Index: libomptarget/deviceRTLs/nvptx/src/data_sharing.cu
===================================================================
--- libomptarget/deviceRTLs/nvptx/src/data_sharing.cu
+++ libomptarget/deviceRTLs/nvptx/src/data_sharing.cu
@@ -378,6 +378,12 @@
 // as long as the size requested fits the pre-allocated size.
 EXTERN void* __kmpc_data_sharing_push_stack(size_t DataSize,
     int16_t UseSharedMemory) {
+  if (isRuntimeUninitialized()) {
+    ASSERT0(LT_FUSSY, isSPMDMode(),
+            "Expected SPMD mode with uninitialized runtime.");
+    return omptarget_nvptx_simpleThreadPrivateContext->Allocate(DataSize);
+  }
+
   // Frame pointer must be visible to all workers in the same warp.
   unsigned WID = getWarpId();
   void *&FrameP = DataSharingState.FramePtr[WID];
@@ -456,6 +462,12 @@
 // reclaim all outstanding global memory slots since it is
 // likely we have reached the end of the kernel.
 EXTERN void __kmpc_data_sharing_pop_stack(void *FrameStart) {
+  if (isRuntimeUninitialized()) {
+    ASSERT0(LT_FUSSY, isSPMDMode(),
+            "Expected SPMD mode with uninitialized runtime.");
+    return omptarget_nvptx_simpleThreadPrivateContext->Deallocate(FrameStart);
+  }
+
   if (IsWarpMasterActiveThread()) {
     unsigned WID = getWarpId();
 
Index: libomptarget/deviceRTLs/nvptx/src/omptarget-nvptx.h
===================================================================
--- libomptarget/deviceRTLs/nvptx/src/omptarget-nvptx.h
+++ libomptarget/deviceRTLs/nvptx/src/omptarget-nvptx.h
@@ -113,6 +113,10 @@
   DS_Worker_Warp_Slot_Size = WARPSIZE * DS_Slot_Size,
   // The maximum number of warps in use
   DS_Max_Warp_Number = 32,
+  // The size of the preallocated shared memory buffer per team
+  DS_Shared_Memory_Size = 128,
+  // The size of the preallocated global memory buffer per team
+  DS_Global_Memory_Size = 4096,
 };
 
 // Data structure to keep in shared memory that traces the current slot, stack,
@@ -386,12 +390,15 @@
 
 class omptarget_nvptx_SimpleThreadPrivateContext {
   uint16_t par_level[MAX_THREADS_PER_TEAM];
+  char global_buffer[DS_Global_Memory_Size];
 public:
   INLINE void Init() {
     ASSERT0(LT_FUSSY, isSPMDMode() && isRuntimeUninitialized(),
             "Expected SPMD + uninitialized runtime modes.");
     par_level[GetThreadIdInBlock()] = 0;
   }
+  INLINE void *Allocate(size_t DataSize);
+  INLINE void Deallocate(void *Ptr);
   INLINE void IncParLevel() {
     ASSERT0(LT_FUSSY, isSPMDMode() && isRuntimeUninitialized(),
             "Expected SPMD + uninitialized runtime modes.");
Index: libomptarget/deviceRTLs/nvptx/src/omptarget-nvptx.cu
===================================================================
--- libomptarget/deviceRTLs/nvptx/src/omptarget-nvptx.cu
+++ libomptarget/deviceRTLs/nvptx/src/omptarget-nvptx.cu
@@ -29,9 +29,17 @@
 // init entry points
 ////////////////////////////////////////////////////////////////////////////////
 
+INLINE unsigned nsmid() {
+  unsigned n;
+  asm("mov.u32 %0, %%nsmid;" : "=r"(n));
+  return n;
+}
+
 INLINE unsigned smid() {
   unsigned id;
   asm("mov.u32 %0, %%smid;" : "=r"(id));
+  ASSERT0(LT_FUSSY, nsmid() <= MAX_SM,
+          "Expectednumber of SMs is less than reported.");
   return id;
 }
 
Index: libomptarget/deviceRTLs/nvptx/src/omptarget-nvptxi.h
===================================================================
--- libomptarget/deviceRTLs/nvptx/src/omptarget-nvptxi.h
+++ libomptarget/deviceRTLs/nvptx/src/omptarget-nvptxi.h
@@ -202,3 +202,31 @@
 INLINE omptarget_nvptx_TaskDescr *getMyTopTaskDescriptor() {
   return getMyTopTaskDescriptor(GetLogicalThreadIdInBlock());
 }
+
+////////////////////////////////////////////////////////////////////////////////
+// Lightweight runtime functions.
+////////////////////////////////////////////////////////////////////////////////
+
+// Shared memory buffer for globalization support.
+static __align__(16) __device__ __shared__ char
+    omptarget_static_buffer[DS_Shared_Memory_Size];
+static __device__ __shared__ void *omptarget_spmd_allocated;
+INLINE void *
+omptarget_nvptx_SimpleThreadPrivateContext::Allocate(size_t DataSize) {
+  if (DataSize <= DS_Shared_Memory_Size)
+    return ::omptarget_static_buffer;
+  if (DataSize <= DS_Global_Memory_Size)
+    return global_buffer;
+  if (threadIdx.x == 0)
+    omptarget_spmd_allocated = SafeMalloc(DataSize, "SPMD teams alloc");
+  __syncthreads();
+  return omptarget_spmd_allocated;
+}
+
+INLINE void omptarget_nvptx_SimpleThreadPrivateContext::Deallocate(void *Ptr) {
+  if (Ptr != ::omptarget_static_buffer && Ptr != global_buffer) {
+    __syncthreads();
+    if (threadIdx.x == 0)
+      SafeFree(Ptr, "SPMD teams dealloc");
+  }
+}
Index: libomptarget/deviceRTLs/nvptx/src/option.h
===================================================================
--- libomptarget/deviceRTLs/nvptx/src/option.h
+++ libomptarget/deviceRTLs/nvptx/src/option.h
@@ -34,7 +34,10 @@
 
 // Maximum number of omp state objects per SM allocated statically in global
 // memory.
-#if __CUDA_ARCH__ >= 600
+#if __CUDA_ARCH__ >= 700
+#define OMP_STATE_COUNT 32
+#define MAX_SM 84
+#elif __CUDA_ARCH__ >= 600
 #define OMP_STATE_COUNT 32
 #define MAX_SM 56
 #else