+ * 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.
+ *
+ * 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.