/* $Id$ */
-
/* Copyright (c) 2007 Arnaud Legrand, Pedro Velho. All rights reserved. */
-
/* This program is free software; you can redistribute it and/or modify it
* under the terms of the license (GNU LGPL) which comes with this package. */
-
/*
* Modelling the proportional fairness using the Lagrange Optimization
* Approach. For a detailed description see:
XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_lagrange, surf,
"Logging specific to SURF (lagrange)");
+XBT_LOG_NEW_SUBCATEGORY(surf_lagrange_dichotomy, surf,
+ "Logging specific to SURF (lagrange dichotomy)");
-XBT_LOG_NEW_SUBCATEGORY(surf_writelambda, surf,
- "Generates the lambda.in file. WARNING: the size of this file might be a few GBs.");
-
+/*
+ * Local prototypes to implement the lagrangian optimization with optimal step, also called dichotomy.
+ */
+//solves the proportional fairness using a lagrange optimizition with dichotomy step
void lagrange_solve(lmm_system_t sys);
+//computes the value of the dichotomy using a initial values, init, with a specific variable or constraint
+double dichotomy(double init, double diff(double, void *), void *var_cnst,
+ double min_error);
+//computes the value of the differential of variable param_var applied to mu
+double partial_diff_mu(double mu, void *param_var);
+//computes the value of the differential of constraint param_cnst applied to lambda
+double partial_diff_lambda(double lambda, void *param_cnst);
+//auxiliar function to compute the partial_diff
+double diff_aux(lmm_variable_t var, double x);
+
+
+static int __check_kkt(xbt_swag_t cnst_list, xbt_swag_t var_list, int warn)
+{
+ xbt_swag_t elem_list = NULL;
+ lmm_element_t elem = NULL;
+ lmm_constraint_t cnst = NULL;
+ lmm_variable_t var = NULL;
+
+ double tmp;
+
+ //verify the KKT property for each link
+ xbt_swag_foreach(cnst, cnst_list) {
+ tmp = 0;
+ elem_list = &(cnst->element_set);
+ xbt_swag_foreach(elem, elem_list) {
+ var = elem->variable;
+ if (var->weight <= 0)
+ continue;
+ tmp += var->value;
+ }
+
+ if (double_positive(tmp - cnst->bound)) {
+ if (warn)
+ WARN3
+ ("The link (%p) is over-used. Expected less than %f and got %f",
+ cnst, cnst->bound, tmp);
+ return 0;
+ }
+ DEBUG3("Checking KKT for constraint (%p): sat = %f, lambda = %f ",
+ cnst, tmp - cnst->bound, cnst->lambda);
+
+/* if(!((fabs(tmp - cnst->bound)<MAXMIN_PRECISION && cnst->lambda>=MAXMIN_PRECISION) || */
+/* (fabs(tmp - cnst->bound)>=MAXMIN_PRECISION && cnst->lambda<MAXMIN_PRECISION))) { */
+/* if(warn) WARN1("The KKT condition is not verified for cnst %p...", cnst); */
+/* return 0; */
+/* } */
+ }
+
+ //verify the KKT property of each flow
+ xbt_swag_foreach(var, var_list) {
+ if (var->bound < 0 || var->weight <= 0)
+ continue;
+ DEBUG3("Checking KKT for variable (%p): sat = %f mu = %f", var,
+ var->value - var->bound, var->mu);
+
+ if (double_positive(var->value - var->bound)) {
+ if (warn)
+ WARN3
+ ("The variable (%p) is too large. Expected less than %f and got %f",
+ var, var->bound, var->value);
+ return 0;
+ }
+
+/* if(!((fabs(var->value - var->bound)<MAXMIN_PRECISION && var->mu>=MAXMIN_PRECISION) || */
+/* (fabs(var->value - var->bound)>=MAXMIN_PRECISION && var->mu<MAXMIN_PRECISION))) { */
+/* if(warn) WARN1("The KKT condition is not verified for var %p...",var); */
+/* return 0; */
+/* } */
+ }
+ return 1;
+}
void lagrange_solve(lmm_system_t sys)
{
-
/*
* Lagrange Variables.
*/
+ int max_iterations = 10000;
double epsilon_min_error = 1e-6;
+ double dichotomy_min_error = 1e-8;
double overall_error = 1;
- double sigma_step = 1e-3;
- double capacity_error=0, bound_error=0;
-
/*
* Variables to manipulate the data structure proposed to model the maxmin
* fairness. See docummentation for more details.
*/
- xbt_swag_t elem_list = NULL;
- lmm_element_t elem1 = NULL;
- lmm_element_t elem = NULL;
-
xbt_swag_t cnst_list = NULL;
- lmm_constraint_t cnst1 = NULL;
- lmm_constraint_t cnst2 = NULL;
lmm_constraint_t cnst = NULL;
- double sum;
+
xbt_swag_t var_list = NULL;
- lmm_variable_t var1 = NULL;
lmm_variable_t var = NULL;
- lmm_variable_t var2 = NULL;
-
/*
* Auxiliar variables.
*/
- int iteration=0;
- int max_iterations= 1000;
- double mu_partial=0;
- double lambda_partial=0;
- double tmp=0;
- int i,j;
- FILE *gnuplot_file=NULL;
- char print_buf[1024];
- char *trace_buf=xbt_malloc0(sizeof(char));
-
-
-
+ int iteration = 0;
+ double tmp = 0;
+ int i;
+ DEBUG0("Iterative method configuration snapshot =====>");
+ DEBUG1("#### Maximum number of iterations : %d", max_iterations);
+ DEBUG1("#### Minimum error tolerated : %e",
+ epsilon_min_error);
+ DEBUG1("#### Minimum error tolerated (dichotomy) : %e",
+ dichotomy_min_error);
- if ( !(sys->modified))
+ if (!(sys->modified))
return;
-
+
/*
* Initialize the var list variable with only the active variables.
* Associate an index in the swag variables. Initialize mu.
*/
var_list = &(sys->variable_set);
- i=0;
- xbt_swag_foreach(var1, var_list) {
- if((var1->bound > 0.0) || (var1->weight <= 0.0)){
- DEBUG1("## NOTE var1(%d) is a boundless variable", i);
- var1->mu = -1.0;
- } else
- var1->mu = 1.0;
- DEBUG2("## var1(%d)->mu: %e", i, var1->mu);
- DEBUG2("## var1(%d)->weight: %e", i, var1->weight);
+ i = 0;
+ xbt_swag_foreach(var, var_list) {
+ if ((var->bound < 0.0) || (var->weight <= 0.0)) {
+ DEBUG1("#### NOTE var(%d) is a boundless (or inactive) variable", i);
+ var->mu = -1.0;
+ } else {
+ var->mu = 1.0;
+ var->new_mu = 2.0;
+ }
+ DEBUG3("#### var(%d) %p ->mu : %e", i, var, var->mu);
+ DEBUG3("#### var(%d) %p ->weight: %e", i, var, var->weight);
+ DEBUG3("#### var(%d) %p ->bound: %e", i, var, var->bound);
i++;
}
/*
* Initialize lambda.
*/
- cnst_list=&(sys->active_constraint_set);
- xbt_swag_foreach(cnst1, cnst_list) {
- cnst1->lambda = 1.0;
- DEBUG2("## cnst1(%p)->lambda: %e", cnst1, cnst1->lambda);
- }
-
- if(XBT_LOG_ISENABLED(surf_writelambda, xbt_log_priority_debug)) {
- gnuplot_file = fopen("lambda.in", "w");
- fprintf(gnuplot_file, "# iteration lambda1 lambda2 lambda3 ... lambdaP");
+ cnst_list = &(sys->active_constraint_set);
+ xbt_swag_foreach(cnst, cnst_list) {
+ cnst->lambda = 1.0;
+ cnst->new_lambda = 2.0;
+ DEBUG2("#### cnst(%p)->lambda : %e", cnst, cnst->lambda);
}
-
/*
* While doesn't reach a minimun error or a number maximum of iterations.
*/
- while(overall_error > epsilon_min_error && iteration < max_iterations){
- iteration++;
- /* d Dual
- * Compute the value of ----------- (\lambda^k, \mu^k) this portion
- * d \mu_i^k
- * of code depends on function f(x).
- */
- var_list = &(sys->variable_set);
- xbt_swag_foreach(var1, var_list) {
- mu_partial = 0;
- if((var1->bound > 0) || (var1->weight <=0) ){
- //for each link with capacity cnsts[i] that uses flow of variable var1 do
- for(i=0; i<var1->cnsts_number; i++)
- mu_partial += (var1->cnsts[i].constraint)->lambda;
-
- mu_partial = -1.0 / mu_partial + var1->bound;
- var1->new_mu = var1->mu - sigma_step * mu_partial;
- /* Assert that var1->new_mu is positive */
- }
- }
+ while (overall_error > epsilon_min_error && iteration < max_iterations) {
- if(XBT_LOG_ISENABLED(surf_writelambda, xbt_log_priority_debug)) {
- fprintf(gnuplot_file, "\n%d ", iteration);
- }
+ iteration++;
+ DEBUG1("************** ITERATION %d **************", iteration);
- /* d Dual
- * Compute the value of ------------- (\lambda^k, \mu^k) this portion
- * d \lambda_i^k
- * of code depends on function f(x).
+ /*
+ * Compute the value of mu_i
*/
-
- DEBUG1("######Lambda partial at iteration %d", iteration);
- cnst_list=&(sys->active_constraint_set);
- j=0;
- xbt_swag_foreach(cnst1, cnst_list) {
- j++;
-
- lambda_partial = 0;
-
- elem_list = &(cnst1->element_set);
- xbt_swag_foreach(elem1, elem_list) {
- lambda_partial = 0;
-
- var2 = elem1->variable;
-
- if(var2->weight<=0) continue;
-
- tmp = 0;
-
- //for each link with capacity cnsts[i] that uses flow of variable var1 do
- if(var2->bound > 0)
- tmp += var2->mu;
-
- for(i=0; i<var2->cnsts_number; i++)
- tmp += (var2->cnsts[i].constraint)->lambda;
-
- lambda_partial += -1 / tmp;
+ //forall mu_i in mu_1, mu_2, ..., mu_n
+ xbt_swag_foreach(var, var_list) {
+ if ((var->bound >= 0) && (var->weight > 0)) {
+ DEBUG1("====> Working on var (%p)", var);
+ var->new_mu =
+ dichotomy(var->mu, partial_diff_mu, var, dichotomy_min_error);
+ if (var->new_mu < 0)
+ var->new_mu = 0;
+ DEBUG3("====> var->mu (%p) : %g -> %g", var, var->mu, var->new_mu);
+ var->mu = var->new_mu;
}
+ }
- lambda_partial += cnst1->bound;
-
- DEBUG2("###########Lambda partial %p : %e", cnst1, lambda_partial);
-
- cnst1->new_lambda = cnst1->lambda - sigma_step * lambda_partial;
-
- if(XBT_LOG_ISENABLED(surf_writelambda, xbt_log_priority_debug)) {
- fprintf(gnuplot_file, " %f", cnst1->lambda);
- }
+ /*
+ * Compute the value of lambda_i
+ */
+ //forall lambda_i in lambda_1, lambda_2, ..., lambda_n
+ xbt_swag_foreach(cnst, cnst_list) {
+ DEBUG1("====> Working on cnst (%p)", cnst);
+ cnst->new_lambda =
+ dichotomy(cnst->lambda, partial_diff_lambda, cnst,
+ dichotomy_min_error);
+ DEBUG2("====> cnst->lambda (%p) = %e", cnst, cnst->new_lambda);
+ cnst->lambda = cnst->new_lambda;
}
- /* Updating lambda's and mu's */
- var_list = &(sys->variable_set);
- xbt_swag_foreach(var1, var_list)
- if(!((var1->bound > 0.0) || (var1->weight <= 0.0)))
- var1->mu = var1->new_mu;
-
-
- cnst_list=&(sys->active_constraint_set);
- xbt_swag_foreach(cnst1, cnst_list)
- cnst1->lambda = cnst1->new_lambda;
-
/*
* Now computes the values of each variable (\rho) based on
* the values of \lambda and \mu.
*/
- var_list = &(sys->variable_set);
- xbt_swag_foreach(var1, var_list) {
- if(var1->weight <=0)
- var1->value = 0.0;
+ overall_error = 0;
+ xbt_swag_foreach(var, var_list) {
+ if (var->weight <= 0)
+ var->value = 0.0;
else {
+ //compute sigma_i + mu_i
tmp = 0;
- if(var1->bound >0)
- tmp+=var1->mu;
- for(i=0; i<var1->cnsts_number; i++)
- tmp += (var1->cnsts[i].constraint)->lambda;
-
- var1->value = 1 / tmp;
+ for (i = 0; i < var->cnsts_number; i++) {
+ tmp += (var->cnsts[i].constraint)->lambda;
+ }
+ if (var->bound > 0)
+ tmp += var->mu;
+ DEBUG3("\t Working on var (%p). cost = %e; Df = %e", var, tmp,
+ var->df);
+
+ //uses the partial differential inverse function
+ tmp = var->func_fpi(var, tmp);
+
+ //computes de overall_error using normalized value
+ if (overall_error < (fabs(var->value - tmp) / tmp)) {
+ overall_error = (fabs(var->value - tmp) / tmp);
+ }
+
+ var->value = tmp;
}
-
-
- DEBUG2("var1->value (id=%s) : %e", (char *)var1->id, var1->value);
+ DEBUG3("======> value of var (%p) = %e, overall_error = %e", var,
+ var->value, overall_error);
}
- /* Printing Objective */
- var_list = &(sys->variable_set);
- sprintf(print_buf,"MAX-MIN ( ");
- trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
- strcat(trace_buf, print_buf);
- xbt_swag_foreach(var, var_list) {
- sprintf(print_buf,"'%p'(%f) ",var,var->weight);
- trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
- strcat(trace_buf, print_buf);
+ if (!__check_kkt(cnst_list, var_list, 0))
+ overall_error = 1.0;
+ DEBUG2("Iteration %d: Overall_error : %f", iteration, overall_error);
}
- sprintf(print_buf,")");
- trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
- strcat(trace_buf, print_buf);
- DEBUG1("%s",trace_buf);
- trace_buf[0]='\000';
- /* Printing Constraints */
- cnst_list = &(sys->active_constraint_set);
- xbt_swag_foreach(cnst, cnst_list) {
- sum=0.0;
- elem_list = &(cnst->element_set);
- sprintf(print_buf,"\t");
- trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
- strcat(trace_buf, print_buf);
- xbt_swag_foreach(elem, elem_list) {
- sprintf(print_buf,"%f.'%p'(%f) + ",elem->value,
- elem->variable,elem->variable->value);
- trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
- strcat(trace_buf, print_buf);
- sum += elem->value * elem->variable->value;
- }
- sprintf(print_buf,"0 <= %f ('%p')",cnst->bound,cnst);
- trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
- strcat(trace_buf, print_buf);
-
- if(!cnst->shared) {
- sprintf(print_buf," [MAX-Constraint]");
- trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
- strcat(trace_buf, print_buf);
- }
- DEBUG1("%s",trace_buf);
- trace_buf[0]='\000';
- if(!(sum<=cnst->bound))
- DEBUG3("Incorrect value (%f is not smaller than %f): %g",
- sum,cnst->bound,sum-cnst->bound);
+
+ __check_kkt(cnst_list, var_list, 1);
+
+ if (overall_error <= epsilon_min_error) {
+ DEBUG1("The method converges in %d iterations.", iteration);
+ }
+ if (iteration >= max_iterations) {
+ WARN1
+ ("Method reach %d iterations, which is the maximum number of iterations allowed.",
+ iteration);
}
+/* INFO1("Method converged after %d iterations", iteration); */
- /* Printing Result */
- xbt_swag_foreach(var, var_list) {
- if(var->bound>0) {
- DEBUG4("'%p'(%f) : %f (<=%f)",var,var->weight,var->value, var->bound);
- if(var->value<=var->bound)
- DEBUG0("Incorrect value");
- }
- else
- DEBUG3("'%p'(%f) : %f",var,var->weight,var->value);
+ if (XBT_LOG_ISENABLED(surf_lagrange, xbt_log_priority_debug)) {
+ lmm_print(sys);
}
+}
+/*
+ * Returns a double value corresponding to the result of a dichotomy proccess with
+ * respect to a given variable/constraint (\mu in the case of a variable or \lambda in
+ * case of a constraint) and a initial value init.
+ *
+ * @param init initial value for \mu or \lambda
+ * @param diff a function that computes the differential of with respect a \mu or \lambda
+ * @param var_cnst a pointer to a variable or constraint
+ * @param min_erro a minimun error tolerated
+ *
+ * @return a double correponding to the result of the dichotomyal process
+ */
+double dichotomy(double init, double diff(double, void *), void *var_cnst,
+ double min_error)
+{
+ double min, max;
+ double overall_error;
+ double middle;
+ double min_diff, max_diff, middle_diff;
+ double diff_0 = 0.0;
+ min = max = init;
- /*
- * Verify for each capacity constraint (lambda) the error associated.
- */
- capacity_error = 0;
- cnst_list=&(sys->active_constraint_set);
- xbt_swag_foreach(cnst1, cnst_list) {
- cnst2 = xbt_swag_getNext(cnst1,(var_list)->offset);
- if(cnst2 != NULL){
- capacity_error += fabs( cnst1->lambda - cnst2->lambda );
+ XBT_IN;
+
+ if (init == 0.0) {
+ min = max = 0.5;
+ }
+
+ min_diff = max_diff = middle_diff = 0.0;
+ overall_error = 1;
+
+ if ((diff_0 = diff(1e-16, var_cnst)) >= 0) {
+ CDEBUG1(surf_lagrange_dichotomy, "====> returning 0.0 (diff = %e)",
+ diff_0);
+ return 0.0;
+ }
+
+ CDEBUG1(surf_lagrange_dichotomy,
+ "====> not detected positive diff in 0 (%e)", diff_0);
+
+ while (overall_error > min_error) {
+
+ min_diff = diff(min, var_cnst);
+ max_diff = diff(max, var_cnst);
+
+ CDEBUG2(surf_lagrange_dichotomy,
+ "DICHOTOMY ===> min = %1.20f , max = %1.20f", min, max);
+ CDEBUG2(surf_lagrange_dichotomy,
+ "DICHOTOMY ===> diffmin = %1.20f , diffmax = %1.20f", min_diff,
+ max_diff);
+
+ if (min_diff > 0 && max_diff > 0) {
+ if (min == max) {
+ CDEBUG0(surf_lagrange_dichotomy, "Decreasing min");
+ min = min / 2.0;
+ } else {
+ CDEBUG0(surf_lagrange_dichotomy, "Decreasing max");
+ max = min;
}
- }
+ } else if (min_diff < 0 && max_diff < 0) {
+ if (min == max) {
+ CDEBUG0(surf_lagrange_dichotomy, "Increasing max");
+ max = max * 2.0;
+ } else {
+ CDEBUG0(surf_lagrange_dichotomy, "Increasing min");
+ min = max;
+ }
+ } else if (min_diff < 0 && max_diff > 0) {
+ middle = (max + min) / 2.0;
+ middle_diff = diff(middle, var_cnst);
- /*
- * Verify for each variable the error of round trip time constraint (mu).
- */
- bound_error = 0;
- var_list = &(sys->variable_set);
- xbt_swag_foreach(var1, var_list) {
- var2 = xbt_swag_getNext(var1,(var_list)->offset);
- if(var2 != NULL){
- bound_error += fabs( var2->mu - var1->mu);
+ if (max != 0.0 && min != 0.0) {
+ overall_error = fabs(min - max) / max;
}
- }
- overall_error = capacity_error + bound_error;
+ if (middle_diff < 0) {
+ min = middle;
+ } else if (middle_diff > 0) {
+ max = middle;
+ } else {
+ CWARN0(surf_lagrange_dichotomy,
+ "Found an optimal solution with 0 error!");
+ overall_error = 0;
+ return middle;
+ }
+
+ } else if (min_diff == 0) {
+ return min;
+ } else if (max_diff == 0) {
+ return max;
+ } else if (min_diff > 0 && max_diff < 0) {
+ CWARN0(surf_lagrange_dichotomy,
+ "The impossible happened, partial_diff(min) > 0 && partial_diff(max) < 0");
+ } else {
+ CWARN2(surf_lagrange_dichotomy,
+ "diffmin (%1.20f) or diffmax (%1.20f) are something I don't know, taking no action.",
+ min_diff, max_diff);
+ abort();
+ }
}
+ XBT_OUT;
+ CDEBUG1(surf_lagrange_dichotomy, "====> returning %e",
+ (min + max) / 2.0);
+ return ((min + max) / 2.0);
+}
+/*
+ *
+ */
+double partial_diff_mu(double mu, void *param_var)
+{
+ double mu_partial = 0.0;
+ double sigma_mu = 0.0;
+ lmm_variable_t var = (lmm_variable_t) param_var;
+ int i;
+ XBT_IN;
+ //compute sigma_i
+ for (i = 0; i < var->cnsts_number; i++)
+ sigma_mu += (var->cnsts[i].constraint)->lambda;
+
+ //compute sigma_i + mu_i
+ sigma_mu += mu;
+
+ //use auxiliar function passing (sigma_i + mu_i)
+ mu_partial = diff_aux(var, sigma_mu);
+
+ //add the RTT limit
+ mu_partial += var->bound;
+
+ XBT_OUT;
+ return mu_partial;
+}
- if(overall_error <= epsilon_min_error){
- DEBUG1("The method converge in %d iterations.", iteration);
- }else{
- WARN1("Method reach %d iterations, which is the maxmimun number of iterations allowed.", iteration);
- }
+/*
+ *
+ */
+double partial_diff_lambda(double lambda, void *param_cnst)
+{
+ int i;
+ xbt_swag_t elem_list = NULL;
+ lmm_element_t elem = NULL;
+ lmm_variable_t var = NULL;
+ lmm_constraint_t cnst = (lmm_constraint_t) param_cnst;
+ double lambda_partial = 0.0;
+ double sigma_i = 0.0;
- if(XBT_LOG_ISENABLED(surf_writelambda, xbt_log_priority_debug)) {
- fclose(gnuplot_file);
- }
+ XBT_IN;
+ elem_list = &(cnst->element_set);
+ CDEBUG1(surf_lagrange_dichotomy,"Computting diff of cnst (%p)", cnst);
- /*
- * Now computes the values of each variable (\rho) based on
- * the values of \lambda and \mu.
- */
- var_list = &(sys->variable_set);
- xbt_swag_foreach(var1, var_list) {
- tmp = 0;
- for(i=0; i<var1->cnsts_number; i++){
- elem1 = &(var1->cnsts[i]);
- tmp += (elem1->constraint)->lambda + var1->mu;
+ xbt_swag_foreach(elem, elem_list) {
+ var = elem->variable;
+ if (var->weight <= 0)
+ continue;
+
+ //initilize de sumation variable
+ sigma_i = 0.0;
+
+ //compute sigma_i of variable var
+ for (i = 0; i < var->cnsts_number; i++) {
+ sigma_i += (var->cnsts[i].constraint)->lambda;
}
- var1->weight = 1 / tmp;
- DEBUG2("var1->weight (id=%s) : %e", (char *)var1->id, var1->weight);
+ //add mu_i if this flow has a RTT constraint associated
+ if (var->bound > 0)
+ sigma_i += var->mu;
+
+ //replace value of cnst->lambda by the value of parameter lambda
+ sigma_i = (sigma_i - cnst->lambda) + lambda;
+
+ //use the auxiliar function passing (\sigma_i + \mu_i)
+ lambda_partial += diff_aux(var, sigma_i);
}
+ lambda_partial += cnst->bound;
+
+
+ CDEBUG1(surf_lagrange_dichotomy, "returning = %1.20f", lambda_partial);
+
+ XBT_OUT;
+ return lambda_partial;
+}
+
+
+double diff_aux(lmm_variable_t var, double x)
+{
+ double tmp_fpi, result;
+
+ XBT_IN2("(var (%p), x (%1.20f))", var, x);
+ xbt_assert0(var->func_fp,
+ "Initialize the protocol functions first create variables before.");
+ tmp_fpi = var->func_fpi(var, x);
+ result = - tmp_fpi;
+ CDEBUG1(surf_lagrange_dichotomy, "returning %1.20f", result);
+ XBT_OUT;
+ return result;
}
