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locks.c revision 1.63
      1  1.63  pooka /*	$NetBSD: locks.c,v 1.63 2013/05/02 21:35:19 pooka Exp $	*/
      2   1.1  pooka 
      3   1.1  pooka /*
      4  1.54  pooka  * Copyright (c) 2007-2011 Antti Kantee.  All Rights Reserved.
      5   1.1  pooka  *
      6   1.1  pooka  * Redistribution and use in source and binary forms, with or without
      7   1.1  pooka  * modification, are permitted provided that the following conditions
      8   1.1  pooka  * are met:
      9   1.1  pooka  * 1. Redistributions of source code must retain the above copyright
     10   1.1  pooka  *    notice, this list of conditions and the following disclaimer.
     11   1.1  pooka  * 2. Redistributions in binary form must reproduce the above copyright
     12   1.1  pooka  *    notice, this list of conditions and the following disclaimer in the
     13   1.1  pooka  *    documentation and/or other materials provided with the distribution.
     14   1.1  pooka  *
     15   1.1  pooka  * THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS
     16   1.1  pooka  * OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
     17   1.1  pooka  * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
     18   1.1  pooka  * DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
     19   1.1  pooka  * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
     20   1.1  pooka  * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
     21   1.1  pooka  * SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
     22   1.1  pooka  * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
     23   1.1  pooka  * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
     24   1.1  pooka  * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
     25   1.1  pooka  * SUCH DAMAGE.
     26   1.1  pooka  */
     27   1.1  pooka 
     28  1.23  pooka #include <sys/cdefs.h>
     29  1.63  pooka __KERNEL_RCSID(0, "$NetBSD: locks.c,v 1.63 2013/05/02 21:35:19 pooka Exp $");
     30  1.23  pooka 
     31   1.1  pooka #include <sys/param.h>
     32  1.26  pooka #include <sys/kmem.h>
     33   1.1  pooka #include <sys/mutex.h>
     34   1.1  pooka #include <sys/rwlock.h>
     35   1.1  pooka 
     36  1.18  pooka #include <rump/rumpuser.h>
     37  1.18  pooka 
     38   1.2  pooka #include "rump_private.h"
     39   1.2  pooka 
     40  1.22  pooka /*
     41  1.45  pooka  * Simple lockdebug.  If it's compiled in, it's always active.
     42  1.45  pooka  * Currently available only for mtx/rwlock.
     43  1.45  pooka  */
     44  1.45  pooka #ifdef LOCKDEBUG
     45  1.45  pooka #include <sys/lockdebug.h>
     46  1.45  pooka 
     47  1.45  pooka static lockops_t mutex_lockops = {
     48  1.45  pooka 	"mutex",
     49  1.45  pooka 	LOCKOPS_SLEEP,
     50  1.45  pooka 	NULL
     51  1.45  pooka };
     52  1.45  pooka static lockops_t rw_lockops = {
     53  1.46  pooka 	"rwlock",
     54  1.45  pooka 	LOCKOPS_SLEEP,
     55  1.45  pooka 	NULL
     56  1.45  pooka };
     57  1.45  pooka 
     58  1.45  pooka #define ALLOCK(lock, ops)		\
     59  1.45  pooka     lockdebug_alloc(lock, ops, (uintptr_t)__builtin_return_address(0))
     60  1.45  pooka #define FREELOCK(lock)			\
     61  1.45  pooka     lockdebug_free(lock)
     62  1.45  pooka #define WANTLOCK(lock, shar, try)	\
     63  1.45  pooka     lockdebug_wantlock(lock, (uintptr_t)__builtin_return_address(0), shar, try)
     64  1.45  pooka #define LOCKED(lock, shar)		\
     65  1.45  pooka     lockdebug_locked(lock, NULL, (uintptr_t)__builtin_return_address(0), shar)
     66  1.45  pooka #define UNLOCKED(lock, shar)		\
     67  1.45  pooka     lockdebug_unlocked(lock, (uintptr_t)__builtin_return_address(0), shar)
     68  1.45  pooka #else
     69  1.45  pooka #define ALLOCK(a, b)
     70  1.45  pooka #define FREELOCK(a)
     71  1.45  pooka #define WANTLOCK(a, b, c)
     72  1.45  pooka #define LOCKED(a, b)
     73  1.45  pooka #define UNLOCKED(a, b)
     74  1.45  pooka #endif
     75  1.45  pooka 
     76  1.45  pooka /*
     77  1.22  pooka  * We map locks to pthread routines.  The difference between kernel
     78  1.22  pooka  * and rumpuser routines is that while the kernel uses static
     79  1.22  pooka  * storage, rumpuser allocates the object from the heap.  This
     80  1.22  pooka  * indirection is necessary because we don't know the size of
     81  1.38    snj  * pthread objects here.  It is also beneficial, since we can
     82  1.22  pooka  * be easily compatible with the kernel ABI because all kernel
     83  1.22  pooka  * objects regardless of machine architecture are always at least
     84  1.22  pooka  * the size of a pointer.  The downside, of course, is a performance
     85  1.22  pooka  * penalty.
     86  1.22  pooka  */
     87  1.22  pooka 
     88  1.22  pooka #define RUMPMTX(mtx) (*(struct rumpuser_mtx **)(mtx))
     89  1.22  pooka 
     90   1.1  pooka void
     91   1.1  pooka mutex_init(kmutex_t *mtx, kmutex_type_t type, int ipl)
     92   1.1  pooka {
     93  1.57  pooka 	int ruflags = RUMPUSER_MTX_KMUTEX;
     94  1.56  pooka 	int isspin;
     95  1.56  pooka 
     96  1.57  pooka 	CTASSERT(sizeof(kmutex_t) >= sizeof(void *));
     97  1.57  pooka 
     98  1.56  pooka 	/*
     99  1.56  pooka 	 * Try to figure out if the caller wanted a spin mutex or
    100  1.56  pooka 	 * not with this easy set of conditionals.  The difference
    101  1.56  pooka 	 * between a spin mutex and an adaptive mutex for a rump
    102  1.56  pooka 	 * kernel is that the hypervisor does not relinquish the
    103  1.56  pooka 	 * rump kernel CPU context for a spin mutex.  The
    104  1.56  pooka 	 * hypervisor itself may block even when "spinning".
    105  1.56  pooka 	 */
    106  1.56  pooka 	if (type == MUTEX_SPIN) {
    107  1.56  pooka 		isspin = 1;
    108  1.56  pooka 	} else if (ipl == IPL_NONE || ipl == IPL_SOFTCLOCK ||
    109  1.56  pooka 	    ipl == IPL_SOFTBIO || ipl == IPL_SOFTNET ||
    110  1.56  pooka 	    ipl == IPL_SOFTSERIAL) {
    111  1.56  pooka 		isspin = 0;
    112  1.56  pooka 	} else {
    113  1.56  pooka 		isspin = 1;
    114  1.56  pooka 	}
    115   1.1  pooka 
    116  1.57  pooka 	if (isspin)
    117  1.57  pooka 		ruflags |= RUMPUSER_MTX_SPIN;
    118  1.57  pooka 	rumpuser_mutex_init((struct rumpuser_mtx **)mtx, ruflags);
    119  1.45  pooka 	ALLOCK(mtx, &mutex_lockops);
    120   1.1  pooka }
    121   1.1  pooka 
    122   1.1  pooka void
    123   1.1  pooka mutex_destroy(kmutex_t *mtx)
    124   1.1  pooka {
    125   1.1  pooka 
    126  1.45  pooka 	FREELOCK(mtx);
    127  1.22  pooka 	rumpuser_mutex_destroy(RUMPMTX(mtx));
    128   1.1  pooka }
    129   1.1  pooka 
    130   1.1  pooka void
    131   1.1  pooka mutex_enter(kmutex_t *mtx)
    132   1.1  pooka {
    133   1.1  pooka 
    134  1.45  pooka 	WANTLOCK(mtx, false, false);
    135  1.22  pooka 	rumpuser_mutex_enter(RUMPMTX(mtx));
    136  1.45  pooka 	LOCKED(mtx, false);
    137   1.1  pooka }
    138  1.56  pooka 
    139  1.56  pooka void
    140  1.56  pooka mutex_spin_enter(kmutex_t *mtx)
    141  1.56  pooka {
    142  1.56  pooka 
    143  1.56  pooka 	WANTLOCK(mtx, false, false);
    144  1.61  pooka 	rumpuser_mutex_enter_nowrap(RUMPMTX(mtx));
    145  1.56  pooka 	LOCKED(mtx, false);
    146  1.56  pooka }
    147   1.6  pooka 
    148   1.1  pooka int
    149   1.1  pooka mutex_tryenter(kmutex_t *mtx)
    150   1.1  pooka {
    151  1.60  pooka 	int error;
    152   1.1  pooka 
    153  1.60  pooka 	error = rumpuser_mutex_tryenter(RUMPMTX(mtx));
    154  1.60  pooka 	if (error == 0) {
    155  1.45  pooka 		WANTLOCK(mtx, false, true);
    156  1.45  pooka 		LOCKED(mtx, false);
    157  1.45  pooka 	}
    158  1.60  pooka 	return error == 0;
    159   1.1  pooka }
    160   1.1  pooka 
    161   1.1  pooka void
    162   1.1  pooka mutex_exit(kmutex_t *mtx)
    163   1.1  pooka {
    164   1.1  pooka 
    165  1.45  pooka 	UNLOCKED(mtx, false);
    166  1.22  pooka 	rumpuser_mutex_exit(RUMPMTX(mtx));
    167   1.1  pooka }
    168  1.45  pooka __strong_alias(mutex_spin_exit,mutex_exit);
    169   1.6  pooka 
    170   1.1  pooka int
    171   1.1  pooka mutex_owned(kmutex_t *mtx)
    172   1.1  pooka {
    173   1.1  pooka 
    174  1.44  pooka 	return mutex_owner(mtx) == curlwp;
    175  1.44  pooka }
    176  1.44  pooka 
    177  1.44  pooka struct lwp *
    178  1.44  pooka mutex_owner(kmutex_t *mtx)
    179  1.44  pooka {
    180  1.60  pooka 	struct lwp *l;
    181  1.44  pooka 
    182  1.60  pooka 	rumpuser_mutex_owner(RUMPMTX(mtx), &l);
    183  1.60  pooka 	return l;
    184   1.1  pooka }
    185   1.1  pooka 
    186  1.22  pooka #define RUMPRW(rw) (*(struct rumpuser_rw **)(rw))
    187  1.22  pooka 
    188   1.1  pooka /* reader/writer locks */
    189   1.1  pooka 
    190  1.63  pooka static enum rumprwlock
    191  1.63  pooka krw2rumprw(const krw_t op)
    192  1.63  pooka {
    193  1.63  pooka 
    194  1.63  pooka 	switch (op) {
    195  1.63  pooka 	case RW_READER:
    196  1.63  pooka 		return RUMPUSER_RW_READER;
    197  1.63  pooka 	case RW_WRITER:
    198  1.63  pooka 		return RUMPUSER_RW_WRITER;
    199  1.63  pooka 	default:
    200  1.63  pooka 		panic("unknown rwlock type");
    201  1.63  pooka 	}
    202  1.63  pooka }
    203  1.63  pooka 
    204   1.1  pooka void
    205   1.1  pooka rw_init(krwlock_t *rw)
    206   1.1  pooka {
    207   1.1  pooka 
    208  1.22  pooka 	CTASSERT(sizeof(krwlock_t) >= sizeof(void *));
    209  1.22  pooka 
    210  1.22  pooka 	rumpuser_rw_init((struct rumpuser_rw **)rw);
    211  1.45  pooka 	ALLOCK(rw, &rw_lockops);
    212   1.1  pooka }
    213   1.1  pooka 
    214   1.1  pooka void
    215   1.1  pooka rw_destroy(krwlock_t *rw)
    216   1.1  pooka {
    217   1.1  pooka 
    218  1.45  pooka 	FREELOCK(rw);
    219  1.22  pooka 	rumpuser_rw_destroy(RUMPRW(rw));
    220   1.1  pooka }
    221   1.1  pooka 
    222   1.1  pooka void
    223   1.1  pooka rw_enter(krwlock_t *rw, const krw_t op)
    224   1.1  pooka {
    225   1.1  pooka 
    226  1.45  pooka 
    227  1.45  pooka 	WANTLOCK(rw, op == RW_READER, false);
    228  1.63  pooka 	rumpuser_rw_enter(RUMPRW(rw), krw2rumprw(op));
    229  1.45  pooka 	LOCKED(rw, op == RW_READER);
    230   1.1  pooka }
    231   1.1  pooka 
    232   1.1  pooka int
    233   1.1  pooka rw_tryenter(krwlock_t *rw, const krw_t op)
    234   1.1  pooka {
    235  1.60  pooka 	int error;
    236   1.1  pooka 
    237  1.63  pooka 	error = rumpuser_rw_tryenter(RUMPRW(rw), krw2rumprw(op));
    238  1.60  pooka 	if (error == 0) {
    239  1.45  pooka 		WANTLOCK(rw, op == RW_READER, true);
    240  1.45  pooka 		LOCKED(rw, op == RW_READER);
    241  1.45  pooka 	}
    242  1.60  pooka 	return error == 0;
    243   1.1  pooka }
    244   1.1  pooka 
    245   1.1  pooka void
    246   1.1  pooka rw_exit(krwlock_t *rw)
    247   1.1  pooka {
    248   1.1  pooka 
    249  1.45  pooka #ifdef LOCKDEBUG
    250  1.45  pooka 	bool shared = !rw_write_held(rw);
    251  1.45  pooka 
    252  1.45  pooka 	if (shared)
    253  1.45  pooka 		KASSERT(rw_read_held(rw));
    254  1.45  pooka 	UNLOCKED(rw, shared);
    255  1.45  pooka #endif
    256  1.22  pooka 	rumpuser_rw_exit(RUMPRW(rw));
    257   1.1  pooka }
    258   1.1  pooka 
    259   1.1  pooka int
    260   1.1  pooka rw_tryupgrade(krwlock_t *rw)
    261   1.1  pooka {
    262  1.63  pooka 	int rv;
    263   1.1  pooka 
    264  1.63  pooka 	rv = rumpuser_rw_tryupgrade(RUMPRW(rw));
    265  1.63  pooka 	if (rv == 0) {
    266  1.63  pooka 		UNLOCKED(rw, 1);
    267  1.63  pooka 		WANTLOCK(rw, 0, true);
    268  1.63  pooka 		LOCKED(rw, 0);
    269  1.63  pooka 	}
    270  1.63  pooka 	return rv == 0;
    271   1.1  pooka }
    272   1.1  pooka 
    273  1.48   haad void
    274  1.48   haad rw_downgrade(krwlock_t *rw)
    275  1.48   haad {
    276  1.48   haad 
    277  1.63  pooka 	rumpuser_rw_downgrade(RUMPRW(rw));
    278  1.63  pooka 	UNLOCKED(rw, 0);
    279  1.63  pooka 	WANTLOCK(rw, 1, false);
    280  1.63  pooka 	LOCKED(rw, 1);
    281  1.48   haad }
    282  1.48   haad 
    283   1.6  pooka int
    284  1.63  pooka rw_read_held(krwlock_t *rw)
    285   1.6  pooka {
    286  1.60  pooka 	int rv;
    287   1.6  pooka 
    288  1.63  pooka 	rumpuser_rw_held(RUMPRW(rw), RUMPUSER_RW_READER, &rv);
    289  1.60  pooka 	return rv;
    290  1.10     ad }
    291  1.10     ad 
    292  1.10     ad int
    293  1.63  pooka rw_write_held(krwlock_t *rw)
    294  1.10     ad {
    295  1.60  pooka 	int rv;
    296  1.10     ad 
    297  1.63  pooka 	rumpuser_rw_held(RUMPRW(rw), RUMPUSER_RW_WRITER, &rv);
    298  1.60  pooka 	return rv;
    299  1.10     ad }
    300  1.10     ad 
    301  1.10     ad int
    302  1.10     ad rw_lock_held(krwlock_t *rw)
    303  1.10     ad {
    304  1.10     ad 
    305  1.63  pooka 	return rw_read_held(rw) || rw_write_held(rw);
    306   1.6  pooka }
    307   1.6  pooka 
    308   1.1  pooka /* curriculum vitaes */
    309   1.1  pooka 
    310  1.24  pooka #define RUMPCV(cv) (*(struct rumpuser_cv **)(cv))
    311   1.1  pooka 
    312   1.1  pooka void
    313   1.1  pooka cv_init(kcondvar_t *cv, const char *msg)
    314   1.1  pooka {
    315   1.1  pooka 
    316  1.25  pooka 	CTASSERT(sizeof(kcondvar_t) >= sizeof(void *));
    317  1.25  pooka 
    318  1.24  pooka 	rumpuser_cv_init((struct rumpuser_cv **)cv);
    319   1.1  pooka }
    320   1.1  pooka 
    321   1.1  pooka void
    322   1.1  pooka cv_destroy(kcondvar_t *cv)
    323   1.1  pooka {
    324   1.1  pooka 
    325   1.1  pooka 	rumpuser_cv_destroy(RUMPCV(cv));
    326   1.1  pooka }
    327   1.1  pooka 
    328  1.47  pooka static int
    329  1.47  pooka docvwait(kcondvar_t *cv, kmutex_t *mtx, struct timespec *ts)
    330  1.47  pooka {
    331  1.47  pooka 	struct lwp *l = curlwp;
    332  1.47  pooka 	int rv;
    333  1.47  pooka 
    334  1.51  pooka 	if (__predict_false(l->l_flag & LW_RUMP_QEXIT)) {
    335  1.47  pooka 		/*
    336  1.50  pooka 		 * yield() here, someone might want the cpu
    337  1.50  pooka 		 * to set a condition.  otherwise we'll just
    338  1.50  pooka 		 * loop forever.
    339  1.47  pooka 		 */
    340  1.50  pooka 		yield();
    341  1.47  pooka 		return EINTR;
    342  1.47  pooka 	}
    343  1.47  pooka 
    344  1.47  pooka 	UNLOCKED(mtx, false);
    345  1.47  pooka 
    346  1.47  pooka 	l->l_private = cv;
    347  1.47  pooka 	rv = 0;
    348  1.47  pooka 	if (ts) {
    349  1.47  pooka 		if (rumpuser_cv_timedwait(RUMPCV(cv), RUMPMTX(mtx),
    350  1.47  pooka 		    ts->tv_sec, ts->tv_nsec))
    351  1.47  pooka 			rv = EWOULDBLOCK;
    352  1.47  pooka 	} else {
    353  1.47  pooka 		rumpuser_cv_wait(RUMPCV(cv), RUMPMTX(mtx));
    354  1.47  pooka 	}
    355  1.47  pooka 
    356  1.52  pooka 	LOCKED(mtx, false);
    357  1.52  pooka 
    358  1.47  pooka 	/*
    359  1.51  pooka 	 * Check for QEXIT.  if so, we need to wait here until we
    360  1.47  pooka 	 * are allowed to exit.
    361  1.47  pooka 	 */
    362  1.51  pooka 	if (__predict_false(l->l_flag & LW_RUMP_QEXIT)) {
    363  1.47  pooka 		struct proc *p = l->l_proc;
    364  1.47  pooka 
    365  1.53  pooka 		UNLOCKED(mtx, false);
    366  1.47  pooka 		mutex_exit(mtx); /* drop and retake later */
    367  1.47  pooka 
    368  1.47  pooka 		mutex_enter(p->p_lock);
    369  1.51  pooka 		while ((p->p_sflag & PS_RUMP_LWPEXIT) == 0) {
    370  1.47  pooka 			/* avoid recursion */
    371  1.47  pooka 			rumpuser_cv_wait(RUMPCV(&p->p_waitcv),
    372  1.47  pooka 			    RUMPMTX(p->p_lock));
    373  1.47  pooka 		}
    374  1.51  pooka 		KASSERT(p->p_sflag & PS_RUMP_LWPEXIT);
    375  1.47  pooka 		mutex_exit(p->p_lock);
    376  1.47  pooka 
    377  1.47  pooka 		/* ok, we can exit and remove "reference" to l->private */
    378  1.47  pooka 
    379  1.47  pooka 		mutex_enter(mtx);
    380  1.53  pooka 		LOCKED(mtx, false);
    381  1.47  pooka 		rv = EINTR;
    382  1.47  pooka 	}
    383  1.47  pooka 	l->l_private = NULL;
    384  1.47  pooka 
    385  1.47  pooka 	return rv;
    386  1.47  pooka }
    387  1.47  pooka 
    388   1.1  pooka void
    389   1.1  pooka cv_wait(kcondvar_t *cv, kmutex_t *mtx)
    390   1.1  pooka {
    391   1.1  pooka 
    392  1.42  pooka 	if (__predict_false(rump_threads == 0))
    393  1.28  pooka 		panic("cv_wait without threads");
    394  1.47  pooka 	(void) docvwait(cv, mtx, NULL);
    395   1.1  pooka }
    396   1.1  pooka 
    397   1.3  pooka int
    398   1.5  pooka cv_wait_sig(kcondvar_t *cv, kmutex_t *mtx)
    399   1.5  pooka {
    400   1.5  pooka 
    401  1.42  pooka 	if (__predict_false(rump_threads == 0))
    402  1.42  pooka 		panic("cv_wait without threads");
    403  1.47  pooka 	return docvwait(cv, mtx, NULL);
    404   1.5  pooka }
    405   1.5  pooka 
    406   1.5  pooka int
    407   1.3  pooka cv_timedwait(kcondvar_t *cv, kmutex_t *mtx, int ticks)
    408   1.3  pooka {
    409  1.58  pooka 	struct timespec ts;
    410   1.3  pooka 	extern int hz;
    411  1.45  pooka 	int rv;
    412  1.27  pooka 
    413   1.9  pooka 	if (ticks == 0) {
    414  1.47  pooka 		rv = cv_wait_sig(cv, mtx);
    415   1.9  pooka 	} else {
    416  1.58  pooka 		ts.tv_sec = ticks / hz;
    417  1.58  pooka 		ts.tv_nsec = (ticks % hz) * (1000000000/hz);
    418  1.47  pooka 		rv = docvwait(cv, mtx, &ts);
    419   1.9  pooka 	}
    420   1.5  pooka 
    421  1.45  pooka 	return rv;
    422   1.5  pooka }
    423  1.45  pooka __strong_alias(cv_timedwait_sig,cv_timedwait);
    424   1.5  pooka 
    425   1.1  pooka void
    426   1.1  pooka cv_signal(kcondvar_t *cv)
    427   1.1  pooka {
    428   1.1  pooka 
    429   1.1  pooka 	rumpuser_cv_signal(RUMPCV(cv));
    430   1.1  pooka }
    431   1.2  pooka 
    432   1.4  pooka void
    433   1.4  pooka cv_broadcast(kcondvar_t *cv)
    434   1.4  pooka {
    435   1.4  pooka 
    436   1.4  pooka 	rumpuser_cv_broadcast(RUMPCV(cv));
    437   1.4  pooka }
    438   1.4  pooka 
    439  1.17  pooka bool
    440  1.17  pooka cv_has_waiters(kcondvar_t *cv)
    441  1.17  pooka {
    442  1.60  pooka 	int rv;
    443  1.17  pooka 
    444  1.60  pooka 	rumpuser_cv_has_waiters(RUMPCV(cv), &rv);
    445  1.60  pooka 	return rv != 0;
    446  1.17  pooka }
    447  1.17  pooka 
    448  1.35  pooka /* this is not much of an attempt, but ... */
    449  1.35  pooka bool
    450  1.35  pooka cv_is_valid(kcondvar_t *cv)
    451  1.35  pooka {
    452  1.35  pooka 
    453  1.35  pooka 	return RUMPCV(cv) != NULL;
    454  1.35  pooka }
    455