src/surf/maxmin.c

   1 /*      $Id$     */
   2
   3 /* Copyright (c) 2004 Arnaud Legrand. All rights reserved.                  */
   4
   5 /* This program is free software; you can redistribute it and/or modify it
   6  * under the terms of the license (GNU LGPL) which comes with this package. */
   7
   8
   9 #include "xbt/sysdep.h"
  10 #include "xbt/log.h"
  11 #include "xbt/mallocator.h"
  12 #include "maxmin_private.h"
  13 #include <stdlib.h>
  14 #include <math.h>
  15 XBT_LOG_NEW_DEFAULT_SUBCATEGORY(surf_maxmin, surf,
  16                                 "Logging specific to SURF (maxmin)");
  17
  18 static void* lmm_variable_mallocator_new_f(void);
  19 static void lmm_variable_mallocator_free_f(void *var);
  20 static void lmm_variable_mallocator_reset_f(void *var);
  21
  22 lmm_system_t lmm_system_new(void)
  23 {
  24   lmm_system_t l = NULL;
  25   s_lmm_variable_t var;
  26   s_lmm_constraint_t cnst;
  27
  28   l = xbt_new0(s_lmm_system_t, 1);
  29
  30   l->modified = 0;
  31   xbt_swag_init(&(l->variable_set),
  32                 xbt_swag_offset(var, variable_set_hookup));
  33   xbt_swag_init(&(l->constraint_set),
  34                 xbt_swag_offset(cnst, constraint_set_hookup));
  35
  36   xbt_swag_init(&(l->active_constraint_set),
  37                 xbt_swag_offset(cnst, active_constraint_set_hookup));
  38
  39   xbt_swag_init(&(l->saturated_variable_set),
  40                 xbt_swag_offset(var, saturated_variable_set_hookup));
  41   xbt_swag_init(&(l->saturated_constraint_set),
  42                 xbt_swag_offset(cnst, saturated_constraint_set_hookup));
  43
  44   l->variable_mallocator = xbt_mallocator_new(64,
  45                                               lmm_variable_mallocator_new_f,
  46                                               lmm_variable_mallocator_free_f,
  47                                               lmm_variable_mallocator_reset_f);
  48
  49   return l;
  50 }
  51
  52 void lmm_system_free(lmm_system_t sys)
  53 {
  54   lmm_variable_t var = NULL;
  55   lmm_constraint_t cnst = NULL;
  56
  57   while ((var = extract_variable(sys)))
  58     lmm_var_free(sys, var);
  59
  60   while ((cnst = extract_constraint(sys)))
  61     lmm_cnst_free(sys, cnst);
  62
  63   xbt_mallocator_free(sys->variable_mallocator);
  64   free(sys);
  65 }
  66
  67 void lmm_variable_disable(lmm_system_t sys, lmm_variable_t var)
  68 {
  69   int i;
  70   lmm_element_t elem = NULL;
  71
  72   XBT_IN2("(sys=%p, var=%p)",sys,var);
  73   sys->modified = 1;
  74
  75   for (i = 0; i < var->cnsts_number; i++) {
  76     elem = &var->cnsts[i];
  77     xbt_swag_remove(elem, &(elem->constraint->element_set));
  78     xbt_swag_remove(elem, &(elem->constraint->active_element_set));
  79     if (!xbt_swag_size(&(elem->constraint->element_set)))
  80       make_constraint_inactive(sys, elem->constraint);
  81   }
  82   var->cnsts_number = 0;
  83   XBT_OUT;
  84 }
  85
  86 static void lmm_var_free(lmm_system_t sys, lmm_variable_t var)
  87 {
  88
  89   lmm_variable_disable(sys, var);
  90   free(var->cnsts);
  91   xbt_mallocator_release(sys->variable_mallocator, var);
  92 }
  93
  94 static void lmm_cnst_free(lmm_system_t sys, lmm_constraint_t cnst)
  95 {
  96 /*   xbt_assert0(xbt_swag_size(&(cnst->element_set)), */
  97 /*            "This list should be empty!"); */
  98   remove_active_constraint(sys, cnst);
  99   free(cnst);
 100 }
 101
 102 lmm_constraint_t lmm_constraint_new(lmm_system_t sys, void *id,
 103                                     double bound_value)
 104 {
 105   lmm_constraint_t cnst = NULL;
 106   s_lmm_element_t elem;
 107
 108   cnst = xbt_new0(s_lmm_constraint_t, 1);
 109   cnst->id = id;
 110   xbt_swag_init(&(cnst->element_set),
 111                 xbt_swag_offset(elem, element_set_hookup));
 112   xbt_swag_init(&(cnst->active_element_set),
 113                 xbt_swag_offset(elem, active_element_set_hookup));
 114
 115   cnst->bound = bound_value;
 116   cnst->usage = 0;
 117   cnst->shared = 1;
 118   insert_constraint(sys, cnst);
 119
 120   return cnst;
 121 }
 122
 123 void lmm_constraint_shared(lmm_constraint_t cnst)
 124 {
 125   cnst->shared = 0;
 126 }
 127
 128 void lmm_constraint_free(lmm_system_t sys, lmm_constraint_t cnst)
 129 {
 130   remove_constraint(sys, cnst);
 131   lmm_cnst_free(sys, cnst);
 132 }
 133
 134 static void* lmm_variable_mallocator_new_f(void) {
 135   return xbt_new(s_lmm_variable_t, 1);
 136 }
 137
 138 static void lmm_variable_mallocator_free_f(void *var) {
 139   xbt_free(var);
 140 }
 141
 142 static void lmm_variable_mallocator_reset_f(void *var) {
 143   /* memset to zero like calloc */
 144   memset(var, 0, sizeof(s_lmm_variable_t));
 145 }
 146
 147 lmm_variable_t lmm_variable_new(lmm_system_t sys, void *id,
 148                                 double weight,
 149                                 double bound, int number_of_constraints)
 150 {
 151   lmm_variable_t var = NULL;
 152   int i;
 153
 154   XBT_IN5("(sys=%p, id=%p, weight=%f, bound=%f, num_cons =%d)",
 155           sys,id,weight,bound,number_of_constraints);
 156
 157   var = xbt_mallocator_get(sys->variable_mallocator);
 158   var->id = id;
 159   var->cnsts = xbt_new0(s_lmm_element_t, number_of_constraints);
 160   for(i=0; i<number_of_constraints; i++) {
 161     /* Should be useless because of the
 162        calloc but it seems to help valgrind... */
 163     var->cnsts[i].element_set_hookup.next = NULL;
 164     var->cnsts[i].element_set_hookup.prev = NULL;
 165     var->cnsts[i].active_element_set_hookup.next = NULL;
 166     var->cnsts[i].active_element_set_hookup.prev = NULL;
 167     var->cnsts[i].constraint = NULL;
 168     var->cnsts[i].variable = NULL;
 169     var->cnsts[i].value = 0.0;
 170   }
 171   var->cnsts_size = number_of_constraints;
 172   var->cnsts_number = 0; /* Should be useless because of the
 173                             calloc but it seems to help valgrind... */
 174   var->weight = weight;
 175   var->bound = bound;
 176   var->value = 0.0;
 177   var->df    = 0.0;
 178   if(weight) xbt_swag_insert_at_head(var,&(sys->variable_set));
 179   else xbt_swag_insert_at_tail(var,&(sys->variable_set));
 180   XBT_OUT;
 181   return var;
 182 }
 183
 184 void lmm_variable_free(lmm_system_t sys, lmm_variable_t var)
 185 {
 186   remove_variable(sys, var);
 187   lmm_var_free(sys, var);
 188 }
 189
 190 double lmm_variable_getvalue(lmm_variable_t var)
 191 {
 192   return (var->value);
 193 }
 194
 195 void lmm_expand(lmm_system_t sys, lmm_constraint_t cnst,
 196                 lmm_variable_t var, double value)
 197 {
 198   lmm_element_t elem = NULL;
 199
 200   sys->modified = 1;
 201
 202   xbt_assert0(var->cnsts_number < var->cnsts_size,
 203               "Too much constraints");
 204
 205   elem = &(var->cnsts[var->cnsts_number++]);
 206
 207   elem->value = value;
 208   elem->constraint = cnst;
 209   elem->variable = var;
 210
 211   if(var->weight) xbt_swag_insert_at_head(elem,&(elem->constraint->element_set));
 212   else xbt_swag_insert_at_tail(elem,&(elem->constraint->element_set));
 213
 214   make_constraint_active(sys, cnst);
 215 }
 216
 217 void lmm_expand_add(lmm_system_t sys, lmm_constraint_t cnst,
 218                     lmm_variable_t var, double value)
 219 {
 220   int i ;
 221   sys->modified = 1;
 222
 223   for(i=0; i< var->cnsts_number ; i++)
 224     if(var->cnsts[i].constraint == cnst) break;
 225
 226   if(i<var->cnsts_number) var->cnsts[i].value +=value;
 227   else lmm_expand(sys,cnst,var,value);
 228 }
 229
 230 void lmm_elem_set_value(lmm_system_t sys, lmm_constraint_t cnst,
 231                         lmm_variable_t var, double value)
 232 {
 233   int i ;
 234
 235   for(i=0; i< var->cnsts_number ; i++)
 236     if(var->cnsts[i].constraint == cnst) break;
 237
 238   if(i<var->cnsts_number) {
 239     var->cnsts[i].value =value;
 240     sys->modified = 1;
 241   } else DIE_IMPOSSIBLE;
 242 }
 243
 244 lmm_constraint_t lmm_get_cnst_from_var(lmm_system_t sys,
 245                                        lmm_variable_t var, int num)
 246 {
 247   if (num < var->cnsts_number)
 248     return (var->cnsts[num].constraint);
 249   else
 250     return NULL;
 251 }
 252
 253 int lmm_get_number_of_cnst_from_var(lmm_system_t sys, lmm_variable_t var)
 254 {
 255   return (var->cnsts_number);
 256 }
 257
 258 lmm_variable_t lmm_get_var_from_cnst(lmm_system_t sys,
 259                                      lmm_constraint_t cnst,
 260                                      lmm_variable_t * var)
 261 {
 262   if (!(*var))
 263     xbt_swag_getFirst(&(cnst->element_set));
 264   else
 265     *var = xbt_swag_getNext(*var, cnst->element_set.offset);
 266   return *var;
 267 }
 268
 269 void *lmm_constraint_id(lmm_constraint_t cnst)
 270 {
 271   return cnst->id;
 272 }
 273
 274 void *lmm_variable_id(lmm_variable_t var)
 275 {
 276   return var->id;
 277 }
 278
 279 static void saturated_constraint_set_update(lmm_system_t sys,
 280                                             lmm_constraint_t cnst,
 281                                             double *min_usage)
 282 {
 283   lmm_constraint_t useless_cnst = NULL;
 284
 285   XBT_IN3("sys=%p, cnst=%p, min_usage=%f",sys,cnst,*min_usage);
 286   if (cnst->usage <= 0) {
 287     XBT_OUT;
 288     return;
 289   }
 290   if (cnst->remaining <= 0) {
 291     XBT_OUT;
 292     return;
 293   }
 294   if ((*min_usage < 0) || (*min_usage > cnst->remaining / cnst->usage)) {
 295     *min_usage = cnst->remaining / cnst->usage;
 296     LOG3(xbt_log_priority_trace,
 297          "min_usage=%f (cnst->remaining=%f, cnst->usage=%f)",*min_usage,
 298          cnst->remaining, cnst->usage);
 299     while ((useless_cnst =
 300             xbt_swag_getFirst(&(sys->saturated_constraint_set))))
 301       xbt_swag_remove(useless_cnst, &(sys->saturated_constraint_set));
 302
 303     xbt_swag_insert(cnst, &(sys->saturated_constraint_set));
 304   } else if (*min_usage == cnst->remaining / cnst->usage) {
 305     xbt_swag_insert(cnst, &(sys->saturated_constraint_set));
 306   }
 307   XBT_OUT;
 308 }
 309
 310 static void saturated_variable_set_update(lmm_system_t sys)
 311 {
 312   lmm_constraint_t cnst = NULL;
 313   xbt_swag_t cnst_list = NULL;
 314   lmm_element_t elem = NULL;
 315   xbt_swag_t elem_list = NULL;
 316
 317   cnst_list = &(sys->saturated_constraint_set);
 318   while ((cnst = xbt_swag_getFirst(cnst_list))) {
 319     elem_list = &(cnst->active_element_set);
 320     xbt_swag_foreach(elem, elem_list) {
 321       if(elem->variable->weight<=0) break;
 322       if ((elem->value > 0))
 323         xbt_swag_insert(elem->variable, &(sys->saturated_variable_set));
 324     }
 325     xbt_swag_remove(cnst, cnst_list);
 326   }
 327 }
 328
 329 void lmm_print(lmm_system_t sys)
 330 {
 331   lmm_constraint_t cnst = NULL;
 332   lmm_element_t elem = NULL;
 333   lmm_variable_t var = NULL;
 334   xbt_swag_t cnst_list = NULL;
 335   xbt_swag_t var_list = NULL;
 336   xbt_swag_t elem_list = NULL;
 337   char print_buf[1024];
 338   char *trace_buf=xbt_malloc0(sizeof(char));
 339   double sum=0.0;
 340
 341   /* Printing Objective */
 342   var_list = &(sys->variable_set);
 343   sprintf(print_buf,"MAX-MIN ( ");
 344   trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
 345   strcat(trace_buf, print_buf);
 346   xbt_swag_foreach(var, var_list) {
 347     sprintf(print_buf,"'%p'(%f) ",var,var->weight);
 348     trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
 349     strcat(trace_buf, print_buf);
 350   }
 351   sprintf(print_buf,")");
 352   trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
 353   strcat(trace_buf, print_buf);
 354   DEBUG1("%s",trace_buf);
 355   trace_buf[0]='\000';
 356
 357   /* Printing Constraints */
 358   cnst_list = &(sys->active_constraint_set);
 359   xbt_swag_foreach(cnst, cnst_list) {
 360     sum=0.0;
 361     elem_list = &(cnst->element_set);
 362     sprintf(print_buf,"\t");
 363     trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
 364     strcat(trace_buf, print_buf);
 365     xbt_swag_foreach(elem, elem_list) {
 366       sprintf(print_buf,"%f.'%p'(%f) + ",elem->value,
 367               elem->variable,elem->variable->value);
 368       trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
 369       strcat(trace_buf, print_buf);
 370       sum += elem->value * elem->variable->value;
 371     }
 372     sprintf(print_buf,"0 <= %f ('%p')",cnst->bound,cnst);
 373     trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
 374     strcat(trace_buf, print_buf);
 375
 376     if(!cnst->shared) {
 377       sprintf(print_buf," [MAX-Constraint]");
 378       trace_buf = xbt_realloc(trace_buf,strlen(trace_buf)+strlen(print_buf)+1);
 379       strcat(trace_buf, print_buf);
 380     }
 381     DEBUG1("%s",trace_buf);
 382     trace_buf[0]='\000';
 383     xbt_assert3((sum<=cnst->bound), "Incorrect value (%f is not smaller than %f): %g",
 384                 sum,cnst->bound,sum-cnst->bound);
 385   }
 386
 387   /* Printing Result */
 388   xbt_swag_foreach(var, var_list) {
 389     if(var->bound>0) {
 390       DEBUG4("'%p'(%f) : %f (<=%f)",var,var->weight,var->value, var->bound);
 391       xbt_assert0((var->value<=var->bound), "Incorrect value");
 392     }
 393     else
 394       DEBUG3("'%p'(%f) : %f",var,var->weight,var->value);
 395   }
 396
 397   free(trace_buf);
 398 }
 399
 400 void lmm_solve(lmm_system_t sys)
 401 {
 402   lmm_variable_t var = NULL;
 403   lmm_constraint_t cnst = NULL;
 404   lmm_element_t elem = NULL;
 405   xbt_swag_t cnst_list = NULL;
 406   xbt_swag_t var_list = NULL;
 407   xbt_swag_t elem_list = NULL;
 408   double min_usage = -1;
 409
 410   if (!(sys->modified))
 411     return;
 412
 413   /* Init */
 414   var_list = &(sys->variable_set);
 415   DEBUG1("Variable set : %d", xbt_swag_size(var_list));
 416   xbt_swag_foreach(var, var_list) {
 417     var->value = 0.0;
 418   }
 419
 420   /*
 421    * Compute Usage and store the variables that reach the maximum.
 422    */
 423   cnst_list = &(sys->active_constraint_set);
 424   DEBUG1("Active constraints : %d", xbt_swag_size(cnst_list));
 425   xbt_swag_foreach(cnst, cnst_list) {
 426     /* INIT */
 427     cnst->remaining = cnst->bound;
 428     cnst->usage = 0;
 429     elem_list = &(cnst->element_set);
 430     cnst->usage = 0.0;
 431     xbt_swag_foreach(elem, elem_list) {
 432       if(elem->variable->weight <=0) break;
 433       if ((elem->value > 0)) {
 434         if(cnst->shared)
 435           cnst->usage += elem->value / elem->variable->weight;
 436         else
 437           if(cnst->usage<elem->value / elem->variable->weight)
 438             cnst->usage = elem->value / elem->variable->weight;
 439         DEBUG2("Constraint Usage %p : %f",cnst,cnst->usage);
 440         make_elem_active(elem);
 441       }
 442     }
 443     /* Saturated constraints update */
 444     saturated_constraint_set_update(sys, cnst, &min_usage);
 445   }
 446   saturated_variable_set_update(sys);
 447
 448   /* Saturated variables update */
 449
 450   do {
 451     /* Fix the variables that have to be */
 452     var_list = &(sys->saturated_variable_set);
 453
 454     xbt_swag_foreach(var, var_list) {
 455       /* First check if some of these variables have reach their upper
 456          bound and update min_usage accordingly. */
 457       DEBUG5("var=%p, var->bound=%f, var->weight=%f, min_usage=%f, var->bound*var->weight=%f",
 458              var, var->bound, var->weight, min_usage,var->bound * var->weight);
 459       if ((var->bound > 0) && (var->bound * var->weight < min_usage)) {
 460         min_usage = var->bound * var->weight;
 461         DEBUG1("Updated min_usage=%f",min_usage);
 462       }
 463     }
 464
 465
 466     while ((var = xbt_swag_getFirst(var_list))) {
 467       int i;
 468
 469       var->value = min_usage / var->weight;
 470       DEBUG5("Min usage: %f, Var(%p)->weight: %f, Var(%p)->value: %f ",min_usage,var,var->weight,var,var->value);
 471
 472
 473       /* Update usage */
 474
 475       for (i = 0; i < var->cnsts_number; i++) {
 476         elem = &var->cnsts[i];
 477         cnst = elem->constraint;
 478         if(cnst->shared) {
 479           double_update(&(cnst->remaining), elem->value * var->value);
 480           double_update(&(cnst->usage), elem->value / var->weight);
 481           make_elem_inactive(elem);
 482         } else { /* FIXME one day: We recompute usage.... :( */
 483           cnst->usage = 0.0;
 484           make_elem_inactive(elem);
 485           xbt_swag_foreach(elem, elem_list) {
 486             if(elem->variable->weight <=0) break;
 487             if(elem->variable->value > 0) break;
 488             if ((elem->value > 0)) {
 489               if(cnst->usage<elem->value / elem->variable->weight)
 490                 cnst->usage = elem->value / elem->variable->weight;
 491               DEBUG2("Constraint Usage %p : %f",cnst,cnst->usage);
 492               make_elem_active(elem);
 493             }
 494           }
 495         }
 496       }
 497       xbt_swag_remove(var, var_list);
 498     }
 499
 500     /* Find out which variables reach the maximum */
 501     cnst_list = &(sys->active_constraint_set);
 502     min_usage = -1;
 503     xbt_swag_foreach(cnst, cnst_list) {
 504       saturated_constraint_set_update(sys, cnst, &min_usage);
 505     }
 506     saturated_variable_set_update(sys);
 507
 508   } while (xbt_swag_size(&(sys->saturated_variable_set)));
 509
 510   sys->modified = 0;
 511   if(XBT_LOG_ISENABLED(surf_maxmin, xbt_log_priority_debug)) {
 512     lmm_print(sys);
 513   }
 514 }
 515
 516 /* Not a O(1) function */
 517
 518 void lmm_update(lmm_system_t sys, lmm_constraint_t cnst,
 519                 lmm_variable_t var, double value)
 520 {
 521   int i;
 522
 523   sys->modified = 1;
 524   for (i = 0; i < var->cnsts_number; i++)
 525     if (var->cnsts[i].constraint == cnst) {
 526       var->cnsts[i].value = value;
 527       return;
 528     }
 529 }
 530
 531 /** \brief Attribute the value bound to var->bound.
 532  *
 533  *  \param sys the lmm_system_t
 534  *  \param var the lmm_variable_t
 535  *  \param bound the new bound to associate with var
 536  *
 537  *  Makes var->bound equal to bound. Whenever this function is called
 538  *  a change is  signed in the system. To
 539  *  avoid false system changing detection it is a good idea to test
 540  *  (bound != 0) before calling it.
 541  *
 542  */
 543 void lmm_update_variable_bound(lmm_system_t sys, lmm_variable_t var,
 544                                double bound)
 545 {
 546   sys->modified = 1;
 547   var->bound = bound;
 548 }
 549
 550 /** \brief Add the value delta to var->df (the sum of latencies).
 551  *
 552  *  \param sys the lmm_system_t associated
 553  *  \param var the lmm_variable_t which need to updated
 554  *  \param delta the variation of the latency
 555  *
 556  *  Add the value delta to var->df (the sum of latencys associated to the
 557  *  flow). Whenever this function is called a change is  signed in the system. To
 558  *  avoid false system changing detection it is a good idea to test
 559  *  (delta != 0) before calling it.
 560  *
 561  */
 562 void lmm_update_variable_latency(lmm_system_t sys, lmm_variable_t var,
 563                                double delta)
 564 {
 565   sys->modified = 1;
 566   var->df += delta;
 567 }
 568
 569 void lmm_update_variable_weight(lmm_system_t sys, lmm_variable_t var,
 570                                 double weight)
 571 {
 572   int i ;
 573   lmm_element_t elem;
 574
 575   XBT_IN3("(sys=%p, var=%p, weight=%f)",sys,var,weight);
 576   sys->modified = 1;
 577   var->weight = weight;
 578   xbt_swag_remove(var,&(sys->variable_set));
 579   if(weight) xbt_swag_insert_at_head(var,&(sys->variable_set));
 580   else xbt_swag_insert_at_tail(var,&(sys->variable_set));
 581
 582   for (i = 0; i < var->cnsts_number; i++) {
 583     elem = &var->cnsts[i];
 584     xbt_swag_remove(elem, &(elem->constraint->element_set));
 585     if(weight) xbt_swag_insert_at_head(elem, &(elem->constraint->element_set));
 586     else xbt_swag_insert_at_tail(elem, &(elem->constraint->element_set));
 587   }
 588   XBT_OUT;
 589 }
 590
 591 double lmm_get_variable_weight(lmm_variable_t var)
 592
 593 {
 594   return var->weight;
 595 }
 596
 597 void lmm_update_constraint_bound(lmm_system_t sys, lmm_constraint_t cnst,
 598                                  double bound)
 599 {
 600   sys->modified = 1;
 601   cnst->bound = bound;
 602 }
 603
 604 int lmm_constraint_used(lmm_system_t sys, lmm_constraint_t cnst)
 605 {
 606   return xbt_swag_belongs(cnst, &(sys->active_constraint_set));
 607 }
 608
 609 lmm_constraint_t lmm_get_first_active_constraint(lmm_system_t sys)
 610 {
 611   return xbt_swag_getFirst(&(sys->active_constraint_set));
 612 }
 613
 614 lmm_constraint_t lmm_get_next_active_constraint(lmm_system_t sys, lmm_constraint_t cnst)
 615 {
 616   return xbt_swag_getNext(cnst,(sys->active_constraint_set).offset);
 617 }
 618
 619 /** \brief Attribute the value bound to var->bound.
 620  *
 621  *  \param func_f    default function f associated with the chosen protocol flavor
 622  *  \param func_fp   partial differential of f (f prime, f')
 623  *  \param func_fpi  inverse of the partial differential of f (f prime inverse, (f')^{-1})
 624  *  \param func_fpip partial differential of the inverse of the partial differential of f (f prime inverse prime, ((f')^{-1})')
 625  *
 626  *  Set default functions to the ones passed as parameters.
 627  *
 628  */
 629 void lmm_set_default_protocol_functions(double (* func_f)    (lmm_variable_t var, double x),
 630                                         double (* func_fp)   (lmm_variable_t var, double x),
 631                                         double (* func_fpi)  (lmm_variable_t var, double x),
 632                                         double (* func_fpip) (lmm_variable_t var, double x))
 633
 634 {
 635   func_f_def    = func_f;
 636   func_fp_def   = func_fp;
 637   func_fpi_def  = func_fpi;
 638   func_fpip_def = func_fpip;
 639 }
 640
 641
 642 /*
 643  * NOTE for Reno: all functions consider the network
 644  * coeficient (alpha) equal to 1.
 645  */
 646
 647 /*
 648  * For Reno f: $\alpha_f d_f \log\left(x_f\right)$
 649  */
 650 double func_reno_f(lmm_variable_t var, double x){
 651   xbt_assert0(x,"Please report this bug.");
 652   return var->df * log(x);
 653 }
 654
 655 /*
 656  * For Reno fp: $\frac{\alpha D_f}{x}$
 657  */
 658 double func_reno_fp(lmm_variable_t var, double x){
 659   xbt_assert0(x,"Please report this bug.");
 660   return var->df/x;
 661 }
 662
 663 /*
 664  * For Reno fpi: $\frac{\alpha D_f}{x}$
 665  */
 666 double func_reno_fpi(lmm_variable_t var, double x){
 667   xbt_assert0(x,"Please report this bug.");
 668   return var->df/x;
 669 }
 670
 671 /*
 672  * For Reno fpip: $-\frac{\alpha D_f}{x^2}$
 673  */
 674 double func_reno_fpip(lmm_variable_t var, double x){
 675   xbt_assert0(x,"Please report this bug.");
 676   return -( var->df/(x*x) ) ;
 677 }
 678
 679
 680 /*
 681  * For Vegas f: $\frac{\sqrt{\frac{3}{2}}}{D_f} \arctan\left(\sqrt{\frac{3}{2}}x_f D_f\right)$
 682  */
 683 double func_vegas_f(lmm_variable_t var, double x){
 684   xbt_assert0(x,"Please report this bug.");
 685   // \sqrt{3/2} = 0.8164965808
 686   return (0.8164965808 / var->df) * atan( (0.8164965808 / var->df)*x );
 687 }
 688
 689 /*
 690  * For Vegas fp: $\frac{3{D_f}^2}{3{D_f}^2x^2 + 2}$
 691  */
 692 double func_vegas_fp(lmm_variable_t var, double x){
 693   xbt_assert0(x,"Please report this bug.");
 694   return (3*var->df*var->df) / (3*var->df*var->df*x*x + 2);
 695 }
 696
 697 /*
 698  * For Vegas fpi: $\sqrt{\frac{1}{x} - \frac{2}{3{D_f}^2}}$
 699  */
 700 double func_vegas_fpi(lmm_variable_t var, double x){
 701   double res_fpi;
 702   xbt_assert0( (x<0.0) ,"Please report this bug.");
 703   xbt_assert0( (var->df<0.0), "Please report this bug.");
 704   res_fpi = (1/x) - 2/(3*var->df*var->df);
 705   return sqrt(res_fpi);
 706 }
 707
 708 /*
 709  * For Vegas fpip:  $-\frac{1}{2x^2\sqrt{\frac{1}{x} - \frac{2}{3{D_f}^2}}}$
 710  */
 711 double func_vegas_fpip(lmm_variable_t var, double x){
 712   double res_fpip;
 713   xbt_assert0(x,"Please report this bug.");
 714   xbt_assert0( (x<0.0), "Please report this bug.");
 715   res_fpip = sqrt(1/x - 2/(3*var->df*var->df));
 716   return -(1/(2*x*x*res_fpip));
 717 }