drivers/block/paride/Transition-notes

   1 Lemma 1:
   2         If ps_tq is scheduled, ps_tq_active is 1.  ps_tq_int() can be called
   3         only when ps_tq_active is 1.
   4 Proof:  All assignments to ps_tq_active and all scheduling of ps_tq happen
   5         under ps_spinlock.  There are three places where that can happen:
   6         one in ps_set_intr() (A) and two in ps_tq_int() (B and C).
   7         Consider the sequnce of these events.  A can not be preceded by
   8         anything except B, since it is under if (!ps_tq_active) under
   9         ps_spinlock.  C is always preceded by B, since we can't reach it
  10         other than through B and we don't drop ps_spinlock between them.
  11         IOW, the sequence is A?(BA|BC|B)*.  OTOH, number of B can not exceed
  12         the sum of numbers of A and C, since each call of ps_tq_int() is
  13         the result of ps_tq execution.  Therefore, the sequence starts with
  14         A and each B is preceded by either A or C.  Moments when we enter
  15         ps_tq_int() are sandwiched between {A,C} and B in that sequence,
  16         since at any time number of B can not exceed the number of these
  17         moments which, in turn, can not exceed the number of A and C.
  18         In other words, the sequence of events is (A or C set ps_tq_active to
  19         1 and schedule ps_tq, ps_tq is executed, ps_tq_int() is entered,
  20         B resets ps_tq_active)*.
  21
  22
  23 consider the following area:
  24         * in do_pd_request1(): to calls of pi_do_claimed() and return in
  25           case when pd_req is NULL.
  26         * in next_request(): to call of do_pd_request1()
  27         * in do_pd_read(): to call of ps_set_intr()
  28         * in do_pd_read_start(): to calls of pi_do_claimed(), next_request()
  29 and ps_set_intr()
  30         * in do_pd_read_drq(): to calls of pi_do_claimed() and next_request()
  31         * in do_pd_write(): to call of ps_set_intr()
  32         * in do_pd_write_start(): to calls of pi_do_claimed(), next_request()
  33 and ps_set_intr()
  34         * in do_pd_write_done(): to calls of pi_do_claimed() and next_request()
  35         * in ps_set_intr(): to check for ps_tq_active and to scheduling
  36           ps_tq if ps_tq_active was 0.
  37         * in ps_tq_int(): from the moment when we get ps_spinlock() to the
  38           return, call of con() or scheduling ps_tq.
  39         * in pi_schedule_claimed() when called from pi_do_claimed() called from
  40           pd.c, everything until returning 1 or setting or setting ->claim_cont
  41           on the path that returns 0
  42         * in pi_do_claimed() when called from pd.c, everything until the call
  43           of pi_do_claimed() plus the everything until the call of cont() if
  44           pi_do_claimed() has returned 1.
  45         * in pi_wake_up() called for PIA that belongs to pd.c, everything from
  46           the moment when pi_spinlock has been acquired.
  47
  48 Lemma 2:
  49         1) at any time at most one thread of execution can be in that area or
  50         be preempted there.
  51         2) When there is such a thread, pd_busy is set or pd_lock is held by
  52         that thread.
  53         3) When there is such a thread, ps_tq_active is 0 or ps_spinlock is
  54         held by that thread.
  55         4) When there is such a thread, all PIA belonging to pd.c have NULL
  56         ->claim_cont or pi_spinlock is held by thread in question.
  57
  58 Proof:  consider the first moment when the above is not true.
  59
  60 (1) can become not true if some thread enters that area while another is there.
  61         a) do_pd_request1() can be called from next_request() or do_pd_request()
  62            In the first case the thread was already in the area.  In the second,
  63            the thread was holding pd_lock and found pd_busy not set, which would
  64            mean that (2) was already not true.
  65         b) ps_set_intr() and pi_schedule_claimed() can be called only from the
  66            area.
  67         c) pi_do_claimed() is called by pd.c only from the area.
  68         d) ps_tq_int() can enter the area only when the thread is holding
  69            ps_spinlock and ps_tq_active is 1 (due to Lemma 1).  It means that
  70            (3) was already not true.
  71         e) do_pd_{read,write}* could be called only from the area.  The only
  72            case that needs consideration is call from pi_wake_up() and there
  73            we would have to be called for the PIA that got ->claimed_cont
  74            from pd.c.  That could happen only if pi_do_claimed() had been
  75            called from pd.c for that PIA, which happens only for PIA belonging
  76            to pd.c.
  77         f) pi_wake_up() can enter the area only when the thread is holding
  78            pi_spinlock and ->claimed_cont is non-NULL for PIA belonging to
  79            pd.c.  It means that (4) was already not true.
  80
  81 (2) can become not true only when pd_lock is released by the thread in question.
  82         Indeed, pd_busy is reset only in the area and thread that resets
  83         it is holding pd_lock.  The only place within the area where we
  84         release pd_lock is in pd_next_buf() (called from within the area).
  85         But that code does not reset pd_busy, so pd_busy would have to be
  86         0 when pd_next_buf() had acquired pd_lock.  If it become 0 while
  87         we were acquiring the lock, (1) would be already false, since
  88         the thread that had reset it would be in the area simulateously.
  89         If it was 0 before we tried to acquire pd_lock, (2) would be
  90         already false.
  91
  92 For similar reasons, (3) can become not true only when ps_spinlock is released
  93 by the thread in question.  However, all such places within the area are right
  94 after resetting ps_tq_active to 0.
  95
  96 (4) is done the same way - all places where we release pi_spinlock within
  97 the area are either after resetting ->claimed_cont to NULL while holding
  98 pi_spinlock, or after not tocuhing ->claimed_cont since acquiring pi_spinlock
  99 also in the area.  The only place where ->claimed_cont is made non-NULL is
 100 in the area, under pi_spinlock and we do not release it until after leaving
 101 the area.
 102
 103 QED.
 104
 105
 106 Corollary 1: ps_tq_active can be killed.  Indeed, the only place where we
 107 check its value is in ps_set_intr() and if it had been non-zero at that
 108 point, we would have violated either (2.1) (if it was set while ps_set_intr()
 109 was acquiring ps_spinlock) or (2.3) (if it was set when we started to
 110 acquire ps_spinlock).
 111
 112 Corollary 2: ps_spinlock can be killed.  Indeed, Lemma 1 and Lemma 2 show
 113 that the only possible contention is between scheduling ps_tq followed by
 114 immediate release of spinlock and beginning of execution of ps_tq on
 115 another CPU.
 116
 117 Corollary 3: assignment to pd_busy in do_pd_read_start() and do_pd_write_start()
 118 can be killed.  Indeed, we are not holding pd_lock and thus pd_busy is already
 119 1 here.
 120
 121 Corollary 4: in ps_tq_int() uses of con can be replaced with uses of
 122 ps_continuation, since the latter is changed only from the area.
 123 We don't need to reset it to NULL, since we are guaranteed that there
 124 will be a call of ps_set_intr() before we look at ps_continuation again.
 125 We can remove the check for ps_continuation being NULL for the same
 126 reason - the value is guaranteed to be set by the last ps_set_intr() and
 127 we never pass it NULL.  Assignements in the beginning of ps_set_intr()
 128 can be taken to callers as long as they remain within the area.