For whatever it is worth, the following model claims safety and progress
for the sysidle state machine.

Thoughts?

                                                        Thanx, Paul

------------------------------------------------------------------------
sysidle.sh
------------------------------------------------------------------------
spin -a sysidle.spin
cc -DNP -o pan pan.c
# Fair scheduling to focus progress checks in timekeeper.
./pan -f -l -m1280000 -w22

------------------------------------------------------------------------
sysidle.spin
------------------------------------------------------------------------
/*
 * Promela model for CONFIG_NO_HZ_FULL_SYSIDLE=y in the Linux kernel.
 * This model assumes that the dyntick-idle bit manipulation works based
 * on long usage, and substitutes a per-thread boolean "am_busy[]" array
 * for the Linux kernel's dyntick-idle masks.  The focus of this model
 * is therefore on the state machine itself.  Checks for both safety and
 * forward progress.
 *
 * This program is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, you can access it online at
 * http://www.gnu.org/licenses/gpl-2.0.html.
 *
 * Copyright IBM Corporation, 2014
 *
 * Author: Paul E. McKenney <paul...@linux.vnet.ibm.com>
 */

#define NUM_WORKERS 3

byte wakeup_timekeeper = 0; /* Models rcu_kick_nohz_cpu(). */

#define RCU_SYSIDLE_NOT         0       /* Some CPU is not idle. */
#define RCU_SYSIDLE_SHORT       1       /* All CPUs idle for brief period. */
#define RCU_SYSIDLE_LONG        2       /* All CPUs idle for long enough. */
#define RCU_SYSIDLE_FULL        3       /* All CPUs idle, ready for sysidle. */
#define RCU_SYSIDLE_FULL_NOTED  4       /* Actually entered sysidle state. */

byte full_sysidle_state = RCU_SYSIDLE_NOT;

byte am_busy[NUM_WORKERS];  /* Busy is similar to "not dyntick-idle". */
byte am_setup[NUM_WORKERS]; /* Setup means timekeeper knows I am not idle. */

/*
 * Non-timekeeping CPU going into and out of dyntick-idle state.
 */
proctype worker(byte me)
{
        byte oldstate;

        do
        :: 1 ->
                /* Go idle. */
                am_setup[me] = 0;
                am_busy[me] = 0;

                /* Dyntick-idle in the following loop. */
                do
                :: 1 -> skip;
                :: 1 -> break;
                od;

                /* Exit idle loop, model getting out of dyntick idle state. */
                am_busy[me] = 1;

                /* Get state out of full-system idle states. */
                atomic {
                        oldstate = full_sysidle_state;
                        if
                        :: oldstate > RCU_SYSIDLE_SHORT ->
                                full_sysidle_state = RCU_SYSIDLE_NOT;
                        :: else -> skip;
                        fi;
                }

                /* If needed, wake up the timekeeper. */
                if
                :: oldstate == RCU_SYSIDLE_FULL_NOTED ->
                        wakeup_timekeeper = 1;
                :: else -> skip;
                fi;

                /* Mark ourselves fully awake and operational. */
                am_setup[me] = 1;

                /* We are fully awake, so timekeeper must not be asleep. */
                assert(full_sysidle_state < RCU_SYSIDLE_FULL);

                /* Running in kernel in the following loop. */
                do
                :: 1 -> skip;
                :: 1 -> break;
                od;
        od
}

/*
 * Are all the workers in dyntick-idle state?
 */
#define check_idle() \
        i = 0; \
        idle = 1; \
        do \
        :: i < NUM_WORKERS -> \
                if \
                :: am_busy[i] == 1 -> idle = 0; \
                :: else -> skip; \
                fi; \
                i++; \
        :: i >= NUM_WORKERS -> break; \
        od

/*
 * Timekeeping CPU.
 */
proctype timekeeper()
{
        byte i;
        byte idle;
        byte curstate;
        byte newstate;

        do
        :: 1 ->
                /* Capture current state. */
                check_idle();
                curstate = full_sysidle_state;
                newstate = curstate;

                /* Check for acceptance state. */
                if
                :: idle == 0 ->
progress_idle:
                        skip;
                :: curstate == RCU_SYSIDLE_NOT ->
progress_idle_reset:
                        skip;
                :: else -> skip;
                fi;

                /* Manage state... */
                if
                :: idle == 1 && curstate < RCU_SYSIDLE_FULL_NOTED ->
                        /* Idle, advance to next state. */
                        atomic {
                                if
                                :: full_sysidle_state == curstate ->
                                        newstate = curstate + 1;
                                        full_sysidle_state = newstate;
                                :: else -> skip;
                                fi;
                        }
                :: idle == 0 && full_sysidle_state >= RCU_SYSIDLE_LONG ->
                        /* Non-idle and state advanced, revert to base state. */
                        full_sysidle_state = RCU_SYSIDLE_NOT;
                :: else -> skip;
                fi;

                /* If in RCU_SYSIDLE_FULL_NOTED, wait to be awakened. */
                do
                :: newstate != RCU_SYSIDLE_FULL_NOTED &&
                   wakeup_timekeeper == 1 ->
                        assert(0); /* Should never get here. */
                :: newstate != RCU_SYSIDLE_FULL_NOTED &&
                   wakeup_timekeeper == 0 ->
                        break;
                :: newstate == RCU_SYSIDLE_FULL_NOTED &&
                   wakeup_timekeeper == 1 ->
progress_full_system_idle_1:
                        assert(full_sysidle_state == RCU_SYSIDLE_NOT);
                        wakeup_timekeeper = 0;
                        break;
                :: newstate == RCU_SYSIDLE_FULL_NOTED &&
                   wakeup_timekeeper == 0 ->
progress_full_system_idle_2:

                        /* We are asleep, so all workers better be idle. */
                        atomic {
                                i = 0;
                                idle = 1;
                                do
                                :: i < NUM_WORKERS ->
                                        if
                                        :: am_setup[i] -> idle = 0;
                                        :: else -> skip;
                                        fi;
                                        i++;
                                :: i >= NUM_WORKERS -> break;
                                od;
                                assert(idle == 1 ||
                                       full_sysidle_state < RCU_SYSIDLE_FULL);
                        }
                od;
                assert(full_sysidle_state <= RCU_SYSIDLE_FULL_NOTED);
        od;
}

init {
        byte i = 0;

        do
        :: i < NUM_WORKERS ->
                am_busy[i] = 1;
                am_setup[i] = 1;
                run worker(i);
                i++;
        :: i >= NUM_WORKERS -> break;
        od;
        run timekeeper();
}

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