From 8f32543b61d7daeddb5b64c80b5ad5f05cc97722 Mon Sep 17 00:00:00 2001 From: "Paul E. McKenney" Date: Tue, 20 Feb 2018 15:25:04 -0800 Subject: [PATCH] EXP litmus_tests: Add comments explaining tests' purposes This commit adds comments to the litmus tests summarizing what these tests are intended to demonstrate. [ paulmck: Apply Andrea's and Alan's feedback. ] Suggested-by: Ingo Molnar Signed-off-by: Paul E. McKenney Acked-by: Peter Zijlstra Cc: Linus Torvalds Cc: Thomas Gleixner Cc: akiyks@gmail.com Cc: boqun.feng@gmail.com Cc: dhowells@redhat.com Cc: j.alglave@ucl.ac.uk Cc: linux-arch@vger.kernel.org Cc: luc.maranget@inria.fr Cc: nborisov@suse.com Cc: npiggin@gmail.com Cc: parri.andrea@gmail.com Cc: stern@rowland.harvard.edu Cc: will.deacon@arm.com Link: http://lkml.kernel.org/r/1519169112-20593-4-git-send-email-paulmck@linux.vnet.ibm.com Signed-off-by: Ingo Molnar --- .../litmus-tests/CoRR+poonceonce+Once.litmus | 7 +++++++ .../litmus-tests/CoRW+poonceonce+Once.litmus | 7 +++++++ .../litmus-tests/CoWR+poonceonce+Once.litmus | 7 +++++++ .../litmus-tests/CoWW+poonceonce.litmus | 7 +++++++ .../litmus-tests/IRIW+mbonceonces+OnceOnce.litmus | 10 ++++++++++ .../litmus-tests/IRIW+poonceonces+OnceOnce.litmus | 10 ++++++++++ .../litmus-tests/ISA2+poonceonces.litmus | 9 +++++++++ ...cerelease+poacquirerelease+poacquireonce.litmus | 11 +++++++++++ .../litmus-tests/LB+ctrlonceonce+mbonceonce.litmus | 11 +++++++++++ .../LB+poacquireonce+pooncerelease.litmus | 8 ++++++++ .../litmus-tests/LB+poonceonces.litmus | 7 +++++++ .../litmus-tests/MP+onceassign+derefonce.litmus | 11 ++++++++++- tools/memory-model/litmus-tests/MP+polocks.litmus | 11 +++++++++++ .../litmus-tests/MP+poonceonces.litmus | 7 +++++++ .../MP+pooncerelease+poacquireonce.litmus | 8 ++++++++ .../memory-model/litmus-tests/MP+porevlocks.litmus | 11 +++++++++++ .../litmus-tests/MP+wmbonceonce+rmbonceonce.litmus | 8 ++++++++ .../memory-model/litmus-tests/R+mbonceonces.litmus | 9 +++++++++ .../memory-model/litmus-tests/R+poonceonces.litmus | 8 ++++++++ .../memory-model/litmus-tests/S+poonceonces.litmus | 9 +++++++++ .../S+wmbonceonce+poacquireonce.litmus | 7 +++++++ .../litmus-tests/SB+mbonceonces.litmus | 9 +++++++++ .../litmus-tests/SB+poonceonces.litmus | 8 ++++++++ .../litmus-tests/WRC+poonceonces+Once.litmus | 8 ++++++++ .../WRC+pooncerelease+rmbonceonce+Once.litmus | 8 ++++++++ .../Z6.0+pooncelock+poonceLock+pombonce.litmus | 9 +++++++++ .../Z6.0+pooncelock+pooncelock+pombonce.litmus | 8 ++++++++ ...ooncerelease+poacquirerelease+mbonceonce.litmus | 14 ++++++++++++++ 28 files changed, 246 insertions(+), 1 deletion(-) diff --git a/tools/memory-model/litmus-tests/CoRR+poonceonce+Once.litmus b/tools/memory-model/litmus-tests/CoRR+poonceonce+Once.litmus index 5b83d57f6ac5..967f9f2a6226 100644 --- a/tools/memory-model/litmus-tests/CoRR+poonceonce+Once.litmus +++ b/tools/memory-model/litmus-tests/CoRR+poonceonce+Once.litmus @@ -1,5 +1,12 @@ C CoRR+poonceonce+Once +(* + * Result: Never + * + * Test of read-read coherence, that is, whether or not two successive + * reads from the same variable are ordered. + *) + {} 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..4635739f3974 100644 --- a/tools/memory-model/litmus-tests/CoRW+poonceonce+Once.litmus +++ b/tools/memory-model/litmus-tests/CoRW+poonceonce+Once.litmus @@ -1,5 +1,12 @@ C CoRW+poonceonce+Once +(* + * Result: Never + * + * Test of read-write coherence, that is, whether or not a read from + * a given variable and a later write to that same variable are ordered. + *) + {} 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..bb068c92d8da 100644 --- a/tools/memory-model/litmus-tests/CoWR+poonceonce+Once.litmus +++ b/tools/memory-model/litmus-tests/CoWR+poonceonce+Once.litmus @@ -1,5 +1,12 @@ C CoWR+poonceonce+Once +(* + * Result: Never + * + * Test of write-read coherence, that is, whether or not a write to a + * given variable and a later read from that same variable are ordered. + *) + {} 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..0d9f0a958799 100644 --- a/tools/memory-model/litmus-tests/CoWW+poonceonce.litmus +++ b/tools/memory-model/litmus-tests/CoWW+poonceonce.litmus @@ -1,5 +1,12 @@ C CoWW+poonceonce +(* + * Result: Never + * + * Test of write-write coherence, that is, whether or not two successive + * writes to the same variable are ordered. + *) + {} 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..50d5db9ea983 100644 --- a/tools/memory-model/litmus-tests/IRIW+mbonceonces+OnceOnce.litmus +++ b/tools/memory-model/litmus-tests/IRIW+mbonceonces+OnceOnce.litmus @@ -1,5 +1,15 @@ C IRIW+mbonceonces+OnceOnce +(* + * Result: Never + * + * 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? + *) + {} 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..4b54dd6a6cd9 100644 --- a/tools/memory-model/litmus-tests/IRIW+poonceonces+OnceOnce.litmus +++ b/tools/memory-model/litmus-tests/IRIW+poonceonces+OnceOnce.litmus @@ -1,5 +1,15 @@ C IRIW+poonceonces+OnceOnce +(* + * Result: Sometimes + * + * 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? + *) + {} 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..b321aa6f4ea5 100644 --- a/tools/memory-model/litmus-tests/ISA2+poonceonces.litmus +++ b/tools/memory-model/litmus-tests/ISA2+poonceonces.litmus @@ -1,5 +1,14 @@ C ISA2+poonceonces +(* + * Result: Sometimes + * + * 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 are replaced by WRITE_ONCE() and all + * of the smp_load_acquire() invocations are replaced by READ_ONCE()? + *) + {} 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..025b0462ec9b 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 +1,16 @@ C ISA2+pooncerelease+poacquirerelease+poacquireonce +(* + * Result: Never + * + * 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..de6708229dd1 100644 --- a/tools/memory-model/litmus-tests/LB+ctrlonceonce+mbonceonce.litmus +++ b/tools/memory-model/litmus-tests/LB+ctrlonceonce+mbonceonce.litmus @@ -1,5 +1,16 @@ C LB+ctrlonceonce+mbonceonce +(* + * Result: Never + * + * 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 enough + * 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..07b9904b0e49 100644 --- a/tools/memory-model/litmus-tests/LB+poacquireonce+pooncerelease.litmus +++ b/tools/memory-model/litmus-tests/LB+poacquireonce+pooncerelease.litmus @@ -1,5 +1,13 @@ C LB+poacquireonce+pooncerelease +(* + * Result: Never + * + * 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? + *) + {} 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..74c49cb3c37b 100644 --- a/tools/memory-model/litmus-tests/LB+poonceonces.litmus +++ b/tools/memory-model/litmus-tests/LB+poonceonces.litmus @@ -1,5 +1,12 @@ C LB+poonceonces +(* + * Result: Sometimes + * + * Can the counter-intuitive outcome for the load-buffering pattern + * be prevented even with no explicit ordering? + *) + {} 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..97731b4bbdd8 100644 --- a/tools/memory-model/litmus-tests/MP+onceassign+derefonce.litmus +++ b/tools/memory-model/litmus-tests/MP+onceassign+derefonce.litmus @@ -1,4 +1,13 @@ -C MP+onceassign+derefonce.litmus +C MP+onceassign+derefonce + +(* + * Result: Never + * + * 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; diff --git a/tools/memory-model/litmus-tests/MP+polocks.litmus b/tools/memory-model/litmus-tests/MP+polocks.litmus index 5fe6f1e3c452..712a4fcdf6ce 100644 --- a/tools/memory-model/litmus-tests/MP+polocks.litmus +++ b/tools/memory-model/litmus-tests/MP+polocks.litmus @@ -1,5 +1,16 @@ C MP+polocks +(* + * Result: Never + * + * 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 releasing a + * given lock), a CPU is not only guaranteed to see the accesses that other + * CPUs made while previously holding that lock, it is 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..b2b60b84fb9d 100644 --- a/tools/memory-model/litmus-tests/MP+poonceonces.litmus +++ b/tools/memory-model/litmus-tests/MP+poonceonces.litmus @@ -1,5 +1,12 @@ C MP+poonceonces +(* + * Result: Maybe + * + * Can the counter-intuitive message-passing outcome be prevented with + * no ordering at all? + *) + {} 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..d52c68429722 100644 --- a/tools/memory-model/litmus-tests/MP+pooncerelease+poacquireonce.litmus +++ b/tools/memory-model/litmus-tests/MP+pooncerelease+poacquireonce.litmus @@ -1,5 +1,13 @@ C MP+pooncerelease+poacquireonce +(* + * Result: Never + * + * 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..72c9276b363e 100644 --- a/tools/memory-model/litmus-tests/MP+porevlocks.litmus +++ b/tools/memory-model/litmus-tests/MP+porevlocks.litmus @@ -1,5 +1,16 @@ C MP+porevlocks +(* + * Result: Never + * + * 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 releasing a + * given lock), a CPU is not only guaranteed to see the accesses that other + * CPUs made while previously holding that lock, it is 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..c078f38ff27a 100644 --- a/tools/memory-model/litmus-tests/MP+wmbonceonce+rmbonceonce.litmus +++ b/tools/memory-model/litmus-tests/MP+wmbonceonce+rmbonceonce.litmus @@ -1,5 +1,13 @@ C MP+wmbonceonce+rmbonceonce +(* + * Result: Never + * + * 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..a0e884ad2132 100644 --- a/tools/memory-model/litmus-tests/R+mbonceonces.litmus +++ b/tools/memory-model/litmus-tests/R+mbonceonces.litmus @@ -1,5 +1,14 @@ C R+mbonceonces +(* + * Result: Never + * + * 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. Note that weakening 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..5386f128a131 100644 --- a/tools/memory-model/litmus-tests/R+poonceonces.litmus +++ b/tools/memory-model/litmus-tests/R+poonceonces.litmus @@ -1,5 +1,13 @@ C R+poonceonces +(* + * Result: Sometimes + * + * This is the unordered (thus lacking smp_mb()) version of one of the + * classic counterintuitive litmus tests that illustrates the effects of + * store propagation delays. + *) + {} 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..8c9c2f81a580 100644 --- a/tools/memory-model/litmus-tests/S+poonceonces.litmus +++ b/tools/memory-model/litmus-tests/S+poonceonces.litmus @@ -1,5 +1,14 @@ C S+poonceonces +(* + * Result: Sometimes + * + * 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? + *) + {} 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..c53350205d28 100644 --- a/tools/memory-model/litmus-tests/S+wmbonceonce+poacquireonce.litmus +++ b/tools/memory-model/litmus-tests/S+wmbonceonce+poacquireonce.litmus @@ -1,5 +1,12 @@ C S+wmbonceonce+poacquireonce +(* + * Result: Never + * + * Can a smp_wmb(), instead of a release, and an acquire order a prior + * store against a subsequent store? + *) + {} 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..74b874ffa8da 100644 --- a/tools/memory-model/litmus-tests/SB+mbonceonces.litmus +++ b/tools/memory-model/litmus-tests/SB+mbonceonces.litmus @@ -1,5 +1,14 @@ C SB+mbonceonces +(* + * Result: Never + * + * 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 reads. (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..10d550730b25 100644 --- a/tools/memory-model/litmus-tests/SB+poonceonces.litmus +++ b/tools/memory-model/litmus-tests/SB+poonceonces.litmus @@ -1,5 +1,13 @@ C SB+poonceonces +(* + * Result: Sometimes + * + * 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 reads. + *) + {} 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..6a2bc12a1af1 100644 --- a/tools/memory-model/litmus-tests/WRC+poonceonces+Once.litmus +++ b/tools/memory-model/litmus-tests/WRC+poonceonces+Once.litmus @@ -1,5 +1,13 @@ C WRC+poonceonces+Once +(* + * Result: Sometimes + * + * This litmus test is an extension of the message-passing pattern, + * where the first write is moved to a separate process. Note that this + * test has no ordering at all. + *) + {} 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..97fcbffde9a0 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 +1,13 @@ C WRC+pooncerelease+rmbonceonce+Once +(* + * Result: Never + * + * 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..415248fb6699 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 +1,14 @@ C Z6.0+pooncelock+poonceLock+pombonce +(* + * Result: Never + * + * 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..10a2aa04cd07 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 +1,13 @@ C Z6.0+pooncelock+pooncelock+pombonce +(* + * Result: Sometimes + * + * 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..a20fc3fafb53 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 +1,19 @@ C Z6.0+pooncerelease+poacquirerelease+mbonceonce +(* + * Result: Sometimes + * + * 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)