               AnalysisHistogramEval* histogram=
+                       g_hash_table_lookup(analysisData->graphs->histograms, &rttKey);
+
+               if (histogram == NULL)
+               {
+                       struct RttKey* tableKey= malloc(sizeof(*tableKey));
+
+                       histogram= constructAnalysisHistogramEval(syncState->graphsDir, &rttKey);
+                       memcpy(tableKey, &rttKey, sizeof(*tableKey));
+                       g_hash_table_insert(analysisData->graphs->histograms, tableKey, histogram);
+               }
+
+               if (message->inE->event.udpEvent->datagramKey->saddr <
+                       message->inE->event.udpEvent->datagramKey->daddr)
+               {
+                       hitBin(&histogram->ttSendBins, tt);
+               }
+               else
+               {
+                       hitBin(&histogram->ttRecvBins, tt);
+               }
        }
 
-       g_assert(message->inE->type == TCP);
-       rttKey.saddr=
-               message->inE->event.tcpEvent->segmentKey->connectionKey.saddr;
-       rttKey.daddr=
-               message->inE->event.tcpEvent->segmentKey->connectionKey.daddr;
-       rtt= g_hash_table_lookup(analysisData->rttInfo, &rttKey);
-       g_debug("rttInfo, looking up (%u, %u)->(%f)", rttKey.saddr,
-               rttKey.daddr, rtt ? *rtt : NAN);
-
-       if (rtt)
-       {
-               g_debug("rttInfo, tt: %f rtt / 2: %f", tt, *rtt / 2.);
-               if (tt < *rtt / 2.)
+       if (syncState->stats)
+       {
+               rttKey.saddr=
+                       message->inE->event.tcpEvent->segmentKey->connectionKey.saddr;
+               rttKey.daddr=
+                       message->inE->event.tcpEvent->segmentKey->connectionKey.daddr;
+               rtt= g_hash_table_lookup(analysisData->rttInfo, &rttKey);
+               g_debug("rttInfo, looking up (%u, %u)->(%f)", rttKey.saddr,
+                       rttKey.daddr, rtt ? *rtt : NAN);
+
+               if (rtt)
+               {
+                       g_debug("rttInfo, tt: %f rtt / 2: %f", tt, *rtt / 2.);
+                       if (tt < *rtt / 2.)
+                       {
+                               messageStats->tooFastNb++;
+                       }
+               }
+               else
                {
-                       messageStats->tooFastNb++;
+                       messageStats->noRTTInfoNb++;
                }
        }
-       else
+
+       if (syncState->graphsStream)
+       {
+               updateBounds(analysisData->graphs->bounds, message->inE,
+                       message->outE);
+       }
+
+       if (syncState->stats || syncState->graphsStream)
        {
-               messageStats->noRTTInfoNb++;
+               analysisData->chullSS->analysisModule->analyzeMessage(analysisData->chullSS,
+                       message);
        }
 }
 
@@ -521,7 +724,8 @@ static void analyzeMessageEval(SyncState* const syncState, Message* const messag
  *   syncState     container for synchronization data
  *   exchange      structure containing the messages
  */
-static void analyzeExchangeEval(SyncState* const syncState, Exchange* const exchange)
+static void analyzeExchangeEval(SyncState* const syncState, Exchange* const
+       exchange)
 {
        AnalysisDataEval* analysisData= syncState->analysisData;
        Message* m1= g_queue_peek_tail(exchange->acks);
@@ -529,26 +733,13 @@ static void analyzeExchangeEval(SyncState* const syncState, Exchange* const exch
        struct RttKey* rttKey;
        double* rtt, * exchangeRtt;
 
-       if (!syncState->stats)
-       {
-               return;
-       }
+       g_assert(m1->inE->type == TCP);
 
        // (T2 - T1) - (T3 - T4)
        rtt= malloc(sizeof(double));
        *rtt= wallTimeSub(&m1->inE->wallTime, &m1->outE->wallTime) -
                wallTimeSub(&m2->outE->wallTime, &m2->inE->wallTime);
 
-       if (syncState->graphsStream)
-       {
-               unsigned int row= MAX(m1->inE->traceNum, m1->outE->traceNum);
-               unsigned int col= MIN(m1->inE->traceNum, m1->outE->traceNum);
-
-               analysisData->graphs->hrttBinsArray[row][col][binNum(*rtt / 2.)]++;
-               analysisData->graphs->hrttBinsTotal[row][col]++;
-       }
-
-       g_assert(m1->inE->type == TCP);
        rttKey= malloc(sizeof(struct RttKey));
        rttKey->saddr=
                MIN(m1->inE->event.tcpEvent->segmentKey->connectionKey.saddr,
@@ -556,19 +747,52 @@ static void analyzeExchangeEval(SyncState* const syncState, Exchange* const exch
        rttKey->daddr=
                MAX(m1->inE->event.tcpEvent->segmentKey->connectionKey.saddr,
                        m1->inE->event.tcpEvent->segmentKey->connectionKey.daddr);
-       exchangeRtt= g_hash_table_lookup(analysisData->stats->exchangeRtt,
-               rttKey);
 
-       if (exchangeRtt)
+       if (syncState->graphsStream)
+       {
+               AnalysisHistogramEval* histogram=
+                       g_hash_table_lookup(analysisData->graphs->histograms, rttKey);
+
+               if (histogram == NULL)
+               {
+                       struct RttKey* tableKey= malloc(sizeof(*tableKey));
+
+                       histogram= constructAnalysisHistogramEval(syncState->graphsDir,
+                               rttKey);
+                       memcpy(tableKey, rttKey, sizeof(*tableKey));
+                       g_hash_table_insert(analysisData->graphs->histograms, tableKey,
+                               histogram);
+               }
+
+               hitBin(&histogram->hrttBins, *rtt / 2);
+       }
+
+       if (syncState->stats)
        {
-               if (*rtt < *exchangeRtt)
+               exchangeRtt= g_hash_table_lookup(analysisData->stats->exchangeRtt,
+                       rttKey);
+
+               if (exchangeRtt)
+               {
+                       if (*rtt < *exchangeRtt)
+                       {
+                               g_hash_table_replace(analysisData->stats->exchangeRtt, rttKey, rtt);
+                       }
+                       else
+                       {
+                               free(rttKey);
+                               free(rtt);
+                       }
+               }
+               else
                {
-                       g_hash_table_replace(analysisData->stats->exchangeRtt, rttKey, rtt);
+                       g_hash_table_insert(analysisData->stats->exchangeRtt, rttKey, rtt);
                }
        }
        else
        {
-               g_hash_table_insert(analysisData->stats->exchangeRtt, rttKey, rtt);
+               free(rttKey);
+               free(rtt);
        }
 }
 
@@ -582,38 +806,61 @@ static void analyzeExchangeEval(SyncState* const syncState, Exchange* const exch
  *   syncState     container for synchronization data
  *   broadcast     structure containing the events
  */
-static void analyzeBroadcastEval(SyncState* const syncState, Broadcast* const broadcast)
+static void analyzeBroadcastEval(SyncState* const syncState, Broadcast* const
+       broadcast)
 {
-       AnalysisDataEval* analysisData;
-       double sum= 0, squaresSum= 0;
-       double y;
+       AnalysisDataEval* analysisData= syncState->analysisData;
 
-       if (!syncState->stats)
+       if (syncState->stats)
        {
-               return;
-       }
+               double sum= 0, squaresSum= 0;
+               double y;
 
-       analysisData= (AnalysisDataEval*) syncState->analysisData;
+               g_queue_foreach(broadcast->events, &gfSum, &sum);
+               g_queue_foreach(broadcast->events, &gfSumSquares, &squaresSum);
 
-       g_queue_foreach(broadcast->events, &gfSum, &sum);
-       g_queue_foreach(broadcast->events, &gfSumSquares, &squaresSum);
+               analysisData->stats->broadcastNb++;
+               // Because of numerical errors, this can at times be < 0
+               y= squaresSum / g_queue_get_length(broadcast->events) - pow(sum /
+                       g_queue_get_length(broadcast->events), 2.);
+               if (y > 0)
+               {
+                       analysisData->stats->broadcastDiffSum+= sqrt(y);
+               }
+       }
 
-       analysisData->stats->broadcastNb++;
-       // Because of numerical errors, this can at times be < 0
-       y= squaresSum / g_queue_get_length(broadcast->events) - pow(sum /
-               g_queue_get_length(broadcast->events), 2.);
-       if (y > 0)
+       if (syncState->graphsStream)
        {
-               analysisData->stats->broadcastDiffSum+= sqrt(y);
+               unsigned int i, j;
+               GArray* events;
+               unsigned int eventNb= broadcast->events->length;
+
+               events= g_array_sized_new(FALSE, FALSE, sizeof(Event*), eventNb);
+               g_queue_foreach(broadcast->events, &gfAddEventToArray, events);
+
+               for (i= 0; i < eventNb; i++)
+               {
+                       for (j= 0; j < eventNb; j++)
+                       {
+                               Event* eventI= g_array_index(events, Event*, i), * eventJ=
+                                       g_array_index(events, Event*, j);
+
+                               if (eventI->traceNum < eventJ->traceNum)
+                               {
+                                       updateBounds(analysisData->graphs->bounds, eventI, eventJ);
+                               }
+                       }
+               }
+
+               g_array_free(events, TRUE);
        }
 }
 
 
 /*
- * Finalize the factor calculations
- *
- * Since this module does not really calculate factors, identity factors are
- * returned.
+ * Finalize the factor calculations. Since this module does not really
+ * calculate factors, identity factors are returned. Instead, histograms are
+ * written out and histogram structures are freed.
  *
  * Args:
  *   syncState     container for synchronization data.
@@ -627,13 +874,17 @@ static GArray* finalizeAnalysisEval(SyncState* const syncState)
        unsigned int i;
        AnalysisDataEval* analysisData= syncState->analysisData;
 
-       if (syncState->graphsStream && analysisData->graphs)
+       if (syncState->graphsStream && analysisData->graphs->histograms)
        {
-               writeGraphFiles(syncState);
-               destroyGraphs(syncState);
-               analysisData->graphs= NULL;
+               g_hash_table_foreach(analysisData->graphs->histograms,
+                       &ghfWriteHistogram, &(struct WriteHistogramInfo) {.rttInfo=
+                       analysisData->rttInfo, .graphsStream= syncState->graphsStream});
+               g_hash_table_destroy(analysisData->graphs->histograms);
+               analysisData->graphs->histograms= NULL;
        }
 
+       finalizeAnalysisEvalLP(syncState);
+
        factors= g_array_sized_new(FALSE, FALSE, sizeof(Factors),
                syncState->traceNb);
        g_array_set_size(factors, syncState->traceNb);
@@ -660,7 +911,9 @@ static GArray* finalizeAnalysisEval(SyncState* const syncState)
 static void printAnalysisStatsEval(SyncState* const syncState)
 {
        AnalysisDataEval* analysisData;
-       unsigned int i, j;
+       unsigned int i, j, k;
+       unsigned int totInversion= 0, totTooFast= 0, totNoInfo= 0, totTotal= 0;
+       int charNb;
 
        if (!syncState->stats)
        {
@@ -670,38 +923,104 @@ static void printAnalysisStatsEval(SyncState* const syncState)
        analysisData= (AnalysisDataEval*) syncState->analysisData;
 
        printf("Synchronization evaluation analysis stats:\n");
-       printf("\tsum of broadcast differential delays: %g\n",
-               analysisData->stats->broadcastDiffSum);
-       printf("\taverage broadcast differential delays: %g\n",
-               analysisData->stats->broadcastDiffSum /
-               analysisData->stats->broadcastNb);
+       if (analysisData->stats->broadcastNb)
+       {
+               printf("\tsum of broadcast differential delays: %g\n",
+                       analysisData->stats->broadcastDiffSum);
+               printf("\taverage broadcast differential delay: %g\n",
+                       analysisData->stats->broadcastDiffSum /
+                       analysisData->stats->broadcastNb);
+       }
 
        printf("\tIndividual evaluation:\n"
-               "\t\tTrace pair  Inversions Too fast   (No RTT info) Total\n");
+               "\t\tTrace pair  Inversions        Too fast          No RTT info  Total\n");
 
        for (i= 0; i < syncState->traceNb; i++)
        {
                for (j= i + 1; j < syncState->traceNb; j++)
                {
                        MessageStats* messageStats;
-                       const char* format= "\t\t%3d - %-3d   %-10u %-10u %-10u    %u\n";
-
-                       messageStats= &analysisData->stats->messageStats[i][j];
-
-                       printf(format, i, j, messageStats->inversionNb, messageStats->tooFastNb,
-                               messageStats->noRTTInfoNb, messageStats->total);
-
-                       messageStats= &analysisData->stats->messageStats[j][i];
-
-                       printf(format, j, i, messageStats->inversionNb, messageStats->tooFastNb,
-                               messageStats->noRTTInfoNb, messageStats->total);
+                       struct {
+                               unsigned int t1, t2;
+                       } loopValues[]= {
+                               {i, j},
+                               {j, i}
+                       };
+
+                       for (k= 0; k < sizeof(loopValues) / sizeof(*loopValues); k++)
+                       {
+                               messageStats=
+                                       &analysisData->stats->messageStats[loopValues[k].t1][loopValues[k].t2];
+
+                               printf("\t\t%3d - %-3d   ", loopValues[k].t1, loopValues[k].t2);
+                               printf("%u (%u%%)%n", messageStats->inversionNb, (unsigned
+                                               int) ceil((double) messageStats->inversionNb /
+                                               messageStats->total * 100), &charNb);
+                               printf("%*s", 17 - charNb > 0 ? 17 - charNb + 1: 1, " ");
+                               printf("%u (%u%%)%n", messageStats->tooFastNb, (unsigned int)
+                                       ceil((double) messageStats->tooFastNb /
+                                               messageStats->total * 100), &charNb);
+                               printf("%*s%-10u   %u\n", 17 - charNb > 0 ? 17 - charNb + 1:
+                                       1, " ", messageStats->noRTTInfoNb, messageStats->total);
+
+                               totInversion+= messageStats->inversionNb;
+                               totTooFast+= messageStats->tooFastNb;
+                               totNoInfo+= messageStats->noRTTInfoNb;
+                               totTotal+= messageStats->total;
+                       }
                }
        }
 
+       printf("\t\t  total     ");
+       printf("%u (%u%%)%n", totInversion, (unsigned int) ceil((double)
+                       totInversion / totTotal * 100), &charNb);
+       printf("%*s", 17 - charNb > 0 ? 17 - charNb + 1: 1, " ");
+       printf("%u (%u%%)%n", totTooFast, (unsigned int) ceil((double) totTooFast
+                       / totTotal * 100), &charNb);
+       printf("%*s%-10u   %u\n", 17 - charNb > 0 ? 17 - charNb + 1: 1, " ",
+               totNoInfo, totTotal);
+
        printf("\tRound-trip times:\n"
                "\t\tHost pair                          RTT from exchanges  RTTs from file (ms)\n");
        g_hash_table_foreach(analysisData->stats->exchangeRtt,
                &ghfPrintExchangeRtt, analysisData->rttInfo);
+
+       printf("\tConvex hull factors comparisons:\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++)
+               {
+                       FactorsCHull* chFactors= &analysisData->stats->chFactorsArray[i][j];
+                       FactorsCHull* lpFactors= &analysisData->stats->lpFactorsArray[i][j];
+
+                       printf("\t\t%3d - %-3d   ", i, j);
+                       if (lpFactors->type == chFactors->type)
+                       {
+                               if (lpFactors->type == MIDDLE)
+                               {
+                                       printf("%-13s %-10.4g %-10.4g %-10.4g %.4g\n",
+                                               approxNames[lpFactors->type],
+                                               lpFactors->min->offset - chFactors->min->offset,
+                                               lpFactors->max->offset - chFactors->max->offset,
+                                               lpFactors->min->drift - chFactors->min->drift,
+                                               lpFactors->max->drift - chFactors->max->drift);
+                               }
+                               else if (lpFactors->type == ABSENT)
+                               {
+                                       printf("%s\n", approxNames[lpFactors->type]);
+                               }
+                       }
+                       else
+                       {
+                               printf("Different! %s and %s\n", approxNames[lpFactors->type],
+                                       approxNames[chFactors->type]);
+                       }
+               }
+       }
 }
 
 
@@ -713,7 +1032,8 @@ static void printAnalysisStatsEval(SyncState* const syncState)
  *   value:        double*, RTT estimated from exchanges
  *   user_data     GHashTable* rttInfo
  */
-static void ghfPrintExchangeRtt(gpointer key, gpointer value, gpointer user_data)
+static void ghfPrintExchangeRtt(gpointer key, gpointer value, gpointer
+       user_data)
 {
        char addr1[16], addr2[16];
        struct RttKey* rttKey1= key;
@@ -1005,77 +1325,119 @@ static void gfSumSquares(gpointer data, gpointer userData)
 }
 
 
+/*
+ * Update a struct Bins according to a new value
+ *
+ * Args:
+ *   bins:         the structure containing bins to build a histrogram
+ *   value:        the new value
+ */
+static void hitBin(struct Bins* const bins, const double value)
+{
+       unsigned int binN= binNum(value);
+
+       if (binN < bins->min)
+       {
+               bins->min= binN;
+       }
+       else if (binN > bins->max)
+       {
+               bins->max= binN;
+       }
+
+       bins->total++;
+
+       bins->bin[binN]++;
+}
+
+
 /*
  * Figure out the bin in a histogram to which a value belongs.
  *
  * This uses exponentially sized bins that go from 0 to infinity.
  *
  * Args:
- *   value:        the value, must be >=0, or else expect the unexpected
- *                 (floating point exception)
+ *   value:        in the range -INFINITY to INFINITY
+ *
+ * Returns:
+ *   The number of the bin in a struct Bins.bin
  */
 static unsigned int binNum(const double value)
 {
-       if (value == 0)
+       if (value <= 0)
        {
                return 0;
        }
+       else if (value < binEnd(1))
+       {
+               return 1;
+       }
+       else if (value >= binStart(BIN_NB - 1))
+       {
+               return BIN_NB - 1;
+       }
        else
        {
-               double result= floor(log(value) / log(binBase)) + (binNb - 1);
-
-               if (result < 0.)
-               {
-                       return 0.;
-               }
-               else
-               {
-                       return result;
-               }
+               return floor(log(value) / log(binBase)) + BIN_NB + 1;
        }
 }
 
 
 /*
- * Figure out the start of the interval of a bin in a histogram. The starting
- * value is included in the interval.
+ * Figure out the start of the interval of a bin in a histogram. See struct
+ * Bins.
  *
  * This uses exponentially sized bins that go from 0 to infinity.
  *
  * Args:
  *   binNum:       bin number
+ *
+ * Return:
+ *   The start of the interval, this value is included in the interval (except
+ *   for -INFINITY, naturally)
  */
 static double binStart(const unsigned int binNum)
 {
-       g_assert(binNum < binNb);
+       g_assert_cmpuint(binNum, <, BIN_NB);
 
        if (binNum == 0)
        {
-               return 0;
+               return -INFINITY;
+       }
+       else if (binNum == 1)
+       {
+               return 0.;
        }
        else
        {
-               return pow(binBase, (double) binNum - (binNb - 1));
+               return pow(binBase, (double) binNum - BIN_NB + 1);
        }
 }
 
 
 /*
- * Figure out the end of the interval of a bin in a histogram. The end value
- * is not included in the interval.
+ * Figure out the end of the interval of a bin in a histogram. See struct
+ * Bins.
  *
  * This uses exponentially sized bins that go from 0 to infinity.
  *
  * Args:
  *   binNum:       bin number
+ *
+ * Return:
+ *   The end of the interval, this value is not included in the interval
  */
 static double binEnd(const unsigned int binNum)
 {
-       g_assert(binNum < binNb);
+       g_assert_cmpuint(binNum, <, BIN_NB);
 
-       if (binNum < binNb)
+       if (binNum == 0)
+       {
+               return 0.;
+       }
+       else if (binNum < BIN_NB - 1)
        {
-               return pow(binBase, (double) binNum - (binNb - 2));
+               return pow(binBase, (double) binNum - BIN_NB + 2);
        }
        else
        {
@@ -1084,55 +1446,563 @@ static double binEnd(const unsigned int binNum)
 }
 
 
+/*
+ * Return the total number of elements in the "normal" bins (not underflow or
+ * overflow)
+ *
+ * Args:
+ *   bins:         the structure containing bins to build a histrogram
+ */
+static uint32_t normalTotal(struct Bins* const bins)
+{
+       return bins->total - bins->bin[0] - bins->bin[BIN_NB - 1];
+}
+
+
+/* Update the bounds between two traces
+ *
+ * Args:
+ *   bounds:       the array containing all the trace-pair bounds
+ *   e1, e2:       the two related events
+ */
+static void updateBounds(Bounds** const bounds, Event* const e1, Event* const
+       e2)
+{
+       unsigned int traceI, traceJ;
+       uint64_t messageTime;
+       Bounds* tpBounds;
+
+       if (e1->traceNum < e2->traceNum)
+       {
+               traceI= e2->traceNum;
+               traceJ= e1->traceNum;
+               messageTime= e1->cpuTime;
+       }
+       else
+       {
+               traceI= e1->traceNum;
+               traceJ= e2->traceNum;
+               messageTime= e2->cpuTime;
+       }
+       tpBounds= &bounds[traceI][traceJ];
+
+       if (messageTime < tpBounds->min)
+       {
+               tpBounds->min= messageTime;
+       }
+       if (messageTime > tpBounds->max)
+       {
+               tpBounds->max= messageTime;
+       }
+}
+
+
+#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);
+       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* calculateFactors(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.
+ *
+ * Returns:
+ *   Please note that the approximation type may be MIDDLE, INCOMPLETE or
+ *   ABSENT. Unlike in analysis_chull, ABSENT is also used when the hulls do
+ *   not respect assumptions.
+ */
+static void calculateCompleteFactors(glp_prob* const lp, FactorsCHull* factors)
+{
+       factors->min= calculateFactors(lp, GLP_MIN);
+       factors->max= calculateFactors(lp, GLP_MAX);
+
+       if (factors->min && factors->max)
+       {
+               factors->type= MIDDLE;
+               calculateFactorsMiddle(factors);
+       }
+       else if (factors->min || factors->max)
+       {
+               factors->type= INCOMPLETE;
+               factors->approx= NULL;
+       }
+       else
+       {
+               factors->type= ABSENT;
+               factors->approx= NULL;
+       }
+}
+
+
+/*
+ * Create and initialize an array like AnalysisStatsCHull.allFactors
+ *
+ * Args:
+ *   traceNb:      number of traces
+ *
+ * Returns:
+ *   A new array, which can be freed with freeAllFactors()
+ */
+static FactorsCHull** createAllFactors(const unsigned int traceNb)
+{
+       FactorsCHull** factorsArray;
+       unsigned int i;
+
+       factorsArray= malloc(traceNb * sizeof(FactorsCHull*));
+       for (i= 0; i < traceNb; i++)
+       {
+               factorsArray[i]= calloc((i + 1), sizeof(FactorsCHull));
+
+               factorsArray[i][i].type= EXACT;
+               factorsArray[i][i].approx= malloc(sizeof(Factors));
+               factorsArray[i][i].approx->drift= 1.;
+               factorsArray[i][i].approx->offset= 0.;
+       }
+
+       return factorsArray;
+}
+#endif
+
+
+/*
+ * Compute synchronization factors using a linear programming approach.
+ * Compute the factors using analysis_chull. Compare the two.
+ *
+ * There are two definitions of this function. The empty one is used when the
+ * solver library, glpk, is not available at build time. In that case, nothing
+ * is actually produced.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ */
+#ifndef HAVE_LIBGLPK
+static inline void finalizeAnalysisEvalLP(SyncState* const syncState)
+{
+}
+#else
+static void finalizeAnalysisEvalLP(SyncState* const syncState)
+{
+       unsigned int i, j;
+       AnalysisDataEval* analysisData= syncState->analysisData;
+       AnalysisDataCHull* chAnalysisData= analysisData->chullSS->analysisData;
+       FactorsCHull** lpFactorsArray= createAllFactors(syncState->traceNb);
+       FactorsCHull* lpFactors;
+
+       if (!syncState->stats && !syncState->graphsStream)
+       {
+               return;
+       }
+
+       if ((syncState->graphsStream && analysisData->graphs->lps != NULL) ||
+               (syncState->stats && analysisData->stats->chFactorsArray != NULL))
+       {
+               return;
+       }
+
+       if (syncState->stats)
+       {
+               analysisData->stats->chFactorsArray=
+                       calculateAllFactors(analysisData->chullSS);
+               analysisData->stats->lpFactorsArray= lpFactorsArray;
+       }
+
+       if (syncState->graphsStream)
+       {
+               analysisData->graphs->lps= malloc(syncState->traceNb *
+                       sizeof(glp_prob**));
+               for (i= 0; i < syncState->traceNb; i++)
+               {
+                       analysisData->graphs->lps[i]= malloc(i * sizeof(glp_prob*));
+               }
+               analysisData->graphs->lpFactorsArray= lpFactorsArray;
+       }
+
+       for (i= 0; i < syncState->traceNb; i++)
+       {
+               for (j= 0; j < i; j++)
+               {
+                       glp_prob* lp;
+
+                       // Create the LP problem
+                       lp= lpCreateProblem(chAnalysisData->hullArray[i][j],
+                               chAnalysisData->hullArray[j][i]);
+
+                       // Use the LP problem to find the correction factors for this pair of
+                       // traces
+                       calculateCompleteFactors(lp, &lpFactorsArray[i][j]);
+
+                       if (syncState->graphsStream)
+                       {
+                               analysisData->graphs->lps[i][j]= lp;
+                       }
+                       else
+                       {
+                               glp_delete_prob(lp);
+                               destroyFactorsCHull(lpFactors);
+                       }
+               }
+       }
+
+       g_array_free(analysisData->chullSS->analysisModule->finalizeAnalysis(analysisData->chullSS),
+               TRUE);
+}
+#endif
+
+
+/*
+ * Compute synchronization accuracy information using a linear programming
+ * approach. Write the neccessary data files and plot lines in the gnuplot
+ * script.
+ *
+ * When the solver library, glpk, is not available at build time nothing is
+ * actually produced.
+ *
+ * Args:
+ *   syncState:    container for synchronization data
+ *   i:            first trace number
+ *   j:            second trace number, garanteed to be larger than i
+ */
+static void writeAnalysisTraceTimeBackPlotsEval(SyncState* const syncState,
+       const unsigned int i, const unsigned int j)
+{
+#ifdef HAVE_LIBGLPK
+       unsigned int it;
+       AnalysisDataEval* analysisData= syncState->analysisData;
+       AnalysisGraphsEval* graphs= analysisData->graphs;
+       GQueue*** hullArray= ((AnalysisDataCHull*)
+               analysisData->chullSS->analysisData)->hullArray;
+       FactorsCHull* lpFactors= &graphs->lpFactorsArray[j][i];
+       glp_prob* lp= graphs->lps[j][i];
+
+       if (lpFactors->type == MIDDLE)
+       {
+               int retval;
+               char* cwd;
+               char fileName[40];
+               FILE* fp;
+               double* xValues;
+               unsigned int xBegin, xEnd;
+               double interval;
+               const unsigned int graphPointNb= 1000;
+
+               // Open the data file
+               snprintf(fileName, 40, "analysis_eval_accuracy-%03u_and_%03u.data", i, j);
+               fileName[sizeof(fileName) - 1]= '\0';
+
+               cwd= changeToGraphDir(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
+               g_assert_cmpuint(graphPointNb, >=, 4);
+               xValues= malloc(graphPointNb * sizeof(double));
+               xValues[0]= graphs->bounds[j][i].min;
+               xValues[graphPointNb - 1]= graphs->bounds[j][i].max;
+               xValues[1]= MIN(((Point*) g_queue_peek_head(hullArray[i][j]))->x,
+                       ((Point*) g_queue_peek_head(hullArray[j][i]))->x);
+               xValues[graphPointNb - 2]= MAX(((Point*)
+                               g_queue_peek_tail(hullArray[i][j]))->x, ((Point*)
+                               g_queue_peek_tail(hullArray[j][i]))->x);
+
+               if (xValues[0] == xValues[1])
+               {
+                       xBegin= 0;
+               }
+               else
+               {
+                       xBegin= 1;
+               }
+               if (xValues[graphPointNb - 2] == xValues[graphPointNb - 1])
+               {
+                       xEnd= graphPointNb - 1;
+               }
+               else
+               {
+                       xEnd= graphPointNb - 2;
+               }
+               interval= (xValues[xEnd] - xValues[xBegin]) / (graphPointNb - 1);
+
+               for (it= xBegin; it <= xEnd; it++)
+               {
+                       xValues[it]= xValues[xBegin] + interval * (it - xBegin);
+               }
+
+               /* For each absisca value and each optimisation direction, solve the LP
+                * and write a line in the data file */
+               for (it= 0; it < graphPointNb; it++)
+               {
+                       unsigned int it2;
+                       int directions[]= {GLP_MIN, GLP_MAX};
+
+                       glp_set_obj_coef(lp, 1, 1.);
+                       glp_set_obj_coef(lp, 2, xValues[it]);
+
+                       fprintf(fp, "%25.9f %25.9f", xValues[it], lpFactors->approx->offset
+                               + lpFactors->approx->drift * xValues[it]);
+                       for (it2= 0; it2 < sizeof(directions) / sizeof(*directions); it2++)
+                       {
+                               int status;
+
+                               glp_set_obj_dir(lp, directions[it2]);
+                               retval= glp_simplex(lp, NULL);
+                               status= glp_get_status(lp);
+
+                               g_assert(retval == 0 && status == GLP_OPT);
+                               fprintf(fp, " %25.9f", glp_get_obj_val(lp));
+                       }
+                       fprintf(fp, "\n");
+               }
+
+               free(xValues);
+               fclose(fp);
+
+               fprintf(syncState->graphsStream,
+                       "\t\"analysis_eval_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);
+       }
+#endif
+}
+
+
 /*
  * Write the analysis-specific graph lines in the gnuplot script.
  *
+ * When the solver library, glpk, is not available at build time nothing is
+ * actually produced.
+ *
  * Args:
  *   syncState:    container for synchronization data
  *   i:            first trace number
  *   j:            second trace number, garanteed to be larger than i
  */
-static void writeAnalysisGraphsPlotsEval(SyncState* const syncState, const
-       unsigned int i, const unsigned int j)
+static void writeAnalysisTraceTimeForePlotsEval(SyncState* const syncState,
+       const unsigned int i, const unsigned int j)
 {
-       fprintf(syncState->graphsStream,
-               "\t\"analysis_eval_hrtt-%2$03d_and_%1$03d.data\" "
-                       "title \"RTT/2\" with boxes linetype 1 linewidth 3 "
-                       "linecolor rgb \"black\" fill transparent solid 0.75, \\\n"
-               /*"\t\"analysis_eval_tt-%1$03d_to_%2$03d.data\" "
-                       "title \"%1$u to %2$u\" with boxes linetype 1 linewidth 3 "
-                       "linecolor rgb \"black\" fill transparent solid 0.5, \\\n"
-               "\t\"analysis_eval_tt-%2$03d_to_%1$03d.data\" "
-                       "title \"%2$u to %1$u\" with boxes linetype 1 linewidth 3 "
-                       "linecolor rgb \"black\" fill transparent solid 0.25, \\\n"*/
-                       , i, j);
-       /*
-       fprintf(syncState->graphsStream,
-               "\t\"analysis_eval_hrtt-%2$03d_and_%1$03d.data\" "
-                       "title \"RTT/2\" with linespoints linetype 1 linewidth 3 "
-                       "linecolor rgb \"black\", \\\n"
-               "\t\"analysis_eval_tt-%1$03d_to_%2$03d.data\" "
-                       "title \"%1$u to %2$u\" with linespoints linetype 1 linewidth 3 "
-                       "linecolor rgb \"gray70\", \\\n"
-               "\t\"analysis_eval_tt-%2$03d_to_%1$03d.data\" "
-                       "title \"%2$u to %1$u\" with linespoints linetype 1 linewidth 3 "
-                       "linecolor rgb \"gray40\", \\\n", i, j);
-*/
+#ifdef HAVE_LIBGLPK
+       if (((AnalysisDataEval*)
+                       syncState->analysisData)->graphs->lpFactorsArray[j][i].type ==
+               MIDDLE)
+       {
+               fprintf(syncState->graphsStream,
+                       "\t\"analysis_eval_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_eval_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);
+       }
+#endif
 }
 
 
 /*
- * Write the analysis-specific options in the gnuplot script.
+ * 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 writeAnalysisGraphsOptionsEval(SyncState* const syncState, const
-       unsigned int i, const unsigned int j)
+static void writeAnalysisTraceTraceBackPlotsEval(SyncState* const syncState,
+       const unsigned int i, const unsigned int j)
 {
+#ifdef HAVE_LIBGLPK
        fprintf(syncState->graphsStream,
-               "set xlabel \"Message Latency (s)\"\n"
-               "set ylabel \"Proportion of messages per second\"\n");
+               "\t\"analysis_eval_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
+}
+
+
+/*
+ * 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 writeAnalysisTraceTraceForePlotsEval(SyncState* const syncState,
+       const unsigned int i, const unsigned int j)
+{
+       AnalysisDataEval* analysisData= syncState->analysisData;
+
+       analysisData->chullSS->analysisModule->graphFunctions.writeTraceTraceForePlots(analysisData->chullSS,
+               i, j);
 }
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