Show the latency histograms by IP address rather than by trace
[lttv.git] / lttv / lttv / sync / event_analysis_eval.c
index 05a49acca39c9c1114245e53a9e2c6b6f87fd6cb..5dd1f6df16677e502b32d420cef594d45731d697 100644 (file)
@@ -17,6 +17,7 @@
  */
 
 #define _GNU_SOURCE
+#define _ISOC99_SOURCE
 
 #ifdef HAVE_CONFIG_H
 #include <config.h>
 
 #include <arpa/inet.h>
 #include <errno.h>
+#include <math.h>
 #include <netinet/in.h>
 #include <stddef.h>
 #include <stdlib.h>
 #include <stdio.h>
 #include <string.h>
 #include <sys/socket.h>
+#include <unistd.h>
 
 #include "lookup3.h"
 #include "sync_chain.h"
 #include "event_analysis_eval.h"
 
 
+struct WriteGraphInfo
+{
+       GHashTable* rttInfo;
+       FILE* graphsStream;
+};
+
+
 // Functions common to all analysis modules
 static void initAnalysisEval(SyncState* const syncState);
 static void destroyAnalysisEval(SyncState* const syncState);
@@ -59,6 +69,26 @@ static void gdnDestroyDouble(gpointer data);
 static void readRttInfo(GHashTable* rttInfo, FILE* rttFile);
 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 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 AnalysisGraphEval* constructAnalysisGraphEval(const char* const
+       graphsDir, const struct RttKey* const rttKey);
+static void destroyAnalysisGraphEval(AnalysisGraphEval* const graph);
+static void gdnDestroyAnalysisGraphEval(gpointer data);
+static void ghfWriteGraph(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);
+
+
+double binBase;
 
 static AnalysisModule analysisModuleEval= {
        .name= "eval",
@@ -77,7 +107,7 @@ static ModuleOption optionEvalRttFile= {
        .longName= "eval-rtt-file",
        .hasArg= REQUIRED_ARG,
        {.arg= NULL},
-       .optionHelp= "specify the file containing rtt information",
+       .optionHelp= "specify the file containing RTT information",
        .argHelp= "FILE",
 };
 
@@ -133,17 +163,238 @@ static void initAnalysisEval(SyncState* const syncState)
 
        if (syncState->stats)
        {
-               analysisData->stats= malloc(sizeof(AnalysisStatsEval));
+               analysisData->stats= calloc(1, sizeof(AnalysisStatsEval));
                analysisData->stats->broadcastDiffSum= 0.;
 
-               analysisData->stats->allStats= malloc(syncState->traceNb *
-                       sizeof(TracePairStats*));
+               analysisData->stats->messageStats= malloc(syncState->traceNb *
+                       sizeof(MessageStats*));
                for (i= 0; i < syncState->traceNb; i++)
                {
-                       analysisData->stats->allStats[i]= calloc(syncState->traceNb,
-                               sizeof(TracePairStats));
+                       analysisData->stats->messageStats[i]= calloc(syncState->traceNb,
+                               sizeof(MessageStats));
+               }
+
+               analysisData->stats->exchangeRtt=
+                       g_hash_table_new_full(&ghfRttKeyHash, &gefRttKeyEqual,
+                               &gdnDestroyRttKey, &gdnDestroyDouble);
+       }
+
+       if (syncState->graphsStream)
+       {
+               binBase= exp10(6. / (BIN_NB - 3));
+               analysisData->graphs= g_hash_table_new_full(&ghfRttKeyHash,
+                       &gefRttKeyEqual, &gdnDestroyRttKey, &gdnDestroyAnalysisGraphEval);
+       }
+}
+
+
+/*
+ * Create and open files used to store histogram points to generate graphs.
+ * Create data structures to store histogram points during analysis.
+ *
+ * Args:
+ *   graphsDir:    folder where to write files
+ *   rttKey:       host pair, make sure saddr < daddr
+ */
+static AnalysisGraphEval* constructAnalysisGraphEval(const char* const
+       graphsDir, const struct RttKey* const rttKey)
+{
+       int retval;
+       unsigned int i;
+       char* cwd;
+       char name[60], saddr[16], daddr[16];
+       AnalysisGraphEval* graph= calloc(1, sizeof(*graph));
+       const struct {
+               size_t pointsOffset;
+               const char* fileName;
+               const char* host1, *host2;
+       } loopValues[]= {
+               {offsetof(AnalysisGraphEval, ttSendPoints), "analysis_eval_tt-%s_to_%s.data",
+                       saddr, daddr},
+               {offsetof(AnalysisGraphEval, ttRecvPoints), "analysis_eval_tt-%s_to_%s.data",
+                       daddr, saddr},
+               {offsetof(AnalysisGraphEval, hrttPoints), "analysis_eval_hrtt-%s_and_%s.data",
+                       saddr, daddr},
+       };
+
+       graph->ttSendBins.max= BIN_NB - 1;
+       graph->ttRecvBins.max= BIN_NB - 1;
+       graph->hrttBins.max= BIN_NB - 1;
+
+       convertIP(saddr, rttKey->saddr);
+       convertIP(daddr, rttKey->daddr);
+
+       cwd= changeToGraphDir(graphsDir);
+
+       for (i= 0; i < sizeof(loopValues) / sizeof(*loopValues); i++)
+       {
+               retval= snprintf(name, sizeof(name), loopValues[i].fileName,
+                       loopValues[i].host1, loopValues[i].host2);
+               if (retval > sizeof(name) - 1)
+               {
+                       name[sizeof(name) - 1]= '\0';
+               }
+               if ((*(FILE**)((void*) graph + loopValues[i].pointsOffset)=
+                               fopen(name, "w")) == NULL)
+               {
+                       g_error(strerror(errno));
                }
        }
+
+       retval= chdir(cwd);
+       if (retval == -1)
+       {
+               g_error(strerror(errno));
+       }
+       free(cwd);
+
+       return graph;
+}
+
+
+/*
+ * Close files used to store histogram points to generate graphs.
+ *
+ * Args:
+ *   graphsDir:    folder where to write files
+ *   rttKey:       host pair, make sure saddr < daddr
+ */
+static void destroyAnalysisGraphEval(AnalysisGraphEval* const graph)
+{
+       unsigned int i;
+       int retval;
+       const struct {
+               size_t pointsOffset;
+       } loopValues[]= {
+               {offsetof(AnalysisGraphEval, ttSendPoints)},
+               {offsetof(AnalysisGraphEval, ttRecvPoints)},
+               {offsetof(AnalysisGraphEval, hrttPoints)},
+       };
+
+       for (i= 0; i < sizeof(loopValues) / sizeof(*loopValues); i++)
+       {
+               retval= fclose(*(FILE**)((void*) graph + loopValues[i].pointsOffset));
+               if (retval != 0)
+               {
+                       g_error(strerror(errno));
+               }
+       }
+}
+
+
+/*
+ * A GDestroyNotify function for g_hash_table_new_full()
+ *
+ * Args:
+ *   data:         AnalysisGraphEval*
+ */
+static void gdnDestroyAnalysisGraphEval(gpointer data)
+{
+       destroyAnalysisGraphEval(data);
+}
+
+
+/*
+ * A GHFunc for g_hash_table_foreach()
+ *
+ * Args:
+ *   key:          RttKey* where saddr < daddr
+ *   value:        AnalysisGraphEval*
+ *   user_data     struct WriteGraphInfo*
+ */
+static void ghfWriteGraph(gpointer key, gpointer value, gpointer user_data)
+{
+       double* rtt1, * rtt2;
+       struct RttKey* rttKey= key;
+       struct RttKey oppositeRttKey= {.saddr= rttKey->daddr, .daddr=
+               rttKey->saddr};
+       AnalysisGraphEval* graph= value;
+       struct WriteGraphInfo* 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(&graph->ttSendBins, graph->ttSendPoints);
+       dumpBinToFile(&graph->ttRecvBins, graph->ttRecvPoints);
+       dumpBinToFile(&graph->hrttBins, graph->hrttPoints);
+       writeHistogram(info->graphsStream, rttKey, rtt1);
+}
+
+
+/*
+ * Write the content of one bin in a histogram point file
+ *
+ * Args:
+ *   bin:          array of values that make up a histogram
+ *   file:         FILE*, write to this file
+ */
+static void dumpBinToFile(const struct Bins* const bins, FILE* const file)
+{
+       unsigned int i;
+
+       // The first and last bins are skipped, see struct Bins
+       for (i= 1; i < BIN_NB - 1; i++)
+       {
+               if (bins->bin[i] > 0)
+               {
+                       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));
+               }
+       }
+}
+
+
+/*
+ * Write the analysis-specific plot in the gnuplot script.
+ *
+ * Args:
+ *   graphsStream: write to this file
+ *   rttKey:       must be sorted such that saddr < daddr
+ *   minRtt:       if available, else NULL
+ */
+static void writeHistogram(FILE* graphsStream, const struct RttKey* rttKey,
+       double* minRtt)
+{
+       char saddr[16], daddr[16];
+
+       convertIP(saddr, rttKey->saddr);
+       convertIP(daddr, rttKey->daddr);
+
+       fprintf(graphsStream,
+               "reset\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)
+       {
+               fprintf(graphsStream,
+                       "set arrow from %.9f, 0 rto 0, graph 1 "
+                       "nohead linetype 3 linewidth 3 linecolor rgb \"black\"\n", *minRtt / 2);
+       }
+
+       fprintf(graphsStream,
+               "plot \\\n"
+               "\t\"analysis_eval_hrtt-%1$s_and_%2$s.data\" "
+                       "title \"RTT/2\" with linespoints linetype 1 linewidth 2 "
+                       "linecolor rgb \"black\" pointtype 6 pointsize 1,\\\n"
+               "\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"
+               "\t\"analysis_eval_tt-%2$s_to_%1$s.data\" "
+                       "title \"%2$s to %1$s\" with linespoints linetype 4 linewidth 2 "
+                       "linecolor rgb \"gray30\" pointtype 6 pointsize 1\n", saddr, daddr);
 }
 
 
@@ -174,12 +425,20 @@ static void destroyAnalysisEval(SyncState* const syncState)
        {
                for (i= 0; i < syncState->traceNb; i++)
                {
-                       free(analysisData->stats->allStats[i]);
+                       free(analysisData->stats->messageStats[i]);
                }
-               free(analysisData->stats->allStats);
+               free(analysisData->stats->messageStats);
+
+               g_hash_table_destroy(analysisData->stats->exchangeRtt);
+
                free(analysisData->stats);
        }
 
+       if (syncState->graphsStream && analysisData->graphs)
+       {
+               g_hash_table_destroy(analysisData->graphs);
+       }
+
        free(syncState->analysisData);
        syncState->analysisData= NULL;
 }
@@ -188,36 +447,165 @@ static void destroyAnalysisEval(SyncState* const syncState)
 /*
  * Perform analysis on an event pair.
  *
+ * Check if there is message inversion or messages that are too fast.
+ *
  * Args:
  *   syncState     container for synchronization data
  *   message       structure containing the events
  */
 static void analyzeMessageEval(SyncState* const syncState, Message* const message)
 {
-       AnalysisDataEval* analysisData;
+       AnalysisDataEval* analysisData= syncState->analysisData;
+       MessageStats* messageStats=
+               &analysisData->stats->messageStats[message->outE->traceNum][message->inE->traceNum];;
+       double* rtt;
+       double tt;
+       struct RttKey rttKey;
 
-       analysisData= (AnalysisDataEval*) syncState->analysisData;
+       if (!syncState->stats)
+       {
+               return;
+       }
+
+       g_assert(message->inE->type == TCP);
+
+       messageStats->total++;
+
+       tt= wallTimeSub(&message->inE->wallTime, &message->outE->wallTime);
+       if (tt <= 0)
+       {
+               messageStats->inversionNb++;
+       }
+       else if (syncState->graphsStream)
+       {
+               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),
+               };
+               AnalysisGraphEval* graph= g_hash_table_lookup(analysisData->graphs,
+                       &rttKey);
+
+               if (graph == NULL)
+               {
+                       struct RttKey* tableKey= malloc(sizeof(*tableKey));
+
+                       graph= constructAnalysisGraphEval(syncState->graphsDir, &rttKey);
+                       memcpy(tableKey, &rttKey, sizeof(*tableKey));
+                       g_hash_table_insert(analysisData->graphs, tableKey, graph);
+               }
+
+               if (message->inE->event.udpEvent->datagramKey->saddr <
+                       message->inE->event.udpEvent->datagramKey->daddr)
+               {
+                       hitBin(&graph->ttSendBins, tt);
+               }
+               else
+               {
+                       hitBin(&graph->ttRecvBins, tt);
+               }
+       }
+
+       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->noRTTInfoNb++;
+       }
 }
 
 
 /*
  * Perform analysis on multiple messages
  *
+ * Measure the RTT
+ *
  * Args:
  *   syncState     container for synchronization data
  *   exchange      structure containing the messages
  */
 static void analyzeExchangeEval(SyncState* const syncState, Exchange* const exchange)
 {
-       AnalysisDataEval* analysisData;
+       AnalysisDataEval* analysisData= syncState->analysisData;
+       Message* m1= g_queue_peek_tail(exchange->acks);
+       Message* m2= exchange->message;
+       struct RttKey* rttKey;
+       double* rtt, * exchangeRtt;
 
-       analysisData= (AnalysisDataEval*) syncState->analysisData;
+       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);
+
+       rttKey= malloc(sizeof(struct RttKey));
+       rttKey->saddr=
+               MIN(m1->inE->event.tcpEvent->segmentKey->connectionKey.saddr,
+                       m1->inE->event.tcpEvent->segmentKey->connectionKey.daddr);
+       rttKey->daddr=
+               MAX(m1->inE->event.tcpEvent->segmentKey->connectionKey.saddr,
+                       m1->inE->event.tcpEvent->segmentKey->connectionKey.daddr);
+
+       if (syncState->graphsStream)
+       {
+               AnalysisGraphEval* graph= g_hash_table_lookup(analysisData->graphs,
+                       rttKey);
+
+               if (graph == NULL)
+               {
+                       struct RttKey* tableKey= malloc(sizeof(*tableKey));
+
+                       graph= constructAnalysisGraphEval(syncState->graphsDir, rttKey);
+                       memcpy(tableKey, rttKey, sizeof(*tableKey));
+                       g_hash_table_insert(analysisData->graphs, tableKey, graph);
+               }
+
+               hitBin(&graph->hrttBins, *rtt / 2);
+       }
+
+       exchangeRtt= g_hash_table_lookup(analysisData->stats->exchangeRtt,
+               rttKey);
+
+       if (exchangeRtt)
+       {
+               if (*rtt < *exchangeRtt)
+               {
+                       g_hash_table_replace(analysisData->stats->exchangeRtt, rttKey, rtt);
+               }
+       }
+       else
+       {
+               g_hash_table_insert(analysisData->stats->exchangeRtt, rttKey, rtt);
+       }
 }
 
 
 /*
  * Perform analysis on muliple events
  *
+ * Sum the broadcast differential delays
+ *
  * Args:
  *   syncState     container for synchronization data
  *   broadcast     structure containing the events
@@ -225,8 +613,27 @@ static void analyzeExchangeEval(SyncState* const syncState, Exchange* const exch
 static void analyzeBroadcastEval(SyncState* const syncState, Broadcast* const broadcast)
 {
        AnalysisDataEval* analysisData;
+       double sum= 0, squaresSum= 0;
+       double y;
+
+       if (!syncState->stats)
+       {
+               return;
+       }
 
        analysisData= (AnalysisDataEval*) syncState->analysisData;
+
+       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);
+       }
 }
 
 
@@ -240,12 +647,22 @@ static void analyzeBroadcastEval(SyncState* const syncState, Broadcast* const br
  *   syncState     container for synchronization data.
  *
  * Returns:
- *   Factors[traceNb] synchronization factors for each trace
+ *   Factors[traceNb] identity factors for each trace
  */
 static GArray* finalizeAnalysisEval(SyncState* const syncState)
 {
        GArray* factors;
        unsigned int i;
+       AnalysisDataEval* analysisData= syncState->analysisData;
+
+       if (syncState->graphsStream && analysisData->graphs)
+       {
+               g_hash_table_foreach(analysisData->graphs, &ghfWriteGraph, &(struct
+                               WriteGraphInfo) {.rttInfo= analysisData->rttInfo,
+                       .graphsStream= syncState->graphsStream});
+               g_hash_table_destroy(analysisData->graphs);
+               analysisData->graphs= NULL;
+       }
 
        factors= g_array_sized_new(FALSE, FALSE, sizeof(Factors),
                syncState->traceNb);
@@ -285,28 +702,83 @@ static void printAnalysisStatsEval(SyncState* const syncState)
        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);
 
        printf("\tIndividual evaluation:\n"
-               "\t\tTrace pair  Inversions  Too fast    (No RTT info)\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++)
                {
-                       TracePairStats* tpStats;
-                       const char* format= "\t\t%3d - %-3d   %-10u  %-10u  %u\n";
+                       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);
+               }
+       }
 
-                       tpStats= &analysisData->stats->allStats[i][j];
+       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);
+}
+
+
+/*
+ * A GHFunc for g_hash_table_foreach()
+ *
+ * Args:
+ *   key:          RttKey* where saddr < daddr
+ *   value:        double*, RTT estimated from exchanges
+ *   user_data     GHashTable* rttInfo
+ */
+static void ghfPrintExchangeRtt(gpointer key, gpointer value, gpointer user_data)
+{
+       char addr1[16], addr2[16];
+       struct RttKey* rttKey1= key;
+       struct RttKey rttKey2= {rttKey1->daddr, rttKey1->saddr};
+       double* fileRtt1, *fileRtt2;
+       GHashTable* rttInfo= user_data;
 
-                       printf(format, i, j, tpStats->inversionNb, tpStats->tooFastNb,
-                               tpStats->noRTTInfoNb);
+       convertIP(addr1, rttKey1->saddr);
+       convertIP(addr2, rttKey1->daddr);
 
-                       tpStats= &analysisData->stats->allStats[j][i];
+       fileRtt1= g_hash_table_lookup(rttInfo, rttKey1);
+       fileRtt2= g_hash_table_lookup(rttInfo, &rttKey2);
 
-                       printf(format, j, i, tpStats->inversionNb, tpStats->tooFastNb,
-                               tpStats->noRTTInfoNb);
+       printf("\t\t(%15s, %-15s) %-18.3f  ", addr1, addr2, *(double*) value * 1e3);
+
+       if (fileRtt1 || fileRtt2)
+       {
+               if (fileRtt1)
+               {
+                       printf("%.3f", *fileRtt1 * 1e3);
+               }
+               if (fileRtt1 && fileRtt2)
+               {
+                       printf(", ");
+               }
+               if (fileRtt2)
+               {
+                       printf("%.3f", *fileRtt2 * 1e3);
                }
        }
+       else
+       {
+               printf("-");
+       }
+       printf("\n");
 }
 
 
@@ -451,6 +923,9 @@ static void readRttInfo(GHashTable* rttInfo, FILE* rttStream)
                                addr.s_addr;
                }
 
+               *rtt/= 1e3;
+               g_debug("rttInfo, Inserting (%u, %u)->(%f)", rttKey->saddr,
+                       rttKey->daddr, *rtt);
                g_hash_table_insert(rttInfo, rttKey, rtt);
 
                positionStream(rttStream);
@@ -520,3 +995,162 @@ outEof:
                free(line);
        }
 }
+
+
+/*
+ * A GFunc for g_queue_foreach()
+ *
+ * Args:
+ *   data          Event*, a UDP broadcast event
+ *   user_data     double*, the running sum
+ *
+ * Returns:
+ *   Adds the time of the event to the sum
+ */
+static void gfSum(gpointer data, gpointer userData)
+{
+       Event* event= (Event*) data;
+
+       *(double*) userData+= event->wallTime.seconds + event->wallTime.nanosec /
+               1e9;
+}
+
+
+/*
+ * A GFunc for g_queue_foreach()
+ *
+ * Args:
+ *   data          Event*, a UDP broadcast event
+ *   user_data     double*, the running sum
+ *
+ * Returns:
+ *   Adds the square of the time of the event to the sum
+ */
+static void gfSumSquares(gpointer data, gpointer userData)
+{
+       Event* event= (Event*) data;
+
+       *(double*) userData+= pow(event->wallTime.seconds + event->wallTime.nanosec
+               / 1e9, 2.);
+}
+
+
+/*
+ * 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:        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)
+       {
+               return 0;
+       }
+       else if (value < binEnd(1))
+       {
+               return 1;
+       }
+       else if (value >= binStart(BIN_NB - 1))
+       {
+               return BIN_NB - 1;
+       }
+       else
+       {
+               return floor(log(value) / log(binBase)) + BIN_NB + 1;
+       }
+}
+
+
+/*
+ * 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_cmpuint(binNum, <, BIN_NB);
+
+       if (binNum == 0)
+       {
+               return -INFINITY;
+       }
+       else if (binNum == 1)
+       {
+               return 0.;
+       }
+       else
+       {
+               return pow(binBase, (double) binNum - BIN_NB + 1);
+       }
+}
+
+
+/*
+ * 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_cmpuint(binNum, <, BIN_NB);
+
+       if (binNum == 0)
+       {
+               return 0.;
+       }
+       else if (binNum < BIN_NB - 1)
+       {
+               return pow(binBase, (double) binNum - BIN_NB + 2);
+       }
+       else
+       {
+               return INFINITY;
+       }
+}
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