src/surf/network_cm02.cpp

   1 /* Copyright (c) 2013-2015. The SimGrid Team.
   2  * All rights reserved.                                                     */
   3
   4 /* This program is free software; you can redistribute it and/or modify it
   5  * under the terms of the license (GNU LGPL) which comes with this package. */
   6
   7 #include <algorithm>
   8
   9 #include "network_cm02.hpp"
  10 #include "maxmin_private.hpp"
  11 #include "simgrid/sg_config.h"
  12 #include "src/instr/instr_private.h" // TRACE_is_enabled(). FIXME: remove by subscribing tracing to the surf signals
  13
  14 XBT_LOG_EXTERNAL_DEFAULT_CATEGORY(surf_network);
  15
  16 double sg_sender_gap = 0.0;
  17 double sg_latency_factor = 1.0; /* default value; can be set by model or from command line */
  18 double sg_bandwidth_factor = 1.0;       /* default value; can be set by model or from command line */
  19 double sg_weight_S_parameter = 0.0;     /* default value; can be set by model or from command line */
  20
  21 double sg_tcp_gamma = 0.0;
  22 int sg_network_crosstraffic = 0;
  23
  24 /************************************************************************/
  25 /* New model based on optimizations discussed during Pedro Velho's thesis*/
  26 /************************************************************************/
  27 /* @techreport{VELHO:2011:HAL-00646896:1, */
  28 /*      url = {http://hal.inria.fr/hal-00646896/en/}, */
  29 /*      title = {{Flow-level network models: have we reached the limits?}}, */
  30 /*      author = {Velho, Pedro and Schnorr, Lucas and Casanova, Henri and Legrand, Arnaud}, */
  31 /*      type = {Rapport de recherche}, */
  32 /*      institution = {INRIA}, */
  33 /*      number = {RR-7821}, */
  34 /*      year = {2011}, */
  35 /*      month = Nov, */
  36 /*      pdf = {http://hal.inria.fr/hal-00646896/PDF/rr-validity.pdf}, */
  37 /*  } */
  38 void surf_network_model_init_LegrandVelho(void)
  39 {
  40   if (surf_network_model)
  41     return;
  42
  43   surf_network_model = new simgrid::surf::NetworkCm02Model();
  44   xbt_dynar_push(all_existing_models, &surf_network_model);
  45
  46   xbt_cfg_setdefault_double("network/latency-factor",      13.01);
  47   xbt_cfg_setdefault_double("network/bandwidth-factor",     0.97);
  48   xbt_cfg_setdefault_double("network/weight-S",         20537);
  49 }
  50
  51 /***************************************************************************/
  52 /* The nice TCP sharing model designed by Loris Marchal and Henri Casanova */
  53 /***************************************************************************/
  54 /* @TechReport{      rr-lip2002-40, */
  55 /*   author        = {Henri Casanova and Loris Marchal}, */
  56 /*   institution   = {LIP}, */
  57 /*   title         = {A Network Model for Simulation of Grid Application}, */
  58 /*   number        = {2002-40}, */
  59 /*   month         = {oct}, */
  60 /*   year          = {2002} */
  61 /* } */
  62 void surf_network_model_init_CM02(void)
  63 {
  64
  65   if (surf_network_model)
  66     return;
  67
  68   surf_network_model = new simgrid::surf::NetworkCm02Model();
  69   xbt_dynar_push(all_existing_models, &surf_network_model);
  70
  71   xbt_cfg_setdefault_double("network/latency-factor",   1.0);
  72   xbt_cfg_setdefault_double("network/bandwidth-factor", 1.0);
  73   xbt_cfg_setdefault_double("network/weight-S",         0.0);
  74 }
  75
  76 /***************************************************************************/
  77 /* The models from Steven H. Low                                           */
  78 /***************************************************************************/
  79 /* @article{Low03,                                                         */
  80 /*   author={Steven H. Low},                                               */
  81 /*   title={A Duality Model of {TCP} and Queue Management Algorithms},     */
  82 /*   year={2003},                                                          */
  83 /*   journal={{IEEE/ACM} Transactions on Networking},                      */
  84 /*    volume={11}, number={4},                                             */
  85 /*  }                                                                      */
  86 void surf_network_model_init_Reno(void)
  87 {
  88   if (surf_network_model)
  89     return;
  90
  91   surf_network_model = new simgrid::surf::NetworkCm02Model();
  92   xbt_dynar_push(all_existing_models, &surf_network_model);
  93
  94   lmm_set_default_protocol_function(func_reno_f, func_reno_fp, func_reno_fpi);
  95   surf_network_model->f_networkSolve = lagrange_solve;
  96
  97   xbt_cfg_setdefault_double("network/latency-factor",     10.4);
  98   xbt_cfg_setdefault_double("network/bandwidth-factor",    0.92);
  99   xbt_cfg_setdefault_double("network/weight-S",         8775);
 100 }
 101
 102
 103 void surf_network_model_init_Reno2(void)
 104 {
 105   if (surf_network_model)
 106     return;
 107
 108   surf_network_model = new simgrid::surf::NetworkCm02Model();
 109   xbt_dynar_push(all_existing_models, &surf_network_model);
 110
 111   lmm_set_default_protocol_function(func_reno2_f, func_reno2_fp, func_reno2_fpi);
 112   surf_network_model->f_networkSolve = lagrange_solve;
 113
 114   xbt_cfg_setdefault_double("network/latency-factor",    10.4);
 115   xbt_cfg_setdefault_double("network/bandwidth-factor",   0.92);
 116   xbt_cfg_setdefault_double("network/weight-S",        8775);
 117 }
 118
 119 void surf_network_model_init_Vegas(void)
 120 {
 121   if (surf_network_model)
 122     return;
 123
 124   surf_network_model = new simgrid::surf::NetworkCm02Model();
 125   xbt_dynar_push(all_existing_models, &surf_network_model);
 126
 127   lmm_set_default_protocol_function(func_vegas_f, func_vegas_fp, func_vegas_fpi);
 128   surf_network_model->f_networkSolve = lagrange_solve;
 129
 130   xbt_cfg_setdefault_double("network/latency-factor",    10.4);
 131   xbt_cfg_setdefault_double("network/bandwidth-factor",   0.92);
 132   xbt_cfg_setdefault_double("network/weight-S",        8775);
 133 }
 134
 135 namespace simgrid {
 136 namespace surf {
 137
 138 NetworkCm02Model::NetworkCm02Model()
 139   :NetworkModel()
 140 {
 141   char *optim = xbt_cfg_get_string("network/optim");
 142   int select = xbt_cfg_get_boolean("network/maxmin-selective-update");
 143
 144   if (!strcmp(optim, "Full")) {
 145     updateMechanism_ = UM_FULL;
 146     selectiveUpdate_ = select;
 147   } else if (!strcmp(optim, "Lazy")) {
 148     updateMechanism_ = UM_LAZY;
 149     selectiveUpdate_ = 1;
 150     xbt_assert((select == 1) || (xbt_cfg_is_default_value("network/maxmin-selective-update")),
 151                "Disabling selective update while using the lazy update mechanism is dumb!");
 152   } else {
 153     xbt_die("Unsupported optimization (%s) for this model", optim);
 154   }
 155
 156   if (!maxminSystem_)
 157     maxminSystem_ = lmm_system_new(selectiveUpdate_);
 158
 159   routing_model_create(createLink("__loopback__", 498000000, 0.000015, SURF_LINK_FATPIPE, NULL));
 160
 161   if (updateMechanism_ == UM_LAZY) {
 162   actionHeap_ = xbt_heap_new(8, NULL);
 163   xbt_heap_set_update_callback(actionHeap_, surf_action_lmm_update_index_heap);
 164   modifiedSet_ = new ActionLmmList();
 165   maxminSystem_->keep_track = modifiedSet_;
 166   }
 167 }
 168
 169 NetworkCm02Model::~NetworkCm02Model() {}
 170
 171 Link* NetworkCm02Model::createLink(const char *name, double bandwidth, double latency, e_surf_link_sharing_policy_t policy,
 172     xbt_dict_t properties)
 173 {
 174   return new NetworkCm02Link(this, name, properties, bandwidth, latency, policy, maxminSystem_);
 175 }
 176
 177 void NetworkCm02Model::updateActionsStateLazy(double now, double /*delta*/)
 178 {
 179   NetworkCm02Action *action;
 180   while ((xbt_heap_size(actionHeap_) > 0)
 181          && (double_equals(xbt_heap_maxkey(actionHeap_), now, sg_surf_precision))) {
 182     action = static_cast<NetworkCm02Action*> (xbt_heap_pop(actionHeap_));
 183     XBT_DEBUG("Something happened to action %p", action);
 184     if (TRACE_is_enabled()) {
 185       int n = lmm_get_number_of_cnst_from_var(maxminSystem_, action->getVariable());
 186
 187       for (int i = 0; i < n; i++){
 188         lmm_constraint_t constraint = lmm_get_cnst_from_var(maxminSystem_, action->getVariable(), i);
 189         NetworkCm02Link *link = static_cast<NetworkCm02Link*>(lmm_constraint_id(constraint));
 190         TRACE_surf_link_set_utilization(link->getName(),
 191                                         action->getCategory(),
 192                                         (lmm_variable_getvalue(action->getVariable())*
 193                                             lmm_get_cnst_weight_from_var(maxminSystem_,
 194                                                 action->getVariable(),
 195                                                 i)),
 196                                         action->getLastUpdate(),
 197                                         now - action->getLastUpdate());
 198       }
 199     }
 200
 201     // if I am wearing a latency hat
 202     if (action->getHat() == LATENCY) {
 203       XBT_DEBUG("Latency paid for action %p. Activating", action);
 204       lmm_update_variable_weight(maxminSystem_, action->getVariable(), action->weight_);
 205       action->heapRemove(actionHeap_);
 206       action->refreshLastUpdate();
 207
 208         // if I am wearing a max_duration or normal hat
 209     } else if (action->getHat() == MAX_DURATION ||
 210         action->getHat() == NORMAL) {
 211         // no need to communicate anymore
 212         // assume that flows that reached max_duration have remaining of 0
 213       XBT_DEBUG("Action %p finished", action);
 214       action->setRemains(0);
 215       action->finish();
 216       action->setState(Action::State::done);
 217       action->heapRemove(actionHeap_);
 218
 219       action->gapRemove();
 220     }
 221   }
 222   return;
 223 }
 224
 225
 226 void NetworkCm02Model::updateActionsStateFull(double now, double delta)
 227 {
 228   NetworkCm02Action *action;
 229   ActionList *running_actions = getRunningActionSet();
 230
 231   for(ActionList::iterator it(running_actions->begin()), itNext=it, itend(running_actions->end())
 232      ; it != itend ; it=itNext) {
 233   ++itNext;
 234
 235     action = static_cast<NetworkCm02Action*> (&*it);
 236     XBT_DEBUG("Something happened to action %p", action);
 237       double deltap = delta;
 238       if (action->latency_ > 0) {
 239         if (action->latency_ > deltap) {
 240           double_update(&(action->latency_), deltap, sg_surf_precision);
 241           deltap = 0.0;
 242         } else {
 243           double_update(&(deltap), action->latency_, sg_surf_precision);
 244           action->latency_ = 0.0;
 245         }
 246         if (action->latency_ == 0.0 && !(action->isSuspended()))
 247           lmm_update_variable_weight(maxminSystem_, action->getVariable(),
 248               action->weight_);
 249       }
 250       if (TRACE_is_enabled()) {
 251         int n = lmm_get_number_of_cnst_from_var(maxminSystem_, action->getVariable());
 252         for (int i = 0; i < n; i++){
 253           lmm_constraint_t constraint = lmm_get_cnst_from_var(maxminSystem_, action->getVariable(), i);
 254
 255           NetworkCm02Link* link = static_cast<NetworkCm02Link*>(lmm_constraint_id(constraint));
 256           TRACE_surf_link_set_utilization(link->getName(),
 257                                         action->getCategory(),
 258                                         (lmm_variable_getvalue(action->getVariable())*
 259                                             lmm_get_cnst_weight_from_var(maxminSystem_,
 260                                                 action->getVariable(),
 261                                                 i)),
 262                                         action->getLastUpdate(),
 263                                         now - action->getLastUpdate());
 264         }
 265       }
 266       if (!lmm_get_number_of_cnst_from_var (maxminSystem_, action->getVariable())) {
 267         /* There is actually no link used, hence an infinite bandwidth.
 268          * This happens often when using models like vivaldi.
 269          * In such case, just make sure that the action completes immediately.
 270          */
 271         action->updateRemains(action->getRemains());
 272       }
 273     action->updateRemains(lmm_variable_getvalue(action->getVariable()) * delta);
 274
 275     if (action->getMaxDuration() != NO_MAX_DURATION)
 276       action->updateMaxDuration(delta);
 277
 278     if ((action->getRemains() <= 0) &&
 279         (lmm_get_variable_weight(action->getVariable()) > 0)) {
 280       action->finish();
 281       action->setState(Action::State::done);
 282       action->gapRemove();
 283     } else if (((action->getMaxDuration() != NO_MAX_DURATION)
 284         && (action->getMaxDuration() <= 0))) {
 285       action->finish();
 286       action->setState(Action::State::done);
 287       action->gapRemove();
 288     }
 289   }
 290 }
 291
 292 Action *NetworkCm02Model::communicate(NetCard *src, NetCard *dst, double size, double rate)
 293 {
 294   int failed = 0;
 295   double bandwidth_bound;
 296   double latency = 0.0;
 297   std::vector<Link*> * back_route = NULL;
 298   int constraints_per_variable = 0;
 299
 300   std::vector<Link*> *route = new std::vector<Link*>();
 301
 302   XBT_IN("(%s,%s,%g,%g)", src->name(), dst->name(), size, rate);
 303
 304   routing_platf->getRouteAndLatency(src, dst, route, &latency);
 305   xbt_assert(! route->empty() || latency,
 306              "You're trying to send data from %s to %s but there is no connecting path between these two hosts.",
 307              src->name(), dst->name());
 308
 309   for (auto link: *route)
 310     if (link->isOff())
 311       failed = 1;
 312
 313   if (sg_network_crosstraffic == 1) {
 314     back_route = new std::vector<Link*>();
 315     routing_platf->getRouteAndLatency(dst, src, back_route, NULL);
 316     for (auto link: *back_route)
 317       if (link->isOff())
 318         failed = 1;
 319   }
 320
 321   NetworkCm02Action *action = new NetworkCm02Action(this, size, failed);
 322   action->weight_ = action->latency_ = latency;
 323
 324   action->rate_ = rate;
 325   if (updateMechanism_ == UM_LAZY) {
 326     action->indexHeap_ = -1;
 327     action->lastUpdate_ = surf_get_clock();
 328   }
 329
 330   bandwidth_bound = -1.0;
 331   if (sg_weight_S_parameter > 0)
 332     for (auto link : *route)
 333       action->weight_ += sg_weight_S_parameter / link->getBandwidth();
 334
 335   for (auto link : *route) {
 336     double bb = bandwidthFactor(size) * link->getBandwidth();
 337     bandwidth_bound = (bandwidth_bound < 0.0) ? bb : std::min(bandwidth_bound, bb);
 338   }
 339
 340   action->latCurrent_ = action->latency_;
 341   action->latency_ *= latencyFactor(size);
 342   action->rate_ = bandwidthConstraint(action->rate_, bandwidth_bound, size);
 343   if (haveGap_) {
 344     xbt_assert(! route->empty(),
 345                "Using a model with a gap (e.g., SMPI) with a platform without links (e.g. vivaldi)!!!");
 346
 347     gapAppend(size, route->at(0), action);
 348     XBT_DEBUG("Comm %p: %s -> %s gap=%f (lat=%f)", action, src->name(), dst->name(), action->senderGap_, action->latency_);
 349   }
 350
 351   constraints_per_variable = route->size();
 352   if (back_route != NULL)
 353     constraints_per_variable += back_route->size();
 354
 355   if (action->latency_ > 0) {
 356     action->variable_ = lmm_variable_new(maxminSystem_, action, 0.0, -1.0, constraints_per_variable);
 357     if (updateMechanism_ == UM_LAZY) {
 358       // add to the heap the event when the latency is payed
 359       XBT_DEBUG("Added action (%p) one latency event at date %f", action, action->latency_ + action->lastUpdate_);
 360       action->heapInsert(actionHeap_, action->latency_ + action->lastUpdate_, route->empty() ? NORMAL : LATENCY);
 361     }
 362   } else
 363     action->variable_ = lmm_variable_new(maxminSystem_, action, 1.0, -1.0, constraints_per_variable);
 364
 365   if (action->rate_ < 0) {
 366     lmm_update_variable_bound(maxminSystem_, action->getVariable(), (action->latCurrent_ > 0) ? sg_tcp_gamma / (2.0 * action->latCurrent_) : -1.0);
 367   } else {
 368     lmm_update_variable_bound(maxminSystem_, action->getVariable(), (action->latCurrent_ > 0) ? std::min(action->rate_, sg_tcp_gamma / (2.0 * action->latCurrent_)) : action->rate_);
 369   }
 370
 371   for (auto link: *route)
 372     lmm_expand(maxminSystem_, link->getConstraint(), action->getVariable(), 1.0);
 373
 374   if (sg_network_crosstraffic == 1) {
 375     XBT_DEBUG("Fullduplex active adding backward flow using 5%%");
 376     for (auto link : *back_route)
 377       lmm_expand(maxminSystem_, link->getConstraint(), action->getVariable(), .05);
 378
 379     //Change concurrency_share here, if you want that cross-traffic is included in the SURF concurrency
 380     //(You would also have to change lmm_element_concurrency())
 381     //lmm_variable_concurrency_share_set(action->getVariable(),2);
 382   }
 383
 384   delete route;
 385   delete back_route;
 386   XBT_OUT();
 387
 388   Link::onCommunicate(action, src, dst);
 389   return action;
 390 }
 391
 392 bool NetworkCm02Model::next_occuring_event_isIdempotent()
 393 {
 394   return true;
 395 }
 396
 397 void NetworkCm02Model::gapAppend(double size, const Link* link, NetworkAction* action)
 398 {
 399   // Nothing
 400 };
 401
 402 /************
 403  * Resource *
 404  ************/
 405 NetworkCm02Link::NetworkCm02Link(NetworkCm02Model *model, const char *name, xbt_dict_t props,
 406     double bandwidth,  double latency, e_surf_link_sharing_policy_t policy,
 407     lmm_system_t system)
 408 : Link(model, name, props, lmm_constraint_new(system, this, sg_bandwidth_factor * bandwidth))
 409 {
 410   m_bandwidth.scale = 1.0;
 411   m_bandwidth.peak = bandwidth;
 412
 413   m_latency.scale = 1.0;
 414   m_latency.peak = latency;
 415
 416   if (policy == SURF_LINK_FATPIPE)
 417     lmm_constraint_shared(getConstraint());
 418
 419   Link::onCreation(this);
 420 }
 421
 422
 423
 424 void NetworkCm02Link::apply_event(tmgr_trace_iterator_t triggered, double value)
 425 {
 426
 427   /* Find out which of my iterators was triggered, and react accordingly */
 428   if (triggered == m_bandwidth.event) {
 429     updateBandwidth(value);
 430     tmgr_trace_event_unref(&m_bandwidth.event);
 431
 432   } else if (triggered == m_latency.event) {
 433     updateLatency(value);
 434     tmgr_trace_event_unref(&m_latency.event);
 435
 436   } else if (triggered == m_stateEvent) {
 437     if (value > 0)
 438       turnOn();
 439     else {
 440       lmm_variable_t var = NULL;
 441       lmm_element_t elem = NULL;
 442       double now = surf_get_clock();
 443
 444       turnOff();
 445       while ((var = lmm_get_var_from_cnst(getModel()->getMaxminSystem(), getConstraint(), &elem))) {
 446         Action *action = static_cast<Action*>( lmm_variable_id(var) );
 447
 448         if (action->getState() == Action::State::running ||
 449             action->getState() == Action::State::ready) {
 450           action->setFinishTime(now);
 451           action->setState(Action::State::failed);
 452         }
 453       }
 454     }
 455     tmgr_trace_event_unref(&m_stateEvent);
 456   } else {
 457     xbt_die("Unknown event!\n");
 458   }
 459
 460   XBT_DEBUG("There was a resource state event, need to update actions related to the constraint (%p)",
 461        getConstraint());
 462 }
 463
 464 void NetworkCm02Link::updateBandwidth(double value) {
 465
 466   m_bandwidth.peak = value;
 467
 468   lmm_update_constraint_bound(getModel()->getMaxminSystem(), getConstraint(),
 469       sg_bandwidth_factor * (m_bandwidth.peak * m_bandwidth.scale));
 470   TRACE_surf_link_set_bandwidth(surf_get_clock(), getName(), sg_bandwidth_factor * m_bandwidth.peak * m_bandwidth.scale);
 471
 472   if (sg_weight_S_parameter > 0) {
 473     double delta = sg_weight_S_parameter / value - sg_weight_S_parameter / (m_bandwidth.peak * m_bandwidth.scale);
 474
 475     lmm_variable_t var;
 476     lmm_element_t elem = NULL, nextelem = NULL;
 477     int numelem = 0;
 478     while ((var = lmm_get_var_from_cnst_safe(getModel()->getMaxminSystem(), getConstraint(), &elem, &nextelem, &numelem))) {
 479       NetworkCm02Action *action = (NetworkCm02Action*) lmm_variable_id(var);
 480       action->weight_ += delta;
 481       if (!action->isSuspended())
 482         lmm_update_variable_weight(getModel()->getMaxminSystem(), action->getVariable(), action->weight_);
 483     }
 484   }
 485 }
 486
 487 void NetworkCm02Link::updateLatency(double value){
 488   double delta = value - m_latency.peak;
 489   lmm_variable_t var = NULL;
 490   lmm_element_t elem = NULL;
 491   lmm_element_t nextelem = NULL;
 492   int numelem = 0;
 493
 494   m_latency.peak = value;
 495
 496   while ((var = lmm_get_var_from_cnst_safe(getModel()->getMaxminSystem(), getConstraint(), &elem, &nextelem, &numelem))) {
 497     NetworkCm02Action *action = (NetworkCm02Action*) lmm_variable_id(var);
 498     action->latCurrent_ += delta;
 499     action->weight_ += delta;
 500     if (action->rate_ < 0)
 501       lmm_update_variable_bound(getModel()->getMaxminSystem(), action->getVariable(), sg_tcp_gamma / (2.0 * action->latCurrent_));
 502     else {
 503       lmm_update_variable_bound(getModel()->getMaxminSystem(), action->getVariable(),
 504                                 std::min(action->rate_, sg_tcp_gamma / (2.0 * action->latCurrent_)));
 505
 506       if (action->rate_ < sg_tcp_gamma / (2.0 * action->latCurrent_)) {
 507         XBT_INFO("Flow is limited BYBANDWIDTH");
 508       } else {
 509         XBT_INFO("Flow is limited BYLATENCY, latency of flow is %f", action->latCurrent_);
 510       }
 511     }
 512     if (!action->isSuspended())
 513       lmm_update_variable_weight(getModel()->getMaxminSystem(), action->getVariable(), action->weight_);
 514   }
 515 }
 516
 517 NetworkCm02Link::~NetworkCm02Link() {}
 518
 519 /**********
 520  * Action *
 521  **********/
 522
 523 NetworkCm02Action::~NetworkCm02Action() {}
 524
 525 void NetworkCm02Action::updateRemainingLazy(double now)
 526 {
 527   double delta = 0.0;
 528
 529   if (suspended_ != 0)
 530     return;
 531
 532   delta = now - lastUpdate_;
 533
 534   if (remains_ > 0) {
 535     XBT_DEBUG("Updating action(%p): remains was %f, last_update was: %f", this, remains_, lastUpdate_);
 536     double_update(&(remains_), lastValue_ * delta, sg_maxmin_precision*sg_surf_precision);
 537
 538     XBT_DEBUG("Updating action(%p): remains is now %f", this, remains_);
 539   }
 540
 541   if (maxDuration_ != NO_MAX_DURATION)
 542     double_update(&maxDuration_, delta, sg_surf_precision);
 543
 544   if (remains_ <= 0 &&
 545       (lmm_get_variable_weight(getVariable()) > 0)) {
 546     finish();
 547     setState(Action::State::done);
 548
 549     heapRemove(getModel()->getActionHeap());
 550   } else if (((maxDuration_ != NO_MAX_DURATION)
 551       && (maxDuration_ <= 0))) {
 552     finish();
 553     setState(Action::State::done);
 554     heapRemove(getModel()->getActionHeap());
 555   }
 556
 557   lastUpdate_ = now;
 558   lastValue_ = lmm_variable_getvalue(getVariable());
 559 }
 560
 561 void NetworkCm02Link::gapAppend(double size, const Link* link, NetworkAction* action)
 562 {
 563   // Nothing
 564 };
 565
 566 }
 567 }