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4_no_grefs.tla
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4_no_grefs.tla
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(* Copyright (C) 2023 Malte Skarupke
This is free software; you can redistribute it and/or
modify it under the terms of the GNU Lesser General Public
License as published by the Free Software Foundation; either
version 2.1 of the License, or (at your option) any later version.
See https://www.gnu.org/licenses/. *)
-------------------------- MODULE 4_no_grefs --------------------------
EXTENDS Integers, FiniteSets, Sequences
CONSTANT Procs
CONSTANT UseSpinlockForMutex
CONSTANT UseSpinlockForCVMutex
CONSTANT MaxNumLoops
Bit(i) == 2 ^ i
ClearBit(i, b) == (i % Bit(b)) + (i \div Bit(b+1)) * Bit(b+1)
SetBit(i, b) == ClearBit(i, b) + Bit(b)
Xor1(i) == IF (i % 2) = 0 THEN i + 1 ELSE i - 1
AllProcs == Procs
(*
--algorithm lll_mutex_and_cv
{
variables
mutex_index = 0;
g1_orig_size_index = 1;
wrefs_index = 2;
g_signals_index = [i \in {0,1} |-> i + 3];
futexes = [i \in {mutex_index, g1_orig_size_index, wrefs_index, g_signals_index[0], g_signals_index[1]}
|-> [state |-> 0, sleepers |-> {}]];
wseq = 0;
g1_start = 0;
g_size = [i \in {0, 1} |-> 0];
did_switch_g1 = [i \in AllProcs |-> FALSE];
g1index = [i \in AllProcs |-> 0];
waiters = 0;
busy = FALSE;
spinlock_locked = FALSE;
cv_spinlock_locked = FALSE;
procedure futex_wait(wait_index = 0, val = 0)
{
check_state:
if (futexes[wait_index].state /= val)
{
return;
}
else
{
val := 0;
futexes[wait_index].sleepers := futexes[wait_index].sleepers \union {self};
wait_for_wake:
await ~ (self \in futexes[wait_index].sleepers);
return;
};
}
procedure futex_wake_single(wake_index = 0)
{
check_for_sleepers:
if (futexes[wake_index].sleepers = {})
{
return;
}
else
{
with (x \in futexes[wake_index].sleepers)
{
futexes[wake_index].sleepers := futexes[wake_index].sleepers \ {x};
};
return;
};
}
procedure futex_wake_all(wake_all_index = 0)
{
futex_wake_all:
futexes[wake_all_index].sleepers := {};
return;
}
procedure lock_mutex()
variable old_state = 0;
{
lock_mutex_start:
if (UseSpinlockForMutex)
{
await ~spinlock_locked;
spinlock_locked := TRUE;
return;
}
else
{
if (futexes[mutex_index].state = 0)
{
futexes[mutex_index].state := 1;
return;
};
lll_lock_wait:
if (futexes[mutex_index].state = 2)
{
goto futex_wait;
};
exchange_lock:
while (TRUE)
{
old_state := futexes[mutex_index].state;
futexes[mutex_index].state := 2;
check_for_locked:
if (old_state = 0)
{
return;
}
else
{
old_state := 0;
};
futex_wait:
call futex_wait(mutex_index, 2);
};
}
};
procedure unlock_mutex ()
variable old_state = 0;
{
unlock_mutex_start:
if (UseSpinlockForMutex)
{
spinlock_locked := FALSE;
return;
}
else
{
old_state := futexes[mutex_index].state;
futexes[mutex_index].state := 0;
check_if_sleeper:
if (old_state > 1)
{
call futex_wake_single(mutex_index);
return;
}
else
{
return;
};
};
}
procedure condvar_acquire_lock()
variable orig_size = 0;
{
cv_acquire_lock:
if (UseSpinlockForCVMutex)
{
await ~cv_spinlock_locked;
cv_spinlock_locked := TRUE;
return;
}
else
{
orig_size := futexes[g1_orig_size_index].state;
cv_acquire_unlocked:
while ((orig_size % 4) = 0)
{
cv_acquire_lock_exchange:
if (futexes[g1_orig_size_index].state = orig_size)
{
futexes[g1_orig_size_index].state := SetBit(orig_size, 0);
return;
}
else
orig_size := futexes[g1_orig_size_index].state;
};
cv_acquire_lock_sleep_loop:
while (TRUE)
{
cv_acquire_lock_loop_to_set_sleeper:
while ((orig_size % 4) /= 2)
{
cv_acquire_lock_exchange_2:
if (futexes[g1_orig_size_index].state = orig_size)
{
futexes[g1_orig_size_index].state := SetBit(ClearBit(orig_size, 0), 1);
if ((orig_size % 4) = 0)
{
return;
}
else
{
goto cv_acquire_lock_sleeper_flag_set;
};
}
else
{
orig_size := futexes[g1_orig_size_index].state;
};
};
cv_acquire_lock_sleeper_flag_set:
call futex_wait(g1_orig_size_index, SetBit(ClearBit(orig_size, 0), 1));
cv_acquire_re_read_state:
orig_size := futexes[g1_orig_size_index].state;
};
};
};
procedure condvar_release_lock()
variable old_state = 0;
{
cv_release_lock:
if (UseSpinlockForCVMutex)
{
cv_spinlock_locked := FALSE;
return;
}
else
{
old_state := futexes[g1_orig_size_index].state;
futexes[g1_orig_size_index].state := ClearBit(ClearBit(old_state, 0), 1);
cv_release_lock_maybe_notify:
if ((old_state % 4) > 1)
{
old_state := 0;
call futex_wake_single(g1_orig_size_index);
}
else
{
old_state := 0;
};
cv_release_lock_done:
return;
};
}
procedure condvar_quiesce_and_switch_g1(local_wseq = 0, g1 = 0)
variables old_orig_size = 0;
old_g1_start = 0;
r = 0;
s = 0;
lowseq = 0;
{
quiesce_and_switch_start:
g1index[self] := g1;
old_orig_size := futexes[g1_orig_size_index].state \div 4;
quiesce_and_switch_start2:
old_g1_start := g1_start \div 2;
quiesce_and_switch_check_for_no_reader:
if (((local_wseq - old_g1_start - old_orig_size) + g_size[Xor1(g1)]) = 0)
{
did_switch_g1[self] := FALSE;
return;
};
quiesce_update_g1_start:
g1_start := g1_start + (old_orig_size * 2) + (IF g1 = 1 THEN 1 ELSE -1);
lowseq := ((old_g1_start + old_orig_size) * 2);
quiesce_flip_wseq:
wseq := Xor1(wseq);
local_wseq := wseq \div 2;
quiesce_flip_g1:
g1 := Xor1(g1);
g1index[self] := Xor1(g1index[self]);
quiesce_set_lowseq:
futexes[g_signals_index[g1]].state := lowseq;
quiesce_update_orig_size:
old_orig_size := local_wseq - (old_g1_start + old_orig_size);
s := (futexes[g1_orig_size_index].state % 4) + (old_orig_size * 4);
r := futexes[g1_orig_size_index].state;
futexes[g1_orig_size_index].state := s;
quiesce_check_orig_size:
if ((r % 4) /= (s % 4))
{
futexes[g1_orig_size_index].state := (old_orig_size * 4) + 2;
};
quiesce_update_size:
g_size[g1] := g_size[g1] + old_orig_size;
did_switch_g1[self] := g_size[g1] /= 0;
return;
}
procedure cv_wait()
variables local_wseq = 0;
g = 0;
seq = 0;
signals = 0;
local_g1_start = 0;
lowseq = 0;
{
cv_wait_fetch_seq:
local_wseq := wseq;
wseq := wseq + 2;
g := local_wseq % 2;
seq := local_wseq \div 2;
cv_wait_incr_wrefs:
futexes[wrefs_index].state := futexes[wrefs_index].state + 8;
call unlock_mutex();
cv_wait_load_signals:
signals := futexes[g_signals_index[g]].state;
cv_wait_loop:
while (TRUE)
{
cv_wait_inner_loop:
while (TRUE)
{
cv_wait_reload_g1_start:
local_g1_start := g1_start;
lowseq := IF (local_g1_start % 2) = g THEN signals ELSE ClearBit(local_g1_start, 0);
cv_wait_check_group_closed:
if (seq < (g1_start \div 2))
{
goto cv_wait_done
}
else if ((signals - lowseq) >= 2)
{
goto cv_wait_inner_loop_done;
};
cv_wait_block:
call futex_wait(g_signals_index[g], signals);
cv_wait_after_woken_up_reload_signals:
signals := futexes[g_signals_index[g]].state;
};
cv_wait_inner_loop_done:
if (futexes[g_signals_index[g]].state = signals)
{
futexes[g_signals_index[g]].state := signals - 2;
goto cv_wait_done;
}
else
signals := futexes[g_signals_index[g]].state;
};
cv_wait_done:
futexes[wrefs_index].state := futexes[wrefs_index].state - 8;
if (futexes[wrefs_index].state \div 4 = 1)
{
call futex_wake_all(wrefs_index);
};
cv_wait_retake_mutex:
call lock_mutex();
return;
}
procedure cv_signal()
variables local_wseq = 0;
g1 = 0;
do_futex_wake = FALSE;
{
check_for_waiters:
if (futexes[wrefs_index].state \div 8 = 0)
{
return;
}
else
{
call condvar_acquire_lock();
};
cv_signal_load_wseq:
local_wseq := wseq \div 2;
g1 := Xor1(wseq % 2);
cv_signal_check_size:
if (g_size[g1] = 0)
{
call condvar_quiesce_and_switch_g1(local_wseq, g1);
cv_signal_after_switch:
g1 := g1index[self];
cv_signal_check_for_early_out:
if (~did_switch_g1[self])
{
call condvar_release_lock();
return;
(*goto cv_signal_release_lock;*)
};
};
cv_signal_add_signal:
futexes[g_signals_index[g1]].state := futexes[g_signals_index[g1]].state + 2;
cv_signal_decrease_size:
g_size[g1] := g_size[g1] - 1;
do_futex_wake := TRUE;
(*cv_signal_release_lock:*)
call condvar_release_lock();
cv_signal_maybe_wake:
if (do_futex_wake)
{
call futex_wake_single(g_signals_index[g1]);
return;
}
else
{
return;
};
}
procedure cv_broadcast()
variables local_wseq = 0;
g1 = 0;
do_futex_wake = FALSE;
{
check_for_waiters:
if (futexes[wrefs_index].state \div 8 = 0)
{
return;
}
else
{
call condvar_acquire_lock();
};
cv_broadcast_load_wseq:
local_wseq := wseq \div 2;
g1 := Xor1(wseq % 2);
cv_broacast_check_size1:
if (g_size[g1] /= 0)
{
cv_broadcast_signal_g1:
futexes[g_signals_index[g1]].state := futexes[g_signals_index[g1]].state + (g_size[g1] * 2);
cv_broadcast_clear_size1:
g_size[g1] := 0;
call futex_wake_all(g_signals_index[g1]);
};
cv_broadcast_switch_g1:
call condvar_quiesce_and_switch_g1(local_wseq, g1);
cv_broadcast_after_switch:
g1 := g1index[self];
if (did_switch_g1[self])
{
cv_broadcast_signal_g2:
futexes[g_signals_index[g1]].state := futexes[g_signals_index[g1]].state + (g_size[g1] * 2);
cv_broadcast_clear_size2:
g_size[g1] := 0;
do_futex_wake := TRUE;
};
cv_broadcast_release_lock:
call condvar_release_lock();
cv_broadcast_maybe_wake:
if (do_futex_wake)
{
call futex_wake_all(g_signals_index[g1]);
return;
}
else
{
return;
};
}
procedure acquire_masterlock()
{
acquire_masterlock_start:
call lock_mutex();
acquire_masterlock_loop:
while (busy)
{
waiters := waiters + 1;
call cv_wait();
acquire_lock_after_wait:
waiters := waiters - 1;
};
acquire_masterlock_after_loop:
busy := TRUE;
call unlock_mutex();
return;
}
procedure release_masterlock()
{
release_masterlock_start:
call lock_mutex();
release_masterlock_after_lock:
busy := FALSE;
call unlock_mutex();
release_masterlock_signal:
call cv_signal();
return;
};
procedure yield_masterlock()
{
yield_start:
call lock_mutex();
yield_after_lock:
if (waiters = 0)
{
call unlock_mutex();
return;
};
yield_after_waiter_check:
busy := FALSE;
call cv_signal();
yield_after_signal:
waiters := waiters + 1;
yield_loop:
while (TRUE)
{
call cv_wait();
yield_after_wait:
if (~busy)
goto yield_after_loop;
};
yield_after_loop:
busy := TRUE;
yield_dec_waiters:
waiters := waiters - 1;
yield_done:
call unlock_mutex();
return;
};
fair process (Proc \in Procs)
variable num_loops = MaxNumLoops;
{
proc_start:
while (num_loops > 0)
{
num_loops := num_loops - 1;
either
{
call acquire_masterlock();
}
or
{
goto proc_done;
};
(*proc_loop:
while (num_loops > 0)
{
either
{
num_loops := num_loops - 1;
call yield_masterlock();
}
or
{
goto proc_loop_done;
}
};*)
proc_loop_done:
call release_masterlock();
};
proc_done:
skip;
}
}
*)
\* BEGIN TRANSLATION (chksum(pcal) = "7e457055" /\ chksum(tla) = "94cd16b7")
\* Label futex_wake_all of procedure futex_wake_all at line 84 col 5 changed to futex_wake_all_
\* Label futex_wait of procedure lock_mutex at line 125 col 9 changed to futex_wait_
\* Label check_for_waiters of procedure cv_signal at line 360 col 3 changed to check_for_waiters_
\* Procedure variable old_state of procedure lock_mutex at line 89 col 10 changed to old_state_
\* Procedure variable old_state of procedure unlock_mutex at line 131 col 10 changed to old_state_u
\* Procedure variable lowseq of procedure condvar_quiesce_and_switch_g1 at line 247 col 11 changed to lowseq_
\* Procedure variable local_wseq of procedure cv_wait at line 289 col 11 changed to local_wseq_
\* Procedure variable local_wseq of procedure cv_signal at line 355 col 11 changed to local_wseq_c
\* Procedure variable g1 of procedure cv_signal at line 356 col 11 changed to g1_
\* Procedure variable do_futex_wake of procedure cv_signal at line 357 col 11 changed to do_futex_wake_
\* Procedure variable local_wseq of procedure cv_broadcast at line 409 col 11 changed to local_wseq_cv
\* Procedure variable g1 of procedure cv_broadcast at line 410 col 11 changed to g1_c
VARIABLES mutex_index, g1_orig_size_index, wrefs_index, g_signals_index,
futexes, wseq, g1_start, g_size, did_switch_g1, g1index, waiters,
busy, spinlock_locked, cv_spinlock_locked, pc, stack, wait_index,
val, wake_index, wake_all_index, old_state_, old_state_u, orig_size,
old_state, local_wseq, g1, old_orig_size, old_g1_start, r, s,
lowseq_, local_wseq_, g, seq, signals, local_g1_start, lowseq,
local_wseq_c, g1_, do_futex_wake_, local_wseq_cv, g1_c,
do_futex_wake, num_loops
vars == << mutex_index, g1_orig_size_index, wrefs_index, g_signals_index,
futexes, wseq, g1_start, g_size, did_switch_g1, g1index, waiters,
busy, spinlock_locked, cv_spinlock_locked, pc, stack, wait_index,
val, wake_index, wake_all_index, old_state_, old_state_u,
orig_size, old_state, local_wseq, g1, old_orig_size, old_g1_start,
r, s, lowseq_, local_wseq_, g, seq, signals, local_g1_start,
lowseq, local_wseq_c, g1_, do_futex_wake_, local_wseq_cv, g1_c,
do_futex_wake, num_loops >>
ProcSet == (Procs)
Init == (* Global variables *)
/\ mutex_index = 0
/\ g1_orig_size_index = 1
/\ wrefs_index = 2
/\ g_signals_index = [i \in {0,1} |-> i + 3]
/\ futexes = [i \in {mutex_index, g1_orig_size_index, wrefs_index, g_signals_index[0], g_signals_index[1]}
|-> [state |-> 0, sleepers |-> {}]]
/\ wseq = 0
/\ g1_start = 0
/\ g_size = [i \in {0, 1} |-> 0]
/\ did_switch_g1 = [i \in AllProcs |-> FALSE]
/\ g1index = [i \in AllProcs |-> 0]
/\ waiters = 0
/\ busy = FALSE
/\ spinlock_locked = FALSE
/\ cv_spinlock_locked = FALSE
(* Procedure futex_wait *)
/\ wait_index = [ self \in ProcSet |-> 0]
/\ val = [ self \in ProcSet |-> 0]
(* Procedure futex_wake_single *)
/\ wake_index = [ self \in ProcSet |-> 0]
(* Procedure futex_wake_all *)
/\ wake_all_index = [ self \in ProcSet |-> 0]
(* Procedure lock_mutex *)
/\ old_state_ = [ self \in ProcSet |-> 0]
(* Procedure unlock_mutex *)
/\ old_state_u = [ self \in ProcSet |-> 0]
(* Procedure condvar_acquire_lock *)
/\ orig_size = [ self \in ProcSet |-> 0]
(* Procedure condvar_release_lock *)
/\ old_state = [ self \in ProcSet |-> 0]
(* Procedure condvar_quiesce_and_switch_g1 *)
/\ local_wseq = [ self \in ProcSet |-> 0]
/\ g1 = [ self \in ProcSet |-> 0]
/\ old_orig_size = [ self \in ProcSet |-> 0]
/\ old_g1_start = [ self \in ProcSet |-> 0]
/\ r = [ self \in ProcSet |-> 0]
/\ s = [ self \in ProcSet |-> 0]
/\ lowseq_ = [ self \in ProcSet |-> 0]
(* Procedure cv_wait *)
/\ local_wseq_ = [ self \in ProcSet |-> 0]
/\ g = [ self \in ProcSet |-> 0]
/\ seq = [ self \in ProcSet |-> 0]
/\ signals = [ self \in ProcSet |-> 0]
/\ local_g1_start = [ self \in ProcSet |-> 0]
/\ lowseq = [ self \in ProcSet |-> 0]
(* Procedure cv_signal *)
/\ local_wseq_c = [ self \in ProcSet |-> 0]
/\ g1_ = [ self \in ProcSet |-> 0]
/\ do_futex_wake_ = [ self \in ProcSet |-> FALSE]
(* Procedure cv_broadcast *)
/\ local_wseq_cv = [ self \in ProcSet |-> 0]
/\ g1_c = [ self \in ProcSet |-> 0]
/\ do_futex_wake = [ self \in ProcSet |-> FALSE]
(* Process Proc *)
/\ num_loops = [self \in Procs |-> MaxNumLoops]
/\ stack = [self \in ProcSet |-> << >>]
/\ pc = [self \in ProcSet |-> "proc_start"]
check_state(self) == /\ pc[self] = "check_state"
/\ IF futexes[wait_index[self]].state /= val[self]
THEN /\ pc' = [pc EXCEPT ![self] = Head(stack[self]).pc]
/\ wait_index' = [wait_index EXCEPT ![self] = Head(stack[self]).wait_index]
/\ val' = [val EXCEPT ![self] = Head(stack[self]).val]
/\ stack' = [stack EXCEPT ![self] = Tail(stack[self])]
/\ UNCHANGED futexes
ELSE /\ val' = [val EXCEPT ![self] = 0]
/\ futexes' = [futexes EXCEPT ![wait_index[self]].sleepers = futexes[wait_index[self]].sleepers \union {self}]
/\ pc' = [pc EXCEPT ![self] = "wait_for_wake"]
/\ UNCHANGED << stack, wait_index >>
/\ UNCHANGED << mutex_index, g1_orig_size_index,
wrefs_index, g_signals_index, wseq,
g1_start, g_size, did_switch_g1, g1index,
waiters, busy, spinlock_locked,
cv_spinlock_locked, wake_index,
wake_all_index, old_state_, old_state_u,
orig_size, old_state, local_wseq, g1,
old_orig_size, old_g1_start, r, s,
lowseq_, local_wseq_, g, seq, signals,
local_g1_start, lowseq, local_wseq_c, g1_,
do_futex_wake_, local_wseq_cv, g1_c,
do_futex_wake, num_loops >>
wait_for_wake(self) == /\ pc[self] = "wait_for_wake"
/\ ~ (self \in futexes[wait_index[self]].sleepers)
/\ pc' = [pc EXCEPT ![self] = Head(stack[self]).pc]
/\ wait_index' = [wait_index EXCEPT ![self] = Head(stack[self]).wait_index]
/\ val' = [val EXCEPT ![self] = Head(stack[self]).val]
/\ stack' = [stack EXCEPT ![self] = Tail(stack[self])]
/\ UNCHANGED << mutex_index, g1_orig_size_index,
wrefs_index, g_signals_index, futexes,
wseq, g1_start, g_size, did_switch_g1,
g1index, waiters, busy, spinlock_locked,
cv_spinlock_locked, wake_index,
wake_all_index, old_state_, old_state_u,
orig_size, old_state, local_wseq, g1,
old_orig_size, old_g1_start, r, s,
lowseq_, local_wseq_, g, seq, signals,
local_g1_start, lowseq, local_wseq_c,
g1_, do_futex_wake_, local_wseq_cv,
g1_c, do_futex_wake, num_loops >>
futex_wait(self) == check_state(self) \/ wait_for_wake(self)
check_for_sleepers(self) == /\ pc[self] = "check_for_sleepers"
/\ IF futexes[wake_index[self]].sleepers = {}
THEN /\ pc' = [pc EXCEPT ![self] = Head(stack[self]).pc]
/\ wake_index' = [wake_index EXCEPT ![self] = Head(stack[self]).wake_index]
/\ stack' = [stack EXCEPT ![self] = Tail(stack[self])]
/\ UNCHANGED futexes
ELSE /\ \E x \in futexes[wake_index[self]].sleepers:
futexes' = [futexes EXCEPT ![wake_index[self]].sleepers = futexes[wake_index[self]].sleepers \ {x}]
/\ pc' = [pc EXCEPT ![self] = Head(stack[self]).pc]
/\ wake_index' = [wake_index EXCEPT ![self] = Head(stack[self]).wake_index]
/\ stack' = [stack EXCEPT ![self] = Tail(stack[self])]
/\ UNCHANGED << mutex_index, g1_orig_size_index,
wrefs_index, g_signals_index, wseq,
g1_start, g_size, did_switch_g1,
g1index, waiters, busy,
spinlock_locked,
cv_spinlock_locked, wait_index,
val, wake_all_index, old_state_,
old_state_u, orig_size, old_state,
local_wseq, g1, old_orig_size,
old_g1_start, r, s, lowseq_,
local_wseq_, g, seq, signals,
local_g1_start, lowseq,
local_wseq_c, g1_, do_futex_wake_,
local_wseq_cv, g1_c, do_futex_wake,
num_loops >>
futex_wake_single(self) == check_for_sleepers(self)
futex_wake_all_(self) == /\ pc[self] = "futex_wake_all_"
/\ futexes' = [futexes EXCEPT ![wake_all_index[self]].sleepers = {}]
/\ pc' = [pc EXCEPT ![self] = Head(stack[self]).pc]
/\ wake_all_index' = [wake_all_index EXCEPT ![self] = Head(stack[self]).wake_all_index]
/\ stack' = [stack EXCEPT ![self] = Tail(stack[self])]
/\ UNCHANGED << mutex_index, g1_orig_size_index,
wrefs_index, g_signals_index, wseq,
g1_start, g_size, did_switch_g1,
g1index, waiters, busy,
spinlock_locked, cv_spinlock_locked,
wait_index, val, wake_index,
old_state_, old_state_u, orig_size,
old_state, local_wseq, g1,
old_orig_size, old_g1_start, r, s,
lowseq_, local_wseq_, g, seq, signals,
local_g1_start, lowseq, local_wseq_c,
g1_, do_futex_wake_, local_wseq_cv,
g1_c, do_futex_wake, num_loops >>
futex_wake_all(self) == futex_wake_all_(self)
lock_mutex_start(self) == /\ pc[self] = "lock_mutex_start"
/\ IF UseSpinlockForMutex
THEN /\ ~spinlock_locked
/\ spinlock_locked' = TRUE
/\ pc' = [pc EXCEPT ![self] = Head(stack[self]).pc]
/\ old_state_' = [old_state_ EXCEPT ![self] = Head(stack[self]).old_state_]
/\ stack' = [stack EXCEPT ![self] = Tail(stack[self])]
/\ UNCHANGED futexes
ELSE /\ IF futexes[mutex_index].state = 0
THEN /\ futexes' = [futexes EXCEPT ![mutex_index].state = 1]
/\ pc' = [pc EXCEPT ![self] = Head(stack[self]).pc]
/\ old_state_' = [old_state_ EXCEPT ![self] = Head(stack[self]).old_state_]
/\ stack' = [stack EXCEPT ![self] = Tail(stack[self])]
ELSE /\ pc' = [pc EXCEPT ![self] = "lll_lock_wait"]
/\ UNCHANGED << futexes, stack,
old_state_ >>
/\ UNCHANGED spinlock_locked
/\ UNCHANGED << mutex_index, g1_orig_size_index,
wrefs_index, g_signals_index, wseq,
g1_start, g_size, did_switch_g1,
g1index, waiters, busy,
cv_spinlock_locked, wait_index, val,
wake_index, wake_all_index,
old_state_u, orig_size, old_state,
local_wseq, g1, old_orig_size,
old_g1_start, r, s, lowseq_,
local_wseq_, g, seq, signals,
local_g1_start, lowseq, local_wseq_c,
g1_, do_futex_wake_, local_wseq_cv,
g1_c, do_futex_wake, num_loops >>
lll_lock_wait(self) == /\ pc[self] = "lll_lock_wait"
/\ IF futexes[mutex_index].state = 2
THEN /\ pc' = [pc EXCEPT ![self] = "futex_wait_"]
ELSE /\ pc' = [pc EXCEPT ![self] = "exchange_lock"]
/\ UNCHANGED << mutex_index, g1_orig_size_index,
wrefs_index, g_signals_index, futexes,
wseq, g1_start, g_size, did_switch_g1,
g1index, waiters, busy, spinlock_locked,
cv_spinlock_locked, stack, wait_index,
val, wake_index, wake_all_index,
old_state_, old_state_u, orig_size,
old_state, local_wseq, g1,
old_orig_size, old_g1_start, r, s,
lowseq_, local_wseq_, g, seq, signals,
local_g1_start, lowseq, local_wseq_c,
g1_, do_futex_wake_, local_wseq_cv,
g1_c, do_futex_wake, num_loops >>
exchange_lock(self) == /\ pc[self] = "exchange_lock"
/\ old_state_' = [old_state_ EXCEPT ![self] = futexes[mutex_index].state]
/\ futexes' = [futexes EXCEPT ![mutex_index].state = 2]
/\ pc' = [pc EXCEPT ![self] = "check_for_locked"]
/\ UNCHANGED << mutex_index, g1_orig_size_index,
wrefs_index, g_signals_index, wseq,
g1_start, g_size, did_switch_g1,
g1index, waiters, busy, spinlock_locked,
cv_spinlock_locked, stack, wait_index,
val, wake_index, wake_all_index,
old_state_u, orig_size, old_state,
local_wseq, g1, old_orig_size,
old_g1_start, r, s, lowseq_,
local_wseq_, g, seq, signals,
local_g1_start, lowseq, local_wseq_c,
g1_, do_futex_wake_, local_wseq_cv,
g1_c, do_futex_wake, num_loops >>
check_for_locked(self) == /\ pc[self] = "check_for_locked"
/\ IF old_state_[self] = 0
THEN /\ pc' = [pc EXCEPT ![self] = Head(stack[self]).pc]
/\ old_state_' = [old_state_ EXCEPT ![self] = Head(stack[self]).old_state_]
/\ stack' = [stack EXCEPT ![self] = Tail(stack[self])]
ELSE /\ old_state_' = [old_state_ EXCEPT ![self] = 0]
/\ pc' = [pc EXCEPT ![self] = "futex_wait_"]
/\ stack' = stack
/\ UNCHANGED << mutex_index, g1_orig_size_index,
wrefs_index, g_signals_index,
futexes, wseq, g1_start, g_size,
did_switch_g1, g1index, waiters,
busy, spinlock_locked,
cv_spinlock_locked, wait_index, val,
wake_index, wake_all_index,
old_state_u, orig_size, old_state,
local_wseq, g1, old_orig_size,
old_g1_start, r, s, lowseq_,
local_wseq_, g, seq, signals,
local_g1_start, lowseq, local_wseq_c,
g1_, do_futex_wake_, local_wseq_cv,
g1_c, do_futex_wake, num_loops >>
futex_wait_(self) == /\ pc[self] = "futex_wait_"
/\ /\ stack' = [stack EXCEPT ![self] = << [ procedure |-> "futex_wait",
pc |-> "exchange_lock",
wait_index |-> wait_index[self],
val |-> val[self] ] >>
\o stack[self]]
/\ val' = [val EXCEPT ![self] = 2]
/\ wait_index' = [wait_index EXCEPT ![self] = mutex_index]
/\ pc' = [pc EXCEPT ![self] = "check_state"]
/\ UNCHANGED << mutex_index, g1_orig_size_index,
wrefs_index, g_signals_index, futexes,
wseq, g1_start, g_size, did_switch_g1,
g1index, waiters, busy, spinlock_locked,
cv_spinlock_locked, wake_index,
wake_all_index, old_state_, old_state_u,
orig_size, old_state, local_wseq, g1,
old_orig_size, old_g1_start, r, s,
lowseq_, local_wseq_, g, seq, signals,
local_g1_start, lowseq, local_wseq_c, g1_,
do_futex_wake_, local_wseq_cv, g1_c,
do_futex_wake, num_loops >>
lock_mutex(self) == lock_mutex_start(self) \/ lll_lock_wait(self)
\/ exchange_lock(self) \/ check_for_locked(self)
\/ futex_wait_(self)
unlock_mutex_start(self) == /\ pc[self] = "unlock_mutex_start"
/\ IF UseSpinlockForMutex
THEN /\ spinlock_locked' = FALSE
/\ pc' = [pc EXCEPT ![self] = Head(stack[self]).pc]
/\ old_state_u' = [old_state_u EXCEPT ![self] = Head(stack[self]).old_state_u]
/\ stack' = [stack EXCEPT ![self] = Tail(stack[self])]
/\ UNCHANGED futexes
ELSE /\ old_state_u' = [old_state_u EXCEPT ![self] = futexes[mutex_index].state]
/\ futexes' = [futexes EXCEPT ![mutex_index].state = 0]
/\ pc' = [pc EXCEPT ![self] = "check_if_sleeper"]
/\ UNCHANGED << spinlock_locked, stack >>
/\ UNCHANGED << mutex_index, g1_orig_size_index,
wrefs_index, g_signals_index, wseq,
g1_start, g_size, did_switch_g1,
g1index, waiters, busy,
cv_spinlock_locked, wait_index,
val, wake_index, wake_all_index,
old_state_, orig_size, old_state,
local_wseq, g1, old_orig_size,
old_g1_start, r, s, lowseq_,
local_wseq_, g, seq, signals,
local_g1_start, lowseq,
local_wseq_c, g1_, do_futex_wake_,
local_wseq_cv, g1_c, do_futex_wake,
num_loops >>
check_if_sleeper(self) == /\ pc[self] = "check_if_sleeper"
/\ IF old_state_u[self] > 1
THEN /\ /\ old_state_u' = [old_state_u EXCEPT ![self] = Head(stack[self]).old_state_u]
/\ stack' = [stack EXCEPT ![self] = << [ procedure |-> "futex_wake_single",
pc |-> Head(stack[self]).pc,
wake_index |-> wake_index[self] ] >>
\o Tail(stack[self])]
/\ wake_index' = [wake_index EXCEPT ![self] = mutex_index]
/\ pc' = [pc EXCEPT ![self] = "check_for_sleepers"]
ELSE /\ pc' = [pc EXCEPT ![self] = Head(stack[self]).pc]
/\ old_state_u' = [old_state_u EXCEPT ![self] = Head(stack[self]).old_state_u]
/\ stack' = [stack EXCEPT ![self] = Tail(stack[self])]
/\ UNCHANGED wake_index
/\ UNCHANGED << mutex_index, g1_orig_size_index,
wrefs_index, g_signals_index,
futexes, wseq, g1_start, g_size,
did_switch_g1, g1index, waiters,
busy, spinlock_locked,
cv_spinlock_locked, wait_index, val,
wake_all_index, old_state_,
orig_size, old_state, local_wseq, g1,
old_orig_size, old_g1_start, r, s,
lowseq_, local_wseq_, g, seq,
signals, local_g1_start, lowseq,
local_wseq_c, g1_, do_futex_wake_,
local_wseq_cv, g1_c, do_futex_wake,
num_loops >>
unlock_mutex(self) == unlock_mutex_start(self) \/ check_if_sleeper(self)
cv_acquire_lock(self) == /\ pc[self] = "cv_acquire_lock"
/\ IF UseSpinlockForCVMutex
THEN /\ ~cv_spinlock_locked
/\ cv_spinlock_locked' = TRUE
/\ pc' = [pc EXCEPT ![self] = Head(stack[self]).pc]
/\ orig_size' = [orig_size EXCEPT ![self] = Head(stack[self]).orig_size]
/\ stack' = [stack EXCEPT ![self] = Tail(stack[self])]
ELSE /\ orig_size' = [orig_size EXCEPT ![self] = futexes[g1_orig_size_index].state]
/\ pc' = [pc EXCEPT ![self] = "cv_acquire_unlocked"]
/\ UNCHANGED << cv_spinlock_locked, stack >>
/\ UNCHANGED << mutex_index, g1_orig_size_index,
wrefs_index, g_signals_index, futexes,
wseq, g1_start, g_size, did_switch_g1,
g1index, waiters, busy,
spinlock_locked, wait_index, val,
wake_index, wake_all_index,
old_state_, old_state_u, old_state,
local_wseq, g1, old_orig_size,
old_g1_start, r, s, lowseq_,
local_wseq_, g, seq, signals,
local_g1_start, lowseq, local_wseq_c,
g1_, do_futex_wake_, local_wseq_cv,
g1_c, do_futex_wake, num_loops >>
cv_acquire_unlocked(self) == /\ pc[self] = "cv_acquire_unlocked"
/\ IF (orig_size[self] % 4) = 0
THEN /\ pc' = [pc EXCEPT ![self] = "cv_acquire_lock_exchange"]
ELSE /\ pc' = [pc EXCEPT ![self] = "cv_acquire_lock_sleep_loop"]
/\ UNCHANGED << mutex_index, g1_orig_size_index,
wrefs_index, g_signals_index,
futexes, wseq, g1_start, g_size,
did_switch_g1, g1index, waiters,
busy, spinlock_locked,
cv_spinlock_locked, stack,
wait_index, val, wake_index,
wake_all_index, old_state_,
old_state_u, orig_size, old_state,
local_wseq, g1, old_orig_size,
old_g1_start, r, s, lowseq_,
local_wseq_, g, seq, signals,
local_g1_start, lowseq,
local_wseq_c, g1_, do_futex_wake_,
local_wseq_cv, g1_c,
do_futex_wake, num_loops >>
cv_acquire_lock_exchange(self) == /\ pc[self] = "cv_acquire_lock_exchange"
/\ IF futexes[g1_orig_size_index].state = orig_size[self]
THEN /\ futexes' = [futexes EXCEPT ![g1_orig_size_index].state = SetBit(orig_size[self], 0)]
/\ pc' = [pc EXCEPT ![self] = Head(stack[self]).pc]
/\ orig_size' = [orig_size EXCEPT ![self] = Head(stack[self]).orig_size]
/\ stack' = [stack EXCEPT ![self] = Tail(stack[self])]
ELSE /\ orig_size' = [orig_size EXCEPT ![self] = futexes[g1_orig_size_index].state]
/\ pc' = [pc EXCEPT ![self] = "cv_acquire_unlocked"]
/\ UNCHANGED << futexes, stack >>
/\ UNCHANGED << mutex_index,
g1_orig_size_index,
wrefs_index, g_signals_index,
wseq, g1_start, g_size,
did_switch_g1, g1index,
waiters, busy,
spinlock_locked,
cv_spinlock_locked,
wait_index, val, wake_index,
wake_all_index, old_state_,
old_state_u, old_state,
local_wseq, g1,
old_orig_size, old_g1_start,
r, s, lowseq_, local_wseq_,
g, seq, signals,
local_g1_start, lowseq,
local_wseq_c, g1_,
do_futex_wake_,
local_wseq_cv, g1_c,
do_futex_wake, num_loops >>
cv_acquire_lock_sleep_loop(self) == /\ pc[self] = "cv_acquire_lock_sleep_loop"
/\ pc' = [pc EXCEPT ![self] = "cv_acquire_lock_loop_to_set_sleeper"]
/\ UNCHANGED << mutex_index,