Hi!

Here is updated patch with the team == NULL case hopefully handled.
But the testcase I wrote (target-33.c) hangs, the problem is in the
  #pragma omp target nowait map (tofrom: a, b) depend(out: d[3])
  {
    #pragma omp atomic update
    a = a + 9;
    b -= 8;
  }
  #pragma omp target nowait map (tofrom: a, c) depend(out: d[4])
  {
    #pragma omp atomic update
    a = a + 4;
    c >>= 1;
  }
  #pragma omp task if (0) depend (in: d[3], d[4])
  if (a != 50 || b != 4 || c != 20)
    abort ();
part, where (I should change that for the case of no dependencies
eventually) the task with map_vars+async_run is queued in both cases,
then we reach GOMP_task, which calls gomp_task_maybe_wait_for_dependencies
which spawns the first half task (map_vars+async_run), and then
the second half task (map_vars+async_run), but that one gets stuck somewhere
in liboffloadmic, then some other thread (from liboffloadmic) calls
GOMP_PLUGIN_target_task_completion and enqueues the second half of the first
target task (unmap_vars), but as the only normal thread in the main program
is stuck in liboffloadmic (during gomp_map_vars, trying to allocate
target memory in the plugin), there is no thread to schedule the second half
of first target task.  So, if liboffloadmic is stuck waiting for unmap_vars,
it is a deadlock.  Can you please try to debug this?
I'll try tomorrow another testcase like target-33.c, but with
#pragma omp parallel 
#pragma omp single
around everything in main, both with OMP_NUM_THREADS=16 and 1, for 1 I would
expect it would be the same though.

--- liboffloadmic/runtime/offload_host.cpp.jj   2015-11-05 11:31:05.013916598 
+0100
+++ liboffloadmic/runtime/offload_host.cpp      2015-11-10 12:58:55.090951303 
+0100
@@ -64,6 +64,9 @@ static void __offload_fini_library(void)
 #define GET_OFFLOAD_NUMBER(timer_data) \
     timer_data? timer_data->offload_number : 0
 
+extern "C" void
+__gomp_offload_intelmic_async_completed (const void *);
+
 extern "C" {
 #ifdef TARGET_WINNT
 // Windows does not support imports from libraries without actually
@@ -2507,7 +2510,7 @@ extern "C" {
         const void *info
     )
     {
-       /* TODO: Call callback function, pass info.  */
+       __gomp_offload_intelmic_async_completed (info);
     }
 }
 
--- liboffloadmic/plugin/libgomp-plugin-intelmic.cpp.jj 2015-10-14 
10:24:10.922194230 +0200
+++ liboffloadmic/plugin/libgomp-plugin-intelmic.cpp    2015-11-11 
15:48:55.428967827 +0100
@@ -192,11 +192,23 @@ GOMP_OFFLOAD_get_num_devices (void)
 
 static void
 offload (const char *file, uint64_t line, int device, const char *name,
-        int num_vars, VarDesc *vars, VarDesc2 *vars2)
+        int num_vars, VarDesc *vars, VarDesc2 *vars2, const void **async_data)
 {
   OFFLOAD ofld = __offload_target_acquire1 (&device, file, line);
   if (ofld)
-    __offload_offload1 (ofld, name, 0, num_vars, vars, vars2, 0, NULL, NULL);
+    {
+      if (async_data == NULL)
+       __offload_offload1 (ofld, name, 0, num_vars, vars, vars2, 0, NULL,
+                           NULL);
+      else
+       {
+         OffloadFlags flags;
+         flags.flags = 0;
+         flags.bits.omp_async = 1;
+         __offload_offload3 (ofld, name, 0, num_vars, vars, NULL, 0, NULL,
+                             async_data, 0, NULL, flags, NULL);
+       }
+    }
   else
     {
       fprintf (stderr, "%s:%d: Offload target acquire failed\n", file, line);
@@ -218,7 +230,7 @@ GOMP_OFFLOAD_init_device (int device)
   TRACE ("");
   pthread_once (&main_image_is_registered, register_main_image);
   offload (__FILE__, __LINE__, device, "__offload_target_init_proc", 0,
-          NULL, NULL);
+          NULL, NULL, NULL);
 }
 
 extern "C" void
@@ -240,7 +252,7 @@ get_target_table (int device, int &num_f
   VarDesc2 vd1g[2] = { { "num_funcs", 0 }, { "num_vars", 0 } };
 
   offload (__FILE__, __LINE__, device, "__offload_target_table_p1", 2,
-          vd1, vd1g);
+          vd1, vd1g, NULL);
 
   int table_size = num_funcs + 2 * num_vars;
   if (table_size > 0)
@@ -254,7 +266,7 @@ get_target_table (int device, int &num_f
       VarDesc2 vd2g = { "table", 0 };
 
       offload (__FILE__, __LINE__, device, "__offload_target_table_p2", 1,
-              &vd2, &vd2g);
+              &vd2, &vd2g, NULL);
     }
 }
 
@@ -401,8 +413,8 @@ GOMP_OFFLOAD_alloc (int device, size_t s
   vd1[1].size = sizeof (void *);
   VarDesc2 vd1g[2] = { { "size", 0 }, { "tgt_ptr", 0 } };
 
-  offload (__FILE__, __LINE__, device, "__offload_target_alloc", 2, vd1, vd1g);
-
+  offload (__FILE__, __LINE__, device, "__offload_target_alloc", 2, vd1, vd1g,
+          NULL);
   return tgt_ptr;
 }
 
@@ -416,7 +428,8 @@ GOMP_OFFLOAD_free (int device, void *tgt
   vd1.size = sizeof (void *);
   VarDesc2 vd1g = { "tgt_ptr", 0 };
 
-  offload (__FILE__, __LINE__, device, "__offload_target_free", 1, &vd1, 
&vd1g);
+  offload (__FILE__, __LINE__, device, "__offload_target_free", 1, &vd1, &vd1g,
+          NULL);
 }
 
 extern "C" void *
@@ -435,7 +448,7 @@ GOMP_OFFLOAD_host2dev (int device, void
   VarDesc2 vd1g[2] = { { "tgt_ptr", 0 }, { "size", 0 } };
 
   offload (__FILE__, __LINE__, device, "__offload_target_host2tgt_p1", 2,
-          vd1, vd1g);
+          vd1, vd1g, NULL);
 
   VarDesc vd2 = vd_host2tgt;
   vd2.ptr = (void *) host_ptr;
@@ -443,7 +456,7 @@ GOMP_OFFLOAD_host2dev (int device, void
   VarDesc2 vd2g = { "var", 0 };
 
   offload (__FILE__, __LINE__, device, "__offload_target_host2tgt_p2", 1,
-          &vd2, &vd2g);
+          &vd2, &vd2g, NULL);
 
   return tgt_ptr;
 }
@@ -464,7 +477,7 @@ GOMP_OFFLOAD_dev2host (int device, void
   VarDesc2 vd1g[2] = { { "tgt_ptr", 0 }, { "size", 0 } };
 
   offload (__FILE__, __LINE__, device, "__offload_target_tgt2host_p1", 2,
-          vd1, vd1g);
+          vd1, vd1g, NULL);
 
   VarDesc vd2 = vd_tgt2host;
   vd2.ptr = (void *) host_ptr;
@@ -472,7 +485,7 @@ GOMP_OFFLOAD_dev2host (int device, void
   VarDesc2 vd2g = { "var", 0 };
 
   offload (__FILE__, __LINE__, device, "__offload_target_tgt2host_p2", 1,
-          &vd2, &vd2g);
+          &vd2, &vd2g, NULL);
 
   return host_ptr;
 }
@@ -495,22 +508,42 @@ GOMP_OFFLOAD_dev2dev (int device, void *
   VarDesc2 vd1g[3] = { { "dst_ptr", 0 }, { "src_ptr", 0 }, { "size", 0 } };
 
   offload (__FILE__, __LINE__, device, "__offload_target_tgt2tgt", 3, vd1,
-          vd1g);
+          vd1g, NULL);
 
   return dst_ptr;
 }
 
 extern "C" void
+GOMP_OFFLOAD_async_run (int device, void *tgt_fn, void *tgt_vars,
+                       void *async_data)
+{
+  TRACE ("(device = %d, tgt_fn = %p, tgt_vars = %p, async_data = %p)", device,
+        tgt_fn, tgt_vars, async_data);
+
+  VarDesc vd[2] = { vd_host2tgt, vd_host2tgt };
+  vd[0].ptr = &tgt_fn;
+  vd[0].size = sizeof (void *);
+  vd[1].ptr = &tgt_vars;
+  vd[1].size = sizeof (void *);
+
+  offload (__FILE__, __LINE__, device, "__offload_target_run", 2, vd, NULL,
+          (const void **) async_data);
+}
+
+extern "C" void
 GOMP_OFFLOAD_run (int device, void *tgt_fn, void *tgt_vars)
 {
-  TRACE ("(tgt_fn = %p, tgt_vars = %p)", tgt_fn, tgt_vars);
+  TRACE ("(device = %d, tgt_fn = %p, tgt_vars = %p)", device, tgt_fn, 
tgt_vars);
 
-  VarDesc vd1[2] = { vd_host2tgt, vd_host2tgt };
-  vd1[0].ptr = &tgt_fn;
-  vd1[0].size = sizeof (void *);
-  vd1[1].ptr = &tgt_vars;
-  vd1[1].size = sizeof (void *);
-  VarDesc2 vd1g[2] = { { "tgt_fn", 0 }, { "tgt_vars", 0 } };
+  GOMP_OFFLOAD_async_run (device, tgt_fn, tgt_vars, NULL);
+}
+
+/* Called by liboffloadmic when asynchronous function is completed.  */
+
+extern "C" void
+__gomp_offload_intelmic_async_completed (const void *async_data)
+{
+  TRACE ("(async_data = %p)", async_data);
 
-  offload (__FILE__, __LINE__, device, "__offload_target_run", 2, vd1, vd1g);
+  GOMP_PLUGIN_target_task_completion ((void *) async_data);
 }
--- libgomp/parallel.c.jj       2015-10-14 10:24:10.000000000 +0200
+++ libgomp/parallel.c  2015-11-12 15:12:38.349901541 +0100
@@ -85,7 +85,7 @@ gomp_resolve_num_threads (unsigned speci
      nested parallel, so there is just one thread in the
      contention group as well, no need to handle it atomically.  */
   pool = thr->thread_pool;
-  if (thr->ts.team == NULL)
+  if (thr->ts.team == NULL || pool == NULL)
     {
       num_threads = max_num_threads;
       if (num_threads > icv->thread_limit_var)
--- libgomp/libgomp-plugin.h.jj 2015-10-14 10:24:10.000000000 +0200
+++ libgomp/libgomp-plugin.h    2015-11-11 15:48:16.875505434 +0100
@@ -59,10 +59,20 @@ struct addr_pair
   uintptr_t end;
 };
 
+/* Various state of OpenMP async offloading tasks.  */
+enum gomp_target_task_state
+{
+  GOMP_TARGET_TASK_DATA,
+  GOMP_TARGET_TASK_BEFORE_MAP,
+  GOMP_TARGET_TASK_FALLBACK,
+  GOMP_TARGET_TASK_RUNNING
+};
+
 /* Miscellaneous functions.  */
 extern void *GOMP_PLUGIN_malloc (size_t) __attribute__ ((malloc));
 extern void *GOMP_PLUGIN_malloc_cleared (size_t) __attribute__ ((malloc));
 extern void *GOMP_PLUGIN_realloc (void *, size_t);
+void GOMP_PLUGIN_target_task_completion (void *);
 
 extern void GOMP_PLUGIN_debug (int, const char *, ...)
        __attribute__ ((format (printf, 2, 3)));
--- libgomp/testsuite/libgomp.c/target-32.c.jj  2015-11-10 12:58:55.087951346 
+0100
+++ libgomp/testsuite/libgomp.c/target-32.c     2015-11-12 13:28:55.053380366 
+0100
@@ -0,0 +1,54 @@
+#include <stdlib.h>
+#include <unistd.h>
+
+int main ()
+{
+  int a = 0, b = 0, c = 0, d[7];
+
+  #pragma omp parallel
+  #pragma omp single
+  {
+    #pragma omp task depend(out: d[0])
+      a = 2;
+
+    #pragma omp target enter data nowait map(to: a,b,c) depend(in: d[0]) 
depend(out: d[1])
+
+    #pragma omp target nowait map(alloc: a) depend(in: d[1]) depend(out: d[2])
+      a++;
+
+    #pragma omp target nowait map(alloc: b) depend(in: d[2]) depend(out: d[3])
+    {
+      usleep (1000);
+      #pragma omp atomic update
+      b |= 4;
+    }
+
+    #pragma omp target nowait map(alloc: b) depend(in: d[2]) depend(out: d[4])
+    {
+      usleep (5000);
+      #pragma omp atomic update
+      b |= 1;
+    }
+
+    #pragma omp target nowait map(alloc: c) depend(in: d[3], d[4]) depend(out: 
d[5])
+    {
+      usleep (5000);
+      #pragma omp atomic update
+      c |= 8;
+    }
+
+    #pragma omp target nowait map(alloc: c) depend(in: d[3], d[4]) depend(out: 
d[6])
+    {
+      usleep (1000);
+      #pragma omp atomic update
+      c |= 2;
+    }
+
+    #pragma omp target exit data map(always,from: a,b,c) depend(in: d[5], d[6])
+  }
+
+  if (a != 3 || b != 5 || c != 10)
+    abort ();
+
+  return 0;
+}
--- libgomp/testsuite/libgomp.c/target-33.c.jj  2015-11-12 16:20:23.332860573 
+0100
+++ libgomp/testsuite/libgomp.c/target-33.c     2015-11-12 16:20:14.000000000 
+0100
@@ -0,0 +1,93 @@
+extern void abort (void);
+
+int
+main ()
+{
+  int a = 1, b = 2, c = 4, d[7];
+  #pragma omp taskgroup
+  {
+    #pragma omp target enter data nowait map (to: a, b, c) depend(out: d[0])
+    #pragma omp target nowait map (alloc: a, b) depend(in: d[0]) depend(out: 
d[1])
+    {
+      #pragma omp atomic update
+      a |= 4;
+      #pragma omp atomic update
+      b |= 8;
+    }
+    #pragma omp target nowait map (alloc: a, c) depend(in: d[0]) depend(out: 
d[2])
+    {
+      #pragma omp atomic update
+      a |= 16;
+      #pragma omp atomic update
+      c |= 32;
+    }
+    #pragma omp target exit data nowait map (from: a, b, c) depend(in: d[1], 
d[2])
+  }
+  if (a != 21 || b != 10 || c != 36)
+    abort ();
+  #pragma omp target map (tofrom: a, b) nowait
+  {
+    a &= ~16;
+    b &= ~2;
+  }
+  #pragma omp target map (tofrom: c) nowait
+  {
+    c |= 8;
+  }
+  #pragma omp barrier
+  if (a != 5 || b != 8 || c != 44)
+    abort ();
+  #pragma omp target map (tofrom: a, b) nowait
+  {
+    a |= 32;
+    b |= 4;
+  }
+  #pragma omp target map (tofrom: c) nowait
+  {
+    c &= ~4;
+  }
+  #pragma omp taskwait
+  if (a != 37 || b != 12 || c != 40)
+    abort ();
+  #pragma omp target nowait map (tofrom: a, b) depend(out: d[3])
+  {
+    #pragma omp atomic update
+    a = a + 9;
+    b -= 8;
+  }
+  #pragma omp target nowait map (tofrom: a, c) depend(out: d[4])
+  {
+    #pragma omp atomic update
+    a = a + 4;
+    c >>= 1;
+  }
+  #pragma omp task if (0) depend (in: d[3], d[4])
+  if (a != 50 || b != 4 || c != 20)
+    abort ();
+  #pragma omp task
+  a += 50;
+  #pragma omp target nowait map (tofrom: b)
+  b++;
+  #pragma omp target map (tofrom: c) nowait
+  c--;
+  #pragma omp taskwait
+  if (a != 100 || b != 5 || c != 19)
+    abort ();
+  #pragma omp target map (tofrom: a) nowait depend(out: d[5])
+  a++;
+  #pragma omp target map (tofrom: b) nowait depend(out: d[6])
+  b++;
+  #pragma omp target map (tofrom: a, b) depend(in: d[5], d[6])
+  {
+    if (a != 101 || b != 6)
+      a = -9;
+    else
+      {
+       a = 24;
+       b = 38;
+      }
+  }
+  if (a != 24 || b != 38)
+    abort ();
+  return 0;
+}
--- libgomp/team.c.jj   2015-11-09 11:14:37.000000000 +0100
+++ libgomp/team.c      2015-11-12 15:09:23.584644449 +0100
@@ -272,6 +272,8 @@ gomp_free_thread (void *arg __attribute_
       free (pool);
       thr->thread_pool = NULL;
     }
+  if (thr->ts.level == 0 && __builtin_expect (thr->ts.team != NULL, 0))
+    gomp_team_end ();
   if (thr->task != NULL)
     {
       struct gomp_task *task = thr->task;
@@ -301,7 +303,7 @@ gomp_team_start (void (*fn) (void *), vo
   struct gomp_thread **affinity_thr = NULL;
 
   thr = gomp_thread ();
-  nested = thr->ts.team != NULL;
+  nested = thr->ts.level;
   pool = thr->thread_pool;
   task = thr->task;
   icv = task ? &task->icv : &gomp_global_icv;
--- libgomp/target.c.jj 2015-11-09 11:14:37.325239961 +0100
+++ libgomp/target.c    2015-11-12 14:33:56.607481598 +0100
@@ -1348,17 +1348,7 @@ GOMP_target (int device, void (*fn) (voi
   struct target_mem_desc *tgt_vars
     = gomp_map_vars (devicep, mapnum, hostaddrs, NULL, sizes, kinds, false,
                     GOMP_MAP_VARS_TARGET);
-  struct gomp_thread old_thr, *thr = gomp_thread ();
-  old_thr = *thr;
-  memset (thr, '\0', sizeof (*thr));
-  if (gomp_places_list)
-    {
-      thr->place = old_thr.place;
-      thr->ts.place_partition_len = gomp_places_list_len;
-    }
   devicep->run_func (devicep->target_id, fn_addr, (void *) 
tgt_vars->tgt_start);
-  gomp_free_thread (thr);
-  *thr = old_thr;
   gomp_unmap_vars (tgt_vars, true);
 }
 
@@ -1387,10 +1377,52 @@ GOMP_target_ext (int device, void (*fn)
   (void) num_teams;
   (void) thread_limit;
 
-  /* If there are depend clauses, but nowait is not present,
-     block the parent task until the dependencies are resolved
-     and then just continue with the rest of the function as if it
-     is a merged task.  */
+  if (flags & GOMP_TARGET_FLAG_NOWAIT)
+    {
+      struct gomp_thread *thr = gomp_thread ();
+      /* Create a team if we don't have any around, as nowait
+        target tasks make sense to run asynchronously even when
+        outside of any parallel.  */
+      if (__builtin_expect (thr->ts.team == NULL, 0))
+       {
+         struct gomp_team *team = gomp_new_team (1);
+         struct gomp_task *task = thr->task;
+         struct gomp_task_icv *icv = task ? &task->icv : &gomp_global_icv;
+         team->prev_ts = thr->ts;
+         thr->ts.team = team;
+         thr->ts.team_id = 0;
+         thr->ts.work_share = &team->work_shares[0];
+         thr->ts.last_work_share = NULL;
+#ifdef HAVE_SYNC_BUILTINS
+         thr->ts.single_count = 0;
+#endif
+         thr->ts.static_trip = 0;
+         thr->task = &team->implicit_task[0];
+         gomp_init_task (thr->task, NULL, icv);
+         if (task)
+           {
+             thr->task = task;
+             gomp_end_task ();
+             free (task);
+             thr->task = &team->implicit_task[0];
+           }
+         else
+           pthread_setspecific (gomp_thread_destructor, thr);
+       }
+      if (thr->ts.team
+         && !thr->task->final_task)
+       {
+         gomp_create_target_task (devicep, fn, mapnum, hostaddrs,
+                                  sizes, kinds, flags, depend,
+                                  GOMP_TARGET_TASK_BEFORE_MAP);
+         return;
+       }
+    }
+
+  /* If there are depend clauses, but nowait is not present
+     (or we are in a final task), block the parent task until the
+     dependencies are resolved and then just continue with the rest
+     of the function as if it is a merged task.  */
   if (depend != NULL)
     {
       struct gomp_thread *thr = gomp_thread ();
@@ -1410,17 +1442,7 @@ GOMP_target_ext (int device, void (*fn)
   struct target_mem_desc *tgt_vars
     = gomp_map_vars (devicep, mapnum, hostaddrs, NULL, sizes, kinds, true,
                     GOMP_MAP_VARS_TARGET);
-  struct gomp_thread old_thr, *thr = gomp_thread ();
-  old_thr = *thr;
-  memset (thr, '\0', sizeof (*thr));
-  if (gomp_places_list)
-    {
-      thr->place = old_thr.place;
-      thr->ts.place_partition_len = gomp_places_list_len;
-    }
   devicep->run_func (devicep->target_id, fn_addr, (void *) 
tgt_vars->tgt_start);
-  gomp_free_thread (thr);
-  *thr = old_thr;
   gomp_unmap_vars (tgt_vars, true);
 }
 
@@ -1527,23 +1549,25 @@ GOMP_target_update_ext (int device, size
              && thr->ts.team
              && !thr->task->final_task)
            {
-             gomp_create_target_task (devicep, (void (*) (void *)) NULL,
-                                      mapnum, hostaddrs, sizes, kinds,
-                                      flags | GOMP_TARGET_FLAG_UPDATE,
-                                      depend);
-             return;
+             if (gomp_create_target_task (devicep, (void (*) (void *)) NULL,
+                                          mapnum, hostaddrs, sizes, kinds,
+                                          flags | GOMP_TARGET_FLAG_UPDATE,
+                                          depend, GOMP_TARGET_TASK_DATA))
+               return;
            }
+         else
+           {
+             struct gomp_team *team = thr->ts.team;
+             /* If parallel or taskgroup has been cancelled, don't start new
+                tasks.  */
+             if (team
+                 && (gomp_team_barrier_cancelled (&team->barrier)
+                     || (thr->task->taskgroup
+                         && thr->task->taskgroup->cancelled)))
+               return;
 
-         struct gomp_team *team = thr->ts.team;
-         /* If parallel or taskgroup has been cancelled, don't start new
-            tasks.  */
-         if (team
-             && (gomp_team_barrier_cancelled (&team->barrier)
-                 || (thr->task->taskgroup
-                     && thr->task->taskgroup->cancelled)))
-           return;
-
-         gomp_task_maybe_wait_for_dependencies (depend);
+             gomp_task_maybe_wait_for_dependencies (depend);
+           }
        }
     }
 
@@ -1647,22 +1671,25 @@ GOMP_target_enter_exit_data (int device,
              && thr->ts.team
              && !thr->task->final_task)
            {
-             gomp_create_target_task (devicep, (void (*) (void *)) NULL,
-                                      mapnum, hostaddrs, sizes, kinds,
-                                      flags, depend);
-             return;
+             if (gomp_create_target_task (devicep, (void (*) (void *)) NULL,
+                                          mapnum, hostaddrs, sizes, kinds,
+                                          flags, depend,
+                                          GOMP_TARGET_TASK_DATA))
+               return;
            }
+         else
+           {
+             struct gomp_team *team = thr->ts.team;
+             /* If parallel or taskgroup has been cancelled, don't start new
+                tasks.  */
+             if (team
+                 && (gomp_team_barrier_cancelled (&team->barrier)
+                     || (thr->task->taskgroup
+                         && thr->task->taskgroup->cancelled)))
+               return;
 
-         struct gomp_team *team = thr->ts.team;
-         /* If parallel or taskgroup has been cancelled, don't start new
-            tasks.  */
-         if (team
-             && (gomp_team_barrier_cancelled (&team->barrier)
-                 || (thr->task->taskgroup
-                     && thr->task->taskgroup->cancelled)))
-           return;
-
-         gomp_task_maybe_wait_for_dependencies (depend);
+             gomp_task_maybe_wait_for_dependencies (depend);
+           }
        }
     }
 
@@ -1694,38 +1721,65 @@ GOMP_target_enter_exit_data (int device,
     gomp_exit_data (devicep, mapnum, hostaddrs, sizes, kinds);
 }
 
-void
+bool
 gomp_target_task_fn (void *data)
 {
   struct gomp_target_task *ttask = (struct gomp_target_task *) data;
+  struct gomp_device_descr *devicep = ttask->devicep;
+
   if (ttask->fn != NULL)
     {
-      /* GOMP_target_ext */
-    }
-  else if (ttask->devicep == NULL
-          || !(ttask->devicep->capabilities & GOMP_OFFLOAD_CAP_OPENMP_400))
-    return;
+      if (devicep == NULL
+         || !(devicep->capabilities & GOMP_OFFLOAD_CAP_OPENMP_400))
+       {
+         ttask->state = GOMP_TARGET_TASK_FALLBACK;
+         gomp_target_fallback_firstprivate (ttask->fn, ttask->mapnum,
+                                            ttask->hostaddrs, ttask->sizes,
+                                            ttask->kinds);
+         return false;
+       }
+
+      if (ttask->state == GOMP_TARGET_TASK_RUNNING)
+       {
+         gomp_unmap_vars (ttask->tgt, true);
+         return false;
+       }
+
+      void *fn_addr = gomp_get_target_fn_addr (devicep, ttask->fn);
+      ttask->tgt
+       = gomp_map_vars (devicep, ttask->mapnum, ttask->hostaddrs, NULL,
+                        ttask->sizes, ttask->kinds, true,
+                        GOMP_MAP_VARS_TARGET);
+      ttask->state = GOMP_TARGET_TASK_RUNNING;
+
+      devicep->async_run_func (devicep->target_id, fn_addr,
+                              (void *) ttask->tgt->tgt_start, (void *) ttask);
+      return true;
+    }
+  else if (devicep == NULL
+          || !(devicep->capabilities & GOMP_OFFLOAD_CAP_OPENMP_400))
+    return false;
 
   size_t i;
   if (ttask->flags & GOMP_TARGET_FLAG_UPDATE)
-    gomp_update (ttask->devicep, ttask->mapnum, ttask->hostaddrs, ttask->sizes,
+    gomp_update (devicep, ttask->mapnum, ttask->hostaddrs, ttask->sizes,
                 ttask->kinds, true);
   else if ((ttask->flags & GOMP_TARGET_FLAG_EXIT_DATA) == 0)
     for (i = 0; i < ttask->mapnum; i++)
       if ((ttask->kinds[i] & 0xff) == GOMP_MAP_STRUCT)
        {
-         gomp_map_vars (ttask->devicep, ttask->sizes[i] + 1,
-                        &ttask->hostaddrs[i], NULL, &ttask->sizes[i],
-                        &ttask->kinds[i], true, GOMP_MAP_VARS_ENTER_DATA);
+         gomp_map_vars (devicep, ttask->sizes[i] + 1, &ttask->hostaddrs[i],
+                        NULL, &ttask->sizes[i], &ttask->kinds[i], true,
+                        GOMP_MAP_VARS_ENTER_DATA);
          i += ttask->sizes[i];
        }
       else
-       gomp_map_vars (ttask->devicep, 1, &ttask->hostaddrs[i], NULL,
-                      &ttask->sizes[i], &ttask->kinds[i],
-                      true, GOMP_MAP_VARS_ENTER_DATA);
+       gomp_map_vars (devicep, 1, &ttask->hostaddrs[i], NULL, &ttask->sizes[i],
+                      &ttask->kinds[i], true, GOMP_MAP_VARS_ENTER_DATA);
   else
-    gomp_exit_data (ttask->devicep, ttask->mapnum, ttask->hostaddrs,
-                   ttask->sizes, ttask->kinds);
+    gomp_exit_data (devicep, ttask->mapnum, ttask->hostaddrs, ttask->sizes,
+                   ttask->kinds);
+  return false;
 }
 
 void
@@ -2170,6 +2224,7 @@ gomp_load_plugin_for_device (struct gomp
   if (device->capabilities & GOMP_OFFLOAD_CAP_OPENMP_400)
     {
       DLSYM (run);
+      DLSYM (async_run);
       DLSYM (dev2dev);
     }
   if (device->capabilities & GOMP_OFFLOAD_CAP_OPENACC_200)
--- libgomp/libgomp.map.jj      2015-10-26 15:38:20.000000000 +0100
+++ libgomp/libgomp.map 2015-11-11 16:15:23.807818735 +0100
@@ -406,3 +406,8 @@ GOMP_PLUGIN_1.0 {
        GOMP_PLUGIN_async_unmap_vars;
        GOMP_PLUGIN_acc_thread;
 };
+
+GOMP_PLUGIN_1.1 {
+  global:
+       GOMP_PLUGIN_target_task_completion;
+} GOMP_PLUGIN_1.0;
--- libgomp/task.c.jj   2015-11-09 11:14:37.332239862 +0100
+++ libgomp/task.c      2015-11-12 16:24:19.127548800 +0100
@@ -482,11 +482,12 @@ ialias (GOMP_taskgroup_end)
 
 /* Called for nowait target tasks.  */
 
-void
+bool
 gomp_create_target_task (struct gomp_device_descr *devicep,
                         void (*fn) (void *), size_t mapnum, void **hostaddrs,
                         size_t *sizes, unsigned short *kinds,
-                        unsigned int flags, void **depend)
+                        unsigned int flags, void **depend,
+                        enum gomp_target_task_state state)
 {
   struct gomp_thread *thr = gomp_thread ();
   struct gomp_team *team = thr->ts.team;
@@ -495,7 +496,7 @@ gomp_create_target_task (struct gomp_dev
   if (team
       && (gomp_team_barrier_cancelled (&team->barrier)
          || (thr->task->taskgroup && thr->task->taskgroup->cancelled)))
-    return;
+    return true;
 
   struct gomp_target_task *ttask;
   struct gomp_task *task;
@@ -503,19 +504,44 @@ gomp_create_target_task (struct gomp_dev
   struct gomp_taskgroup *taskgroup = parent->taskgroup;
   bool do_wake;
   size_t depend_size = 0;
+  uintptr_t depend_cnt = 0;
+  size_t tgt_align = 0, tgt_size = 0;
 
   if (depend != NULL)
-    depend_size = ((uintptr_t) depend[0]
-                  * sizeof (struct gomp_task_depend_entry));
+    {
+      depend_cnt = (uintptr_t) depend[0];
+      depend_size = depend_cnt * sizeof (struct gomp_task_depend_entry);
+    }
+  if (fn)
+    {
+      /* GOMP_MAP_FIRSTPRIVATE need to be copied first, as they are
+        firstprivate on the target task.  */
+      size_t i;
+      for (i = 0; i < mapnum; i++)
+       if ((kinds[i] & 0xff) == GOMP_MAP_FIRSTPRIVATE)
+         {
+           size_t align = (size_t) 1 << (kinds[i] >> 8);
+           if (tgt_align < align)
+             tgt_align = align;
+           tgt_size = (tgt_size + align - 1) & ~(align - 1);
+           tgt_size += sizes[i];
+         }
+      if (tgt_align)
+       tgt_size += tgt_align - 1;
+      else
+       tgt_size = 0;
+    }
+
   task = gomp_malloc (sizeof (*task) + depend_size
                      + sizeof (*ttask)
                      + mapnum * (sizeof (void *) + sizeof (size_t)
-                                 + sizeof (unsigned short)));
+                                 + sizeof (unsigned short))
+                     + tgt_size);
   gomp_init_task (task, parent, gomp_icv (false));
   task->kind = GOMP_TASK_WAITING;
   task->in_tied_task = parent->in_tied_task;
   task->taskgroup = taskgroup;
-  ttask = (struct gomp_target_task *) &task->depend[(uintptr_t) depend[0]];
+  ttask = (struct gomp_target_task *) &task->depend[depend_cnt];
   ttask->devicep = devicep;
   ttask->fn = fn;
   ttask->mapnum = mapnum;
@@ -524,8 +550,29 @@ gomp_create_target_task (struct gomp_dev
   memcpy (ttask->sizes, sizes, mapnum * sizeof (size_t));
   ttask->kinds = (unsigned short *) &ttask->sizes[mapnum];
   memcpy (ttask->kinds, kinds, mapnum * sizeof (unsigned short));
+  if (tgt_align)
+    {
+      char *tgt = (char *) &ttask->kinds[mapnum];
+      size_t i;
+      uintptr_t al = (uintptr_t) tgt & (tgt_align - 1);
+      if (al)
+       tgt += tgt_align - al;
+      tgt_size = 0;
+      for (i = 0; i < mapnum; i++)
+       if ((kinds[i] & 0xff) == GOMP_MAP_FIRSTPRIVATE)
+         {
+           size_t align = (size_t) 1 << (kinds[i] >> 8);
+           tgt_size = (tgt_size + align - 1) & ~(align - 1);
+           memcpy (tgt + tgt_size, hostaddrs[i], sizes[i]); 
+           ttask->hostaddrs[i] = tgt + tgt_size;
+           tgt_size = tgt_size + sizes[i];
+         }
+    }
   ttask->flags = flags;
-  task->fn = gomp_target_task_fn;
+  ttask->state = state;
+  ttask->task = task;
+  ttask->team = team;
+  task->fn = NULL;
   task->fn_data = ttask;
   task->final_task = 0;
   gomp_mutex_lock (&team->task_lock);
@@ -536,19 +583,26 @@ gomp_create_target_task (struct gomp_dev
       gomp_mutex_unlock (&team->task_lock);
       gomp_finish_task (task);
       free (task);
-      return;
+      return true;
     }
-  if (taskgroup)
-    taskgroup->num_children++;
   if (depend_size)
     {
       gomp_task_handle_depend (task, parent, depend);
       if (task->num_dependees)
        {
          gomp_mutex_unlock (&team->task_lock);
-         return;
+         return true;
        }
     }
+  if (state == GOMP_TARGET_TASK_DATA)
+    {
+      gomp_mutex_unlock (&team->task_lock);
+      gomp_finish_task (task);
+      free (task);
+      return false;
+    }
+  if (taskgroup)
+    taskgroup->num_children++;
   priority_queue_insert (PQ_CHILDREN, &parent->children_queue, task, 0,
                         PRIORITY_INSERT_BEGIN,
                         /*adjust_parent_depends_on=*/false,
@@ -570,6 +624,95 @@ gomp_create_target_task (struct gomp_dev
   gomp_mutex_unlock (&team->task_lock);
   if (do_wake)
     gomp_team_barrier_wake (&team->barrier, 1);
+  return true;
+}
+
+static void inline
+priority_queue_move_task_first (enum priority_queue_type type,
+                               struct priority_queue *head,
+                               struct gomp_task *task)
+{
+#if _LIBGOMP_CHECKING_
+  if (!priority_queue_task_in_queue_p (type, head, task))
+    gomp_fatal ("Attempt to move first missing task %p", task);
+#endif
+  struct priority_list *list;
+  if (priority_queue_multi_p (head))
+    {
+      list = priority_queue_lookup_priority (head, task->priority);
+#if _LIBGOMP_CHECKING_
+      if (!list)
+       gomp_fatal ("Unable to find priority %d", task->priority);
+#endif
+    }
+  else
+    list = &head->l;
+  priority_list_remove (list, task_to_priority_node (type, task), 0);
+  priority_list_insert (type, list, task, task->priority,
+                       PRIORITY_INSERT_BEGIN, type == PQ_CHILDREN,
+                       task->parent_depends_on);
+}
+
+/* Signal that a target task TTASK has completed the asynchronously
+   running phase and should be requeued as a task to handle the
+   variable unmapping.  */
+
+void
+GOMP_PLUGIN_target_task_completion (void *data)
+{
+  struct gomp_target_task *ttask = (struct gomp_target_task *) data;
+  struct gomp_task *task = ttask->task;
+  struct gomp_team *team = ttask->team;
+
+  gomp_mutex_lock (&team->task_lock);
+  struct gomp_task *parent = task->parent;
+  if (parent)
+    priority_queue_move_task_first (PQ_CHILDREN, &parent->children_queue,
+                                   task);
+
+  struct gomp_taskgroup *taskgroup = task->taskgroup;
+  if (taskgroup)
+    priority_queue_move_task_first (PQ_TASKGROUP, &taskgroup->taskgroup_queue,
+                                   task);
+
+  priority_queue_insert (PQ_TEAM, &team->task_queue, task, task->priority,
+                        PRIORITY_INSERT_BEGIN, false,
+                        task->parent_depends_on);
+  task->kind = GOMP_TASK_WAITING;
+  if (parent && parent->taskwait)
+    {
+      if (parent->taskwait->in_taskwait)
+       {
+         /* One more task has had its dependencies met.
+            Inform any waiters.  */
+         parent->taskwait->in_taskwait = false;
+         gomp_sem_post (&parent->taskwait->taskwait_sem);
+       }
+      else if (parent->taskwait->in_depend_wait)
+       {
+         /* One more task has had its dependencies met.
+            Inform any waiters.  */
+         parent->taskwait->in_depend_wait = false;
+         gomp_sem_post (&parent->taskwait->taskwait_sem);
+       }
+    }
+  if (taskgroup && taskgroup->in_taskgroup_wait)
+    {
+      /* One more task has had its dependencies met.
+        Inform any waiters.  */
+      taskgroup->in_taskgroup_wait = false;
+      gomp_sem_post (&taskgroup->taskgroup_sem);
+    }
+
+  ++team->task_queued_count;
+  gomp_team_barrier_set_task_pending (&team->barrier);
+  /* I'm afraid this can't be done after releasing team->task_lock,
+     as gomp_target_task_completion is run from unrelated thread and
+     therefore in between gomp_mutex_unlock and gomp_team_barrier_wake
+     the team could be gone already.  */
+  if (team->nthreads > team->task_running_count)
+    gomp_team_barrier_wake (&team->barrier, 1);
+  gomp_mutex_unlock (&team->task_lock);
 }
 
 /* Given a parent_depends_on task in LIST, move it to the front of its
@@ -1041,7 +1184,20 @@ gomp_barrier_handle_tasks (gomp_barrier_
       if (child_task)
        {
          thr->task = child_task;
-         child_task->fn (child_task->fn_data);
+         if (__builtin_expect (child_task->fn == NULL, 0))
+           {
+             if (gomp_target_task_fn (child_task->fn_data))
+               {
+                 thr->task = task;
+                 gomp_mutex_lock (&team->task_lock);
+                 child_task->kind = GOMP_TASK_ASYNC_RUNNING;
+                 team->task_running_count--;
+                 child_task = NULL;
+                 continue;
+               }
+           }
+         else
+           child_task->fn (child_task->fn_data);
          thr->task = task;
        }
       else
@@ -1170,7 +1326,19 @@ GOMP_taskwait (void)
       if (child_task)
        {
          thr->task = child_task;
-         child_task->fn (child_task->fn_data);
+         if (__builtin_expect (child_task->fn == NULL, 0))
+           {
+             if (gomp_target_task_fn (child_task->fn_data))
+               {
+                 thr->task = task;
+                 gomp_mutex_lock (&team->task_lock);
+                 child_task->kind = GOMP_TASK_ASYNC_RUNNING;
+                 child_task = NULL;
+                 continue;
+               }
+           }
+         else
+           child_task->fn (child_task->fn_data);
          thr->task = task;
        }
       else
@@ -1342,7 +1510,19 @@ gomp_task_maybe_wait_for_dependencies (v
       if (child_task)
        {
          thr->task = child_task;
-         child_task->fn (child_task->fn_data);
+         if (__builtin_expect (child_task->fn == NULL, 0))
+           {
+             if (gomp_target_task_fn (child_task->fn_data))
+               {
+                 thr->task = task;
+                 gomp_mutex_lock (&team->task_lock);
+                 child_task->kind = GOMP_TASK_ASYNC_RUNNING;
+                 child_task = NULL;
+                 continue;
+               }
+           }
+         else
+           child_task->fn (child_task->fn_data);
          thr->task = task;
        }
       else
@@ -1423,6 +1603,17 @@ GOMP_taskgroup_end (void)
   if (team == NULL)
     return;
   taskgroup = task->taskgroup;
+  if (__builtin_expect (taskgroup == NULL, 0)
+      && thr->ts.level == 0)
+    {
+      /* This can happen if GOMP_taskgroup_start is called when
+        thr->ts.team == NULL, but inside of the taskgroup there
+        is #pragma omp target nowait that creates an implicit
+        team with a single thread.  In this case, we want to wait
+        for all outstanding tasks in this team.  */
+      gomp_team_barrier_wait (&team->barrier);
+      return;
+    }
 
   /* The acquire barrier on load of taskgroup->num_children here
      synchronizes with the write of 0 in gomp_task_run_post_remove_taskgroup.
@@ -1450,8 +1641,8 @@ GOMP_taskgroup_end (void)
                = priority_queue_next_task (PQ_CHILDREN, &task->children_queue,
                                            PQ_TEAM, &team->task_queue,
                                            &unused);
-            }
-          else
+           }
+         else
            {
              gomp_mutex_unlock (&team->task_lock);
              if (to_free)
@@ -1506,7 +1697,19 @@ GOMP_taskgroup_end (void)
       if (child_task)
        {
          thr->task = child_task;
-         child_task->fn (child_task->fn_data);
+         if (__builtin_expect (child_task->fn == NULL, 0))
+           {
+             if (gomp_target_task_fn (child_task->fn_data))
+               {
+                 thr->task = task;
+                 gomp_mutex_lock (&team->task_lock);
+                 child_task->kind = GOMP_TASK_ASYNC_RUNNING;
+                 child_task = NULL;
+                 continue;
+               }
+           }
+         else
+           child_task->fn (child_task->fn_data);
          thr->task = task;
        }
       else
--- libgomp/priority_queue.c.jj 2015-11-09 11:15:33.000000000 +0100
+++ libgomp/priority_queue.c    2015-11-10 17:52:33.769414428 +0100
@@ -85,7 +85,7 @@ priority_queue_task_in_queue_p (enum pri
    order.  LIST is a priority list of type TYPE.
 
    The expected order is that GOMP_TASK_WAITING tasks come before
-   GOMP_TASK_TIED ones.
+   GOMP_TASK_TIED/GOMP_TASK_ASYNC_RUNNING ones.
 
    If CHECK_DEPS is TRUE, we also check that parent_depends_on WAITING
    tasks come before !parent_depends_on WAITING tasks.  This is only
@@ -104,7 +104,7 @@ priority_list_verify (enum priority_queu
       struct gomp_task *t = priority_node_to_task (type, p);
       if (seen_tied && t->kind == GOMP_TASK_WAITING)
        gomp_fatal ("priority_queue_verify: WAITING task after TIED");
-      if (t->kind == GOMP_TASK_TIED)
+      if (t->kind >= GOMP_TASK_TIED)
        seen_tied = true;
       else if (check_deps && t->kind == GOMP_TASK_WAITING)
        {
--- libgomp/libgomp.h.jj        2015-11-09 11:14:37.326239947 +0100
+++ libgomp/libgomp.h   2015-11-11 10:46:40.143794155 +0100
@@ -373,7 +373,12 @@ enum gomp_task_kind
   /* Task created by GOMP_task and waiting to be run.  */
   GOMP_TASK_WAITING,
   /* Task currently executing or scheduled and about to execute.  */
-  GOMP_TASK_TIED
+  GOMP_TASK_TIED,
+  /* Used for target tasks that have vars mapped and async run started,
+     but not yet completed.  Once that completes, they will be readded
+     into the queues as GOMP_TASK_WAITING in order to perform the var
+     unmapping.  */
+  GOMP_TASK_ASYNC_RUNNING
 };
 
 struct gomp_task_depend_entry
@@ -453,6 +458,8 @@ struct gomp_task
   struct gomp_task_depend_entry depend[];
 };
 
+/* This structure describes a single #pragma omp taskgroup.  */
+
 struct gomp_taskgroup
 {
   struct gomp_taskgroup *prev;
@@ -464,6 +471,8 @@ struct gomp_taskgroup
   size_t num_children;
 };
 
+/* This structure describes a target task.  */
+
 struct gomp_target_task
 {
   struct gomp_device_descr *devicep;
@@ -472,6 +481,10 @@ struct gomp_target_task
   size_t *sizes;
   unsigned short *kinds;
   unsigned int flags;
+  enum gomp_target_task_state state;
+  struct target_mem_desc *tgt;
+  struct gomp_task *task;
+  struct gomp_team *team;
   void *hostaddrs[];
 };
 
@@ -723,10 +736,10 @@ extern void gomp_init_task (struct gomp_
 extern void gomp_end_task (void);
 extern void gomp_barrier_handle_tasks (gomp_barrier_state_t);
 extern void gomp_task_maybe_wait_for_dependencies (void **);
-extern void gomp_create_target_task (struct gomp_device_descr *,
+extern bool gomp_create_target_task (struct gomp_device_descr *,
                                     void (*) (void *), size_t, void **,
                                     size_t *, unsigned short *, unsigned int,
-                                    void **);
+                                    void **, enum gomp_target_task_state);
 
 static void inline
 gomp_finish_task (struct gomp_task *task)
@@ -747,7 +760,7 @@ extern void gomp_free_thread (void *);
 
 extern void gomp_init_targets_once (void);
 extern int gomp_get_num_devices (void);
-extern void gomp_target_task_fn (void *);
+extern bool gomp_target_task_fn (void *);
 
 /* Splay tree definitions.  */
 typedef struct splay_tree_node_s *splay_tree_node;
@@ -901,6 +914,7 @@ struct gomp_device_descr
   void *(*host2dev_func) (int, void *, const void *, size_t);
   void *(*dev2dev_func) (int, void *, const void *, size_t);
   void (*run_func) (int, void *, void *);
+  void (*async_run_func) (int, void *, void *, void *);
 
   /* Splay tree containing information about mapped memory regions.  */
   struct splay_tree_s mem_map;


        Jakub

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