On Sun, Feb 04, 2018 at 01:16:01AM -0800, Paul E. McKenney wrote:
> On Sat, Feb 03, 2018 at 05:10:06PM -0500, Alan Stern wrote:
> > On Sat, 3 Feb 2018, Paul E. McKenney wrote:
> >
> > > Please see below for an initial patch to this effect. This activity
> > > proved to be more productive than expected for these tests, which certainly
> > > supports our assertion that locking needs more testing...
> > >
> > > MP+polocks.litmus
> > > MP+porevlocks.litmus
> > >
> > > These are allowed by the current model, which surprised me a bit,
> > > given that even powerpc would forbid them. Is the rationale
> > > that a lock-savvy compiler could pull accesses into the lock's
> > > critical section and then reorder those accesses? Or does this
> > > constitute a bug in our model of locking?
> > >
> > > (And these were allowed when I wrote recipes.txt, embarrassingly
> > > enough...)
> > >
> > > Z6.0+pooncelock+poonceLock+pombonce.litmus
> > >
> > > This was forbidden when I wrote recipes.txt, but now is allowed.
> > > The header comment for smp_mb__after_spinlock() makes it pretty
> > > clear that it must be forbidden. So this one is a bug in our
> > > model of locking.
> >
> > I just tried testing these under the most recent version of herd, and
> > all three were forbidden.
>
> And they do for me as well once I upgraded to the most recent version of
> herd. Whew!!!
>
> Boy, we weren't kidding when we said that you need to us the latest
> and greatest herd7, now were we? ;-)
And here is the updated commit adding comments to the litmus test,
which adds comments for the three litmus tests added above. I have also
marked this commit with "EXP" indicating that it has not yet had time
for review. This marking appears only on my commits -- others' commits
don't get pulled until there has been time for review. (I have to put
my commits somewhere, and maintaining two different branches would be
a real mess given the likelihood of depeendencies among comits.)
Thanx, Paul
------------------------------------------------------------------------
commit 49af6e403afab890a54518980d345431d74234a4
Author: Paul E. McKenney <paulmck@xxxxxxxxxxxxxxxxxx>
Date: Sat Feb 3 00:04:49 2018 -0800
EXP litmus_tests: Add comments explaining tests' purposes
This commit adds comments to the litmus tests summarizing what these
tests are intended to demonstrate.
Suggested-by: Ingo Molnar <mingo@xxxxxxxxxx>
Signed-off-by: Paul E. McKenney <paulmck@xxxxxxxxxxxxxxxxxx>
diff --git a/tools/memory-model/litmus-tests/CoRR+poonceonce+Once.litmus b/tools/memory-model/litmus-tests/CoRR+poonceonce+Once.litmus
index 5b83d57f6ac5..8e8ae8989085 100644
--- a/tools/memory-model/litmus-tests/CoRR+poonceonce+Once.litmus
+++ b/tools/memory-model/litmus-tests/CoRR+poonceonce+Once.litmus
@@ -1,5 +1,11 @@
C CoRR+poonceonce+Once
+(*
+ * Test of read-read coherence, that is, whether or not two successive
+ * reads from the same variable are ordered. They should be ordered,
+ * that is, this test should be forbidden.
+ *)
+
{}
P0(int *x)
diff --git a/tools/memory-model/litmus-tests/CoRW+poonceonce+Once.litmus b/tools/memory-model/litmus-tests/CoRW+poonceonce+Once.litmus
index fab91c13d52c..0078ecd76f5e 100644
--- a/tools/memory-model/litmus-tests/CoRW+poonceonce+Once.litmus
+++ b/tools/memory-model/litmus-tests/CoRW+poonceonce+Once.litmus
@@ -1,5 +1,11 @@
C CoRW+poonceonce+Once
+(*
+ * Test of read-write coherence, that is, whether or not a read from a
+ * given variable followed by a write to that same variable are ordered.
+ * This should be ordered, that is, this test should be forbidden.
+ *)
+
{}
P0(int *x)
diff --git a/tools/memory-model/litmus-tests/CoWR+poonceonce+Once.litmus b/tools/memory-model/litmus-tests/CoWR+poonceonce+Once.litmus
index 6a35ec2042ea..c9d342c8fbec 100644
--- a/tools/memory-model/litmus-tests/CoWR+poonceonce+Once.litmus
+++ b/tools/memory-model/litmus-tests/CoWR+poonceonce+Once.litmus
@@ -1,5 +1,11 @@
C CoWR+poonceonce+Once
+(*
+ * Test of write-read coherence, that is, whether or not a write to a
+ * given variable followed by a read from that same variable are ordered.
+ * They should be ordered, that is, this test should be forbidden.
+ *)
+
{}
P0(int *x)
diff --git a/tools/memory-model/litmus-tests/CoWW+poonceonce.litmus b/tools/memory-model/litmus-tests/CoWW+poonceonce.litmus
index 32a96b832021..ad51c7b17f7b 100644
--- a/tools/memory-model/litmus-tests/CoWW+poonceonce.litmus
+++ b/tools/memory-model/litmus-tests/CoWW+poonceonce.litmus
@@ -1,5 +1,11 @@
C CoWW+poonceonce
+(*
+ * Test of write-write coherence, that is, whether or not two successive
+ * writes to the same variable are ordered. They should be ordered, that
+ * is, this test should be forbidden.
+ *)
+
{}
P0(int *x)
diff --git a/tools/memory-model/litmus-tests/IRIW+mbonceonces+OnceOnce.litmus b/tools/memory-model/litmus-tests/IRIW+mbonceonces+OnceOnce.litmus
index 7eba2c68992b..8a58abce69fe 100644
--- a/tools/memory-model/litmus-tests/IRIW+mbonceonces+OnceOnce.litmus
+++ b/tools/memory-model/litmus-tests/IRIW+mbonceonces+OnceOnce.litmus
@@ -1,5 +1,14 @@
C IRIW+mbonceonces+OnceOnce
+(*
+ * Test of independent reads from independent writes with smp_mb()
+ * between each pairs of reads. In other words, is smp_mb() sufficient to
+ * cause two different reading processes to agree on the order of a pair
+ * of writes, where each write is to a different variable by a different
+ * process? The smp_mb()s should be sufficient, that is, this test should
+ * be forbidden.
+ *)
+
{}
P0(int *x)
diff --git a/tools/memory-model/litmus-tests/IRIW+poonceonces+OnceOnce.litmus b/tools/memory-model/litmus-tests/IRIW+poonceonces+OnceOnce.litmus
index b0556c6c75d4..c736cd372207 100644
--- a/tools/memory-model/litmus-tests/IRIW+poonceonces+OnceOnce.litmus
+++ b/tools/memory-model/litmus-tests/IRIW+poonceonces+OnceOnce.litmus
@@ -1,5 +1,14 @@
C IRIW+poonceonces+OnceOnce
+(*
+ * Test of independent reads from independent writes with nothing
+ * between each pairs of reads. In other words, is anything at all
+ * needed to cause two different reading processes to agree on the order
+ * of a pair of writes, where each write is to a different variable by a
+ * different process? Something is needed, in other words, this test
+ * should be allowed.
+ *)
+
{}
P0(int *x)
diff --git a/tools/memory-model/litmus-tests/ISA2+poonceonces.litmus b/tools/memory-model/litmus-tests/ISA2+poonceonces.litmus
index 9a1a233d70c3..1f1c4220c92d 100644
--- a/tools/memory-model/litmus-tests/ISA2+poonceonces.litmus
+++ b/tools/memory-model/litmus-tests/ISA2+poonceonces.litmus
@@ -1,5 +1,13 @@
C ISA2+poonceonces
+(*
+ * Given a release-acquire chain ordering the first process's store
+ * against the last process's load, is ordering preserved if all of the
+ * smp_store_release() invocations be replaced by WRITE_ONCE() and all
+ * of the smp_load_acquire() invocations be replaced by READ_ONCE()?
+ * The answer is "no", that is, this test should be allowed.
+ *)
+
{}
P0(int *x, int *y)
diff --git a/tools/memory-model/litmus-tests/ISA2+pooncerelease+poacquirerelease+poacquireonce.litmus b/tools/memory-model/litmus-tests/ISA2+pooncerelease+poacquirerelease+poacquireonce.litmus
index 235195e87d4e..aa4b25838519 100644
--- a/tools/memory-model/litmus-tests/ISA2+pooncerelease+poacquirerelease+poacquireonce.litmus
+++ b/tools/memory-model/litmus-tests/ISA2+pooncerelease+poacquirerelease+poacquireonce.litmus
@@ -1,5 +1,14 @@
C ISA2+pooncerelease+poacquirerelease+poacquireonce
+(*
+ * This litmus test demonstrates that a release-acquire chain suffices
+ * to order P0()'s initial write against P2()'s final read. The reason
+ * that the release-acquire chain suffices is because in all but one
+ * case (P2() to P0()), each process reads from the preceding process's
+ * write. In memory-model-speak, there is only one non-reads-from
+ * (AKA non-rf) link, so release-acquire is all that is needed.
+ *)
+
{}
P0(int *x, int *y)
diff --git a/tools/memory-model/litmus-tests/LB+ctrlonceonce+mbonceonce.litmus b/tools/memory-model/litmus-tests/LB+ctrlonceonce+mbonceonce.litmus
index dd5ac3a8974a..0b65048ad4db 100644
--- a/tools/memory-model/litmus-tests/LB+ctrlonceonce+mbonceonce.litmus
+++ b/tools/memory-model/litmus-tests/LB+ctrlonceonce+mbonceonce.litmus
@@ -1,5 +1,14 @@
C LB+ctrlonceonce+mbonceonce
+(*
+ * This litmus test demonstrates that lightweight ordering suffices for
+ * the load-buffering pattern, in other words, preventing all processes
+ * reading from the preceding process's write. In this example, the
+ * combination of a control dependency and a full memory barrier are to do
+ * the trick. (But the full memory barrier could be replaced with another
+ * control dependency and order would still be maintained.)
+ *)
+
{}
P0(int *x, int *y)
diff --git a/tools/memory-model/litmus-tests/LB+poacquireonce+pooncerelease.litmus b/tools/memory-model/litmus-tests/LB+poacquireonce+pooncerelease.litmus
index 47bd61319d93..1d1f45ff1940 100644
--- a/tools/memory-model/litmus-tests/LB+poacquireonce+pooncerelease.litmus
+++ b/tools/memory-model/litmus-tests/LB+poacquireonce+pooncerelease.litmus
@@ -1,5 +1,12 @@
C LB+poacquireonce+pooncerelease
+(*
+ * Does a release-acquire pair suffice for the load-buffering litmus
+ * test, where each process reads from one of two variables then writes
+ * to the other? The answer is "yes", that is, this test should be
+ * forbidden.
+ *)
+
{}
P0(int *x, int *y)
diff --git a/tools/memory-model/litmus-tests/LB+poonceonces.litmus b/tools/memory-model/litmus-tests/LB+poonceonces.litmus
index a5cdf027e34b..383e3e0adb4e 100644
--- a/tools/memory-model/litmus-tests/LB+poonceonces.litmus
+++ b/tools/memory-model/litmus-tests/LB+poonceonces.litmus
@@ -1,5 +1,11 @@
C LB+poonceonces
+(*
+ * Can the counter-intuitive outcome for the load-buffering pattern
+ * be prevented even with no explicit ordering? The answer should be
+ * "no", that is, this test should be allowed.
+ *)
+
{}
P0(int *x, int *y)
diff --git a/tools/memory-model/litmus-tests/MP+onceassign+derefonce.litmus b/tools/memory-model/litmus-tests/MP+onceassign+derefonce.litmus
index 1a2fe5830381..86ddc88a26a2 100644
--- a/tools/memory-model/litmus-tests/MP+onceassign+derefonce.litmus
+++ b/tools/memory-model/litmus-tests/MP+onceassign+derefonce.litmus
@@ -1,5 +1,12 @@
C MP+onceassign+derefonce.litmus
+(*
+ * This litmus test demonstrates that rcu_assign_pointer() and
+ * rcu_dereference() suffice to ensure that an RCU reader will not see
+ * pre-initialization garbage when it traverses an RCU-protected data
+ * structure containing a newly inserted element.
+ *)
+
{
y=z;
z=0;
diff --git a/tools/memory-model/litmus-tests/MP+polocks.litmus b/tools/memory-model/litmus-tests/MP+polocks.litmus
index 5fe6f1e3c452..3e5d3fe01054 100644
--- a/tools/memory-model/litmus-tests/MP+polocks.litmus
+++ b/tools/memory-model/litmus-tests/MP+polocks.litmus
@@ -1,5 +1,14 @@
C MP+polocks
+(*
+ * This litmus test demonstrates how lock acquisitions and releases can
+ * stand in for smp_load_acquire() and smp_store_release(), respectively.
+ * In other words, when holding a given lock (or indeed after relaasing a
+ * given lock), a CPU is not only guaranteed to see the accesses that other
+ * CPOs made while previously holding that lock, it are also guaranteed
+ * to see all prior accesses by those other CPUs.
+ *)
+
{}
P0(int *x, int *y, spinlock_t *mylock)
diff --git a/tools/memory-model/litmus-tests/MP+poonceonces.litmus b/tools/memory-model/litmus-tests/MP+poonceonces.litmus
index 46e1ac7ba126..16a1d45e3fde 100644
--- a/tools/memory-model/litmus-tests/MP+poonceonces.litmus
+++ b/tools/memory-model/litmus-tests/MP+poonceonces.litmus
@@ -1,5 +1,11 @@
C MP+poonceonces
+(*
+ * Can the counter-intuitive message-passing outcome be prevented with
+ * no ordering at all? The answer should be "no", that is, this test
+ * should be prohibited.
+ *)
+
{}
P0(int *x, int *y)
diff --git a/tools/memory-model/litmus-tests/MP+pooncerelease+poacquireonce.litmus b/tools/memory-model/litmus-tests/MP+pooncerelease+poacquireonce.litmus
index 0b00cc7293ba..f7fbe2636287 100644
--- a/tools/memory-model/litmus-tests/MP+pooncerelease+poacquireonce.litmus
+++ b/tools/memory-model/litmus-tests/MP+pooncerelease+poacquireonce.litmus
@@ -1,5 +1,11 @@
C MP+pooncerelease+poacquireonce
+(*
+ * This litmus test demonstrates that smp_store_release() and
+ * smp_load_acquire() provide sufficient ordering for the message-passing
+ * pattern.
+ *)
+
{}
P0(int *x, int *y)
diff --git a/tools/memory-model/litmus-tests/MP+porevlocks.litmus b/tools/memory-model/litmus-tests/MP+porevlocks.litmus
index 90d011c34f33..bd68debfaa95 100644
--- a/tools/memory-model/litmus-tests/MP+porevlocks.litmus
+++ b/tools/memory-model/litmus-tests/MP+porevlocks.litmus
@@ -1,5 +1,14 @@
C MP+porevlocks
+(*
+ * This litmus test demonstrates how lock acquisitions and releases can
+ * stand in for smp_load_acquire() and smp_store_release(), respectively.
+ * In other words, when holding a given lock (or indeed after relaasing a
+ * given lock), a CPU is not only guaranteed to see the accesses that other
+ * CPOs made while previously holding that lock, it are also guaranteed
+ * to see all prior accesses by those other CPUs.
+ *)
+
{}
P0(int *x, int *y, spinlock_t *mylock)
diff --git a/tools/memory-model/litmus-tests/MP+wmbonceonce+rmbonceonce.litmus b/tools/memory-model/litmus-tests/MP+wmbonceonce+rmbonceonce.litmus
index 604ad41ea0c2..3d53ba138acd 100644
--- a/tools/memory-model/litmus-tests/MP+wmbonceonce+rmbonceonce.litmus
+++ b/tools/memory-model/litmus-tests/MP+wmbonceonce+rmbonceonce.litmus
@@ -1,5 +1,11 @@
C MP+wmbonceonce+rmbonceonce
+(*
+ * This litmus test demonstrates that smp_wmb() and smp_rmb() provide
+ * sufficient ordering for the message-passing pattern. However, it
+ * is usually better to use smp_store_release() and smp_load_acquire().
+ *)
+
{}
P0(int *x, int *y)
diff --git a/tools/memory-model/litmus-tests/R+mbonceonces.litmus b/tools/memory-model/litmus-tests/R+mbonceonces.litmus
index e69b9e3e9436..4d64e547f1cd 100644
--- a/tools/memory-model/litmus-tests/R+mbonceonces.litmus
+++ b/tools/memory-model/litmus-tests/R+mbonceonces.litmus
@@ -1,5 +1,12 @@
C R+mbonceonces
+(*
+ * This is the fully ordered (via smp_mb()) version of one of the classic
+ * counterintuitive litmus tests that illustrates the effects of store
+ * propagation delays. This test should be forbidden, but weaking either
+ * of the barriers would cause the resulting test to be allowed.
+ *)
+
{}
P0(int *x, int *y)
diff --git a/tools/memory-model/litmus-tests/R+poonceonces.litmus b/tools/memory-model/litmus-tests/R+poonceonces.litmus
index f7a12e00f82d..e75295b4e7c1 100644
--- a/tools/memory-model/litmus-tests/R+poonceonces.litmus
+++ b/tools/memory-model/litmus-tests/R+poonceonces.litmus
@@ -1,5 +1,11 @@
C R+poonceonces
+(*
+ * This is the unordered (via smp_mb()) version of one of the classic
+ * counterintuitive litmus tests that illustrates the effects of store
+ * propagation delays. This test should be allowed.
+ *)
+
{}
P0(int *x, int *y)
diff --git a/tools/memory-model/litmus-tests/S+poonceonces.litmus b/tools/memory-model/litmus-tests/S+poonceonces.litmus
index d0d541c8ec7d..7fe16920a228 100644
--- a/tools/memory-model/litmus-tests/S+poonceonces.litmus
+++ b/tools/memory-model/litmus-tests/S+poonceonces.litmus
@@ -1,5 +1,13 @@
C S+poonceonces
+(*
+ * Starting with a two-process release-acquire chain ordering P0()'s
+ * first store against P1()'s final load, if the smp_store_release()
+ * is replaced by WRITE_ONCE() and the smp_load_acquire() replaced by
+ * READ_ONCE(), is ordering preserved. The answer is "of course not!",
+ * so this test should be allowed.
+ *)
+
{}
P0(int *x, int *y)
diff --git a/tools/memory-model/litmus-tests/S+wmbonceonce+poacquireonce.litmus b/tools/memory-model/litmus-tests/S+wmbonceonce+poacquireonce.litmus
index 1d292d0d6603..f78ce120863b 100644
--- a/tools/memory-model/litmus-tests/S+wmbonceonce+poacquireonce.litmus
+++ b/tools/memory-model/litmus-tests/S+wmbonceonce+poacquireonce.litmus
@@ -1,5 +1,11 @@
C S+wmbonceonce+poacquireonce
+(*
+ * Can a smp_wmb(), instead of a release, and an acquire order a prior
+ * store against a subsequent store? The answer should be "yes", so
+ * this test should be forbidden.
+ *)
+
{}
P0(int *x, int *y)
diff --git a/tools/memory-model/litmus-tests/SB+mbonceonces.litmus b/tools/memory-model/litmus-tests/SB+mbonceonces.litmus
index b76caa5af1af..476542cd4a49 100644
--- a/tools/memory-model/litmus-tests/SB+mbonceonces.litmus
+++ b/tools/memory-model/litmus-tests/SB+mbonceonces.litmus
@@ -1,5 +1,12 @@
C SB+mbonceonces
+(*
+ * This litmus test demonstrates that full memory barriers suffice to
+ * order the store-buffering pattern, where each process writes to the
+ * variable that the preceding process read. (Locking and RCU can also
+ * suffice, but not much else.)
+ *)
+
{}
P0(int *x, int *y)
diff --git a/tools/memory-model/litmus-tests/SB+poonceonces.litmus b/tools/memory-model/litmus-tests/SB+poonceonces.litmus
index c1797e03807e..40d519408ea6 100644
--- a/tools/memory-model/litmus-tests/SB+poonceonces.litmus
+++ b/tools/memory-model/litmus-tests/SB+poonceonces.litmus
@@ -1,5 +1,11 @@
C SB+poonceonces
+(*
+ * This litmus test demonstrates that at least some ordering is required
+ * to order the store-buffering pattern, where each process writes to the
+ * variable that the preceding process read. This test should be allowed.
+ *)
+
{}
P0(int *x, int *y)
diff --git a/tools/memory-model/litmus-tests/WRC+poonceonces+Once.litmus b/tools/memory-model/litmus-tests/WRC+poonceonces+Once.litmus
index f5e7c92f61cc..0780a67cf3bd 100644
--- a/tools/memory-model/litmus-tests/WRC+poonceonces+Once.litmus
+++ b/tools/memory-model/litmus-tests/WRC+poonceonces+Once.litmus
@@ -1,5 +1,11 @@
C WRC+poonceonces+Once
+(*
+ * This litmus test is an extension of the message-passing pattern, where
+ * the first write is moved to a separate process. But because this test
+ * has no ordering at all, it should be allowed.
+ *)
+
{}
P0(int *x)
diff --git a/tools/memory-model/litmus-tests/WRC+pooncerelease+rmbonceonce+Once.litmus b/tools/memory-model/litmus-tests/WRC+pooncerelease+rmbonceonce+Once.litmus
index e3d0018025dd..070166d435e5 100644
--- a/tools/memory-model/litmus-tests/WRC+pooncerelease+rmbonceonce+Once.litmus
+++ b/tools/memory-model/litmus-tests/WRC+pooncerelease+rmbonceonce+Once.litmus
@@ -1,5 +1,11 @@
C WRC+pooncerelease+rmbonceonce+Once
+(*
+ * This litmus test is an extension of the message-passing pattern, where
+ * the first write is moved to a separate process. Because it features
+ * a release and a read memory barrier, it should be forbidden.
+ *)
+
{}
P0(int *x)
diff --git a/tools/memory-model/litmus-tests/Z6.0+pooncelock+poonceLock+pombonce.litmus b/tools/memory-model/litmus-tests/Z6.0+pooncelock+poonceLock+pombonce.litmus
index 9c2cb53e6ef0..4d0a25665655 100644
--- a/tools/memory-model/litmus-tests/Z6.0+pooncelock+poonceLock+pombonce.litmus
+++ b/tools/memory-model/litmus-tests/Z6.0+pooncelock+poonceLock+pombonce.litmus
@@ -1,5 +1,12 @@
C Z6.0+pooncelock+poonceLock+pombonce
+(*
+ * This litmus test demonstrates how smp_mb__after_spinlock() may be
+ * used to ensure that accesses in different critical sections for a
+ * given lock running on different CPUs are nevertheless seen in order
+ * by CPUs not holding that lock.
+ *)
+
{}
P0(int *x, int *y, spinlock_t *mylock)
diff --git a/tools/memory-model/litmus-tests/Z6.0+pooncelock+pooncelock+pombonce.litmus b/tools/memory-model/litmus-tests/Z6.0+pooncelock+pooncelock+pombonce.litmus
index c9a1f1a49ae1..8c723892716f 100644
--- a/tools/memory-model/litmus-tests/Z6.0+pooncelock+pooncelock+pombonce.litmus
+++ b/tools/memory-model/litmus-tests/Z6.0+pooncelock+pooncelock+pombonce.litmus
@@ -1,5 +1,11 @@
C Z6.0+pooncelock+pooncelock+pombonce
+(*
+ * This example demonstrates that a pair of accesses made by different
+ * processes each while holding a given lock will not necessarily be
+ * seen as ordered by a third process not holding that lock.
+ *)
+
{}
P0(int *x, int *y, spinlock_t *mylock)
diff --git a/tools/memory-model/litmus-tests/Z6.0+pooncerelease+poacquirerelease+mbonceonce.litmus b/tools/memory-model/litmus-tests/Z6.0+pooncerelease+poacquirerelease+mbonceonce.litmus
index 25409a033514..8b0b1b3ca348 100644
--- a/tools/memory-model/litmus-tests/Z6.0+pooncerelease+poacquirerelease+mbonceonce.litmus
+++ b/tools/memory-model/litmus-tests/Z6.0+pooncerelease+poacquirerelease+mbonceonce.litmus
@@ -1,5 +1,17 @@
C Z6.0+pooncerelease+poacquirerelease+mbonceonce
+(*
+ * This litmus test shows that a release-acquire chain, while sufficient
+ * when there is but one non-reads-from (AKA non-rf) link, does not suffice
+ * if there is more than one. Of the three processes, only P1() reads from
+ * P0's write, which means that there are two non-rf links: P1() to P2()
+ * is a write-to-write link (AKA a "coherence" or just "co" link) and P2()
+ * to P0() is a read-to-write link (AKA a "from-reads" or just "fr" link).
+ * When there are two or more non-rf links, you typically will need one
+ * full barrier for each non-rf link. (Exceptions include some cases
+ * involving locking.)
+ *)
+
{}
P0(int *x, int *y)
