*/
#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);
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",
.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",
};
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);
}
{
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;
}
/*
* 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
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);
+ }
}
* 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);
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");
}
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);
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;
+ }
+}