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#include "lp_common.h"
// LP-based analysis of semaphore protocols.
// Based on the paper:
// B. Brandenburg, "Improved Analysis and Evaluation of Real-Time Semaphore
// Protocols for P-FP Scheduling", Proceedings of the 19th IEEE Real-Time and
// Embedded Technology and Applications Symposium (RTAS 2013), April 2013.
void set_blocking_objective(
VarMapper& vars,
const ResourceSharingInfo& info, const ResourceLocality& locality,
const TaskInfo& ti,
LinearProgram& lp,
LinearExpression *local_obj,
LinearExpression *remote_obj)
{
LinearExpression *obj;
obj = lp.get_objective();
foreach_task_except(info.get_tasks(), ti, tx)
{
unsigned int t = tx->get_id();
foreach(tx->get_requests(), request)
{
unsigned int q = request->get_resource_id();
bool local = locality[q] == (int) ti.get_cluster();
double length;
// Sanity check topology info in debug mode.
assert(locality[q] != NO_CPU);
length = request->get_request_length();
foreach_request_instance(*request, ti, v)
{
unsigned int var_id;
var_id = vars.lookup(t, q, v, BLOCKING_DIRECT);
obj->add_term(length, var_id);
if (local && local_obj)
local_obj->add_term(length, var_id);
else if (!local && remote_obj)
remote_obj->add_term(length, var_id);
var_id = vars.lookup(t, q, v, BLOCKING_INDIRECT);
obj->add_term(length, var_id);
if (local && local_obj)
local_obj->add_term(length, var_id);
else if (!local && remote_obj)
remote_obj->add_term(length, var_id);
var_id = vars.lookup(t, q, v, BLOCKING_PREEMPT);
obj->add_term(length, var_id);
if (local && local_obj)
local_obj->add_term(length, var_id);
else if (!local && remote_obj)
remote_obj->add_term(length, var_id);
}
}
}
#ifndef CONFIG_MERGED_LINPROGS
// We have enumerated all relevant variables. Do not allow any more to
// be created.
vars.seal();
#endif
}
// This version is for partitioned shared-memory protocols where each
// task executes its critical section on its assigned processor.
void set_blocking_objective_part_shm(
VarMapper& vars,
const ResourceSharingInfo& info,
const TaskInfo& ti,
LinearProgram& lp,
LinearExpression *local_obj,
LinearExpression *remote_obj)
{
LinearExpression *obj;
obj = lp.get_objective();
foreach_task_except(info.get_tasks(), ti, tx)
{
unsigned int t = tx->get_id();
bool local = tx->get_cluster() == ti.get_cluster();
foreach(tx->get_requests(), request)
{
unsigned int q = request->get_resource_id();
double length = request->get_request_length();;
foreach_request_instance(*request, ti, v)
{
unsigned int var_id;
var_id = vars.lookup(t, q, v, BLOCKING_DIRECT);
obj->add_term(length, var_id);
if (local && local_obj)
local_obj->add_term(length, var_id);
else if (!local && remote_obj)
remote_obj->add_term(length, var_id);
var_id = vars.lookup(t, q, v, BLOCKING_INDIRECT);
obj->add_term(length, var_id);
if (local && local_obj)
local_obj->add_term(length, var_id);
else if (!local && remote_obj)
remote_obj->add_term(length, var_id);
var_id = vars.lookup(t, q, v, BLOCKING_PREEMPT);
obj->add_term(length, var_id);
if (local && local_obj)
local_obj->add_term(length, var_id);
else if (!local && remote_obj)
remote_obj->add_term(length, var_id);
}
}
}
}
// Constraint 1 in [Brandenburg 2013]
void add_mutex_constraints(
VarMapper& vars,
const ResourceSharingInfo& info,
const TaskInfo& ti,
LinearProgram& lp)
{
foreach_task_except(info.get_tasks(), ti, tx)
{
unsigned int t = tx->get_id();
foreach(tx->get_requests(), request)
{
unsigned int q = request->get_resource_id();
foreach_request_instance(*request, ti, v)
{
LinearExpression *exp = new LinearExpression();
unsigned int var_id;
var_id = vars.lookup(t, q, v, BLOCKING_DIRECT);
exp->add_var(var_id);
var_id = vars.lookup(t, q, v, BLOCKING_INDIRECT);
exp->add_var(var_id);
var_id = vars.lookup(t, q, v, BLOCKING_PREEMPT);
exp->add_var(var_id);
lp.add_inequality(exp, 1);
}
}
}
}
// Constraint 2 in [Brandenburg 2013]
void add_topology_constraints(
VarMapper& vars,
const ResourceSharingInfo& info,
const ResourceLocality& locality,
const TaskInfo& ti,
LinearProgram& lp)
{
LinearExpression *exp = new LinearExpression();
foreach_task_except(info.get_tasks(), ti, tx)
{
unsigned int t = tx->get_id();
foreach_remote_request(tx->get_requests(), locality, ti, request)
{
unsigned int q = request->get_resource_id();
foreach_request_instance(*request, ti, v)
{
unsigned int var_id;
var_id = vars.lookup(t, q, v, BLOCKING_PREEMPT);
exp->add_var(var_id);
}
}
}
lp.add_equality(exp, 0);
}
static unsigned int max_num_arrivals_remote(
const ResourceLocality& locality,
const TaskInfo& ti)
{
// initialize to 1 to account for job release
unsigned int count = 1;
// count how often resources on remote cores are accessed
foreach(ti.get_requests(), req)
if (locality[req->get_resource_id()] != (int) ti.get_cluster())
count += req->get_num_requests();
return count;
}
// Constraint 3 in [Brandenburg 2013]
// One priority-boosting-related preemption per local task
// each time that Ji arrives (is released or resumed)
void add_local_lower_priority_constraints(
VarMapper& vars,
const ResourceSharingInfo& info,
const ResourceLocality& locality,
const TaskInfo& ti,
LinearProgram& lp)
{
unsigned int num_arrivals = max_num_arrivals_remote(locality, ti);
foreach_local_lowereq_priority_task_except(info.get_tasks(), ti, tx)
{
LinearExpression *exp = new LinearExpression();
unsigned int t = tx->get_id();
foreach(tx->get_requests(), request)
{
unsigned int q = request->get_resource_id();
// is it a resource local to Ti?
if (locality[q] == (int) ti.get_cluster())
{
foreach_request_instance(*request, ti, v)
{
unsigned int var_id;
var_id = vars.lookup(t, q, v,
BLOCKING_PREEMPT);
exp->add_var(var_id);
}
}
}
lp.add_equality(exp, num_arrivals);
}
}
// Constraint 10 in [Brandenburg 2013]
// For shared-memory protocols.
// Remote tasks cannot preempt Ti since they are not scheduled
// on Ti's assigned task; therefore force BLOCKING_PREEMPT to zero.
void add_topology_constraints_shm(
VarMapper& vars,
const ResourceSharingInfo& info,
const TaskInfo& ti,
LinearProgram& lp)
{
LinearExpression *exp = new LinearExpression();
foreach_remote_task(info.get_tasks(), ti, tx)
{
unsigned int t = tx->get_id();
foreach(tx->get_requests(), request)
{
unsigned int q = request->get_resource_id();
foreach_request_instance(*request, ti, v)
{
unsigned int var_id;
var_id = vars.lookup(t, q, v, BLOCKING_PREEMPT);
exp->add_var(var_id);
}
}
}
lp.add_equality(exp, 0);
}
// Constraint 9 in [Brandenburg 2013]
// local higher-priority tasks never cause blocking under SHM protocols
void add_local_higher_priority_constraints_shm(
VarMapper& vars,
const ResourceSharingInfo& info,
const TaskInfo& ti,
LinearProgram& lp)
{
LinearExpression *exp = new LinearExpression();
foreach_local_task(info.get_tasks(), ti, tx)
{
if (tx->get_priority() < ti.get_priority())
{
unsigned int t = tx->get_id();
foreach(tx->get_requests(), request)
{
unsigned int q = request->get_resource_id();
foreach_request_instance(*request, ti, v)
{
unsigned int var_id;
var_id = vars.lookup(t, q, v,
BLOCKING_PREEMPT);
exp->add_var(var_id);
var_id = vars.lookup(t, q, v,
BLOCKING_INDIRECT);
exp->add_var(var_id);
var_id = vars.lookup(t, q, v,
BLOCKING_DIRECT);
exp->add_var(var_id);
}
}
}
}
lp.add_equality(exp, 0);
}
static unsigned int max_num_arrivals_shm(
const ResourceSharingInfo& info,
const TaskInfo& ti)
{
hashmap<unsigned int, unsigned int> request_counts;
foreach(ti.get_requests(), req)
request_counts[req->get_resource_id()] = 0;
// count how often each resource is accessed on remote cores
foreach_remote_task(info.get_tasks(), ti, tx)
{
foreach(tx->get_requests(), req)
{
unsigned int q = req->get_resource_id();
if (request_counts.find(q) != request_counts.end())
request_counts[q] += req->get_max_num_requests(ti.get_response());
}
}
// initialize to 1 to account for job release
unsigned int total = 1;
foreach(ti.get_requests(), req)
total += std::min(request_counts[req->get_resource_id()],
req->get_num_requests());
return total;
}
// Constraint 11 in [Brandenburg 2013]
// Local lower-priority tasks block at most once each time
// that Ti suspends (and once after release).
void add_local_lower_priority_constraints_shm(
VarMapper& vars,
const ResourceSharingInfo& info,
const TaskInfo& ti,
LinearProgram& lp)
{
unsigned int num_arrivals = max_num_arrivals_shm(info, ti);
foreach_local_lowereq_priority_task_except(info.get_tasks(), ti, tx)
{
LinearExpression *exp = new LinearExpression();
unsigned int t = tx->get_id();
foreach(tx->get_requests(), request)
{
unsigned int q = request->get_resource_id();
foreach_request_instance(*request, ti, v)
{
unsigned int var_id;
var_id = vars.lookup(t, q, v,
BLOCKING_PREEMPT);
exp->add_var(var_id);
var_id = vars.lookup(t, q, v,
BLOCKING_INDIRECT);
exp->add_var(var_id);
var_id = vars.lookup(t, q, v,
BLOCKING_DIRECT);
exp->add_var(var_id);
}
}
lp.add_equality(exp, num_arrivals);
}
}
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