diff --git a/INSTALL.md b/INSTALL.md
index f2891672e2..ed0ba5046c 100644
--- a/INSTALL.md
+++ b/INSTALL.md
@@ -43,7 +43,7 @@ Both methods are supported. However, for most users we _strongly_ recommend to b
 - [Range-V3](https://github.com/ericniebler/range-v3.git) -- a Ranges library that served as the basis for Ranges component of C++20 and later.
 - [BTAS](http://github.com/ValeevGroup/BTAS), tag 1cfcb12647c768ccd83b098c64cda723e1275e49 . If usable BTAS installation is not found, TiledArray will download and compile
   BTAS from source. *This is the recommended way to compile BTAS for all users*.
-- [MADNESS](https://github.com/m-a-d-n-e-s-s/madness), tag 95589b0d020a076f93d02eead6da654b23dd3d91 .
+- [MADNESS](https://github.com/m-a-d-n-e-s-s/madness), tag 93a9a5cec2a8fa87fba3afe8056607e6062a9058 .
   Only the MADworld runtime and BLAS/LAPACK C API component of MADNESS is used by TiledArray.
   If usable MADNESS installation is not found, TiledArray will download and compile
   MADNESS from source. *This is the recommended way to compile MADNESS for all users*.
diff --git a/external/umpire.cmake b/external/umpire.cmake
index ee2fa490e1..5b7a4f4078 100644
--- a/external/umpire.cmake
+++ b/external/umpire.cmake
@@ -223,6 +223,8 @@ else()
             "$<BUILD_INTERFACE:${EXTERNAL_SOURCE_DIR}/src>;$<BUILD_INTERFACE:${EXTERNAL_SOURCE_DIR}/src/tpl>;$<BUILD_INTERFACE:${EXTERNAL_SOURCE_DIR}/src/tpl/umpire/camp/include>;$<BUILD_INTERFACE:${EXTERNAL_SOURCE_DIR}/src/tpl/umpire/fmt/include>;$<BUILD_INTERFACE:${EXTERNAL_BUILD_DIR}/src/tpl/umpire/camp/include>;$<BUILD_INTERFACE:${EXTERNAL_BUILD_DIR}/include>;$<INSTALL_INTERFACE:${_UMPIRE_INSTALL_DIR}/include>"
             INTERFACE_LINK_LIBRARIES
             "$<BUILD_INTERFACE:${UMPIRE_BUILD_BYPRODUCTS}>;$<INSTALL_INTERFACE:${_UMPIRE_INSTALL_DIR}/lib/libumpire${UMPIRE_DEFAULT_LIBRARY_SUFFIX}>"
+            INTERFACE_COMPILE_DEFINITIONS
+            FMT_HEADER_ONLY=1
             )
 
 install(TARGETS TiledArray_UMPIRE EXPORT tiledarray COMPONENT tiledarray)
diff --git a/external/versions.cmake b/external/versions.cmake
index fbd0399ee8..ef1505a5b8 100644
--- a/external/versions.cmake
+++ b/external/versions.cmake
@@ -11,8 +11,8 @@ set(TA_INSTALL_EIGEN_PREVIOUS_VERSION 3.3.7)
 set(TA_INSTALL_EIGEN_URL_HASH SHA256=b4c198460eba6f28d34894e3a5710998818515104d6e74e5cc331ce31e46e626)
 set(TA_INSTALL_EIGEN_PREVIOUS_URL_HASH MD5=b9e98a200d2455f06db9c661c5610496)
 
-set(TA_TRACKED_MADNESS_TAG 95589b0d020a076f93d02eead6da654b23dd3d91)
-set(TA_TRACKED_MADNESS_PREVIOUS_TAG 96ac90e8f193ccfaf16f346b4652927d2d362e75)
+set(TA_TRACKED_MADNESS_TAG 93a9a5cec2a8fa87fba3afe8056607e6062a9058)
+set(TA_TRACKED_MADNESS_PREVIOUS_TAG 95589b0d020a076f93d02eead6da654b23dd3d91)
 set(TA_TRACKED_MADNESS_VERSION 0.10.1)
 set(TA_TRACKED_MADNESS_PREVIOUS_VERSION 0.10.1)
 
diff --git a/python/src/TiledArray/python/array.h b/python/src/TiledArray/python/array.h
index 782846df4c..e3cc1c79b7 100644
--- a/python/src/TiledArray/python/array.h
+++ b/python/src/TiledArray/python/array.h
@@ -208,7 +208,7 @@ void make_array_class(py::object m, const char *name) {
                                  py::return_value_policy::reference)
           .def_property_readonly("trange", &array::trange<Array>)
           .def_property_readonly("shape", &array::shape<Array, py::tuple>)
-          .def("fill", &Array::fill, py::arg("value"),
+          .def("fill", &Array::template fill<>, py::arg("value"),
                py::arg("skip_set") = false)
           .def("init", &array::init_tiles<Array>)
           // Array object needs be alive while iterator is used */
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index 80f2a49710..a16c05d0b2 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -225,7 +225,7 @@ if(HIP_FOUND OR CUDA_FOUND)
        TiledArray/external/cuda.h
        TiledArray/device/cpu_cuda_vector.h)
   endif(CUDA_FOUND)
-endif(CUDA_FOUND OR HIP_FOUND)
+endif(HIP_FOUND OR CUDA_FOUND)
 
 set(TILEDARRAY_SOURCE_FILES
 TiledArray/tiledarray.cpp
diff --git a/src/TiledArray/array_impl.h b/src/TiledArray/array_impl.h
index df7138a9e7..9dbf5640c4 100644
--- a/src/TiledArray/array_impl.h
+++ b/src/TiledArray/array_impl.h
@@ -198,6 +198,17 @@ std::ostream& operator<<(std::ostream& os, const TileConstReference<Impl>& a) {
   return os;
 }
 
+/// Callaback used to update counter (typically, task counter)
+template <typename AtomicInt>
+struct IncrementCounter : public madness::CallbackInterface {
+  AtomicInt& counter;
+  IncrementCounter(AtomicInt& counter) : counter(counter) {}
+  void notify() override {
+    ++counter;
+    delete this;
+  }
+};
+
 }  // namespace detail
 }  // namespace TiledArray
 
@@ -770,20 +781,24 @@ class ArrayImpl : public TensorImpl<Policy>,
   /// \tparam Op The type of the functor/function
   /// \param[in] op The operation used to generate tiles
   /// \param[in] skip_set If false, will throw if any tiles are already set
+  /// \return the total number of tiles that have been (or will be) initialized
   /// \throw TiledArray::Exception if the PIMPL is not set. Strong throw
   ///                              guarantee.
   /// \throw TiledArray::Exception if a tile is already set and skip_set is
   ///                              false. Weak throw guarantee.
-  template <HostExecutor Exec = HostExecutor::Default, typename Op>
-  void init_tiles(Op&& op, bool skip_set = false) {
+  template <HostExecutor Exec = HostExecutor::Default, Fence fence = Fence::No,
+            typename Op>
+  std::int64_t init_tiles(Op&& op, bool skip_set = false) {
     // lifetime management of op depends on whether it is a lvalue ref (i.e. has
     // an external owner) or an rvalue ref
     // - if op is an lvalue ref: pass op to tasks
     // - if op is an rvalue ref pass make_shared_function(op) to tasks
     auto op_shared_handle = make_op_shared_handle(std::forward<Op>(op));
 
+    std::int64_t ntiles_initialized{0};
     auto it = this->pmap()->begin();
     const auto end = this->pmap()->end();
+    std::atomic<std::int64_t> ntask_completed{0};
     for (; it != end; ++it) {
       const auto& index = *it;
       if (!this->is_zero(index)) {
@@ -792,19 +807,39 @@ class ArrayImpl : public TensorImpl<Policy>,
           if (fut.probe()) continue;
         }
         if constexpr (Exec == HostExecutor::MADWorld) {
-          Future<value_type> tile = this->world().taskq.add(
-              [this_sptr = this->shared_from_this(),
-               index = ordinal_type(index), op_shared_handle]() -> value_type {
+          Future<value_type> tile =
+              this->world().taskq.add([this_sptr = this->shared_from_this(),
+                                       index = ordinal_type(index),
+                                       op_shared_handle, this]() -> value_type {
                 return op_shared_handle(
                     this_sptr->trange().make_tile_range(index));
               });
+          ++ntiles_initialized;
+          if constexpr (fence == Fence::Local) {
+            tile.register_callback(
+                new IncrementCounter<decltype(ntask_completed)>(
+                    ntask_completed));
+          }
           set(index, std::move(tile));
         } else {
           static_assert(Exec == HostExecutor::Thread);
           set(index, op_shared_handle(this->trange().make_tile_range(index)));
+          ++ntiles_initialized;
         }
       }
     }
+
+    if constexpr (fence == Fence::Local) {
+      if constexpr (Exec == HostExecutor::MADWorld) {
+        if (ntiles_initialized > 0)
+          this->world().await([&ntask_completed, ntiles_initialized]() {
+            return ntask_completed == ntiles_initialized;
+          });
+      }
+    } else if constexpr (fence == Fence::Global) {
+      this->world().gop.fence();
+    }
+    return ntiles_initialized;
   }
 
 };  // class ArrayImpl
diff --git a/src/TiledArray/conversions/foreach.h b/src/TiledArray/conversions/foreach.h
index 20f2d36ec3..2c77c91a0f 100644
--- a/src/TiledArray/conversions/foreach.h
+++ b/src/TiledArray/conversions/foreach.h
@@ -283,11 +283,10 @@ inline std::
       arg.trange().tiles_range(), 0);
 
   // Construct the task function used to construct the result tiles.
-  madness::AtomicInt counter;
-  counter = 0;
-  int task_count = 0;
+  std::atomic<std::int64_t> ntask_completed{0};
+  std::int64_t ntask_created{0};
   auto op_shared_handle = make_op_shared_handle(std::forward<Op>(op));
-  const auto task = [op_shared_handle, &counter, &tile_norms](
+  const auto task = [op_shared_handle, &tile_norms](
                         const ordinal_type ord,
                         const_if_t<not inplace, arg_value_type>& arg_tile,
                         const ArgTiles&... arg_tiles) -> result_value_type {
@@ -295,7 +294,6 @@ inline std::
     auto result_tile =
         op_caller(std::move(op_shared_handle), tile_norms.at_ordinal(ord),
                   arg_tile, arg_tiles...);
-    ++counter;
     return result_tile;
   };
 
@@ -310,7 +308,9 @@ inline std::
           continue;
         auto result_tile =
             world.taskq.add(task, ord, arg.find_local(ord), args.find(ord)...);
-        ++task_count;
+        ++ntask_created;
+        result_tile.register_callback(
+            new IncrementCounter<decltype(ntask_completed)>(ntask_completed));
         tiles.emplace_back(ord, std::move(result_tile));
         if (op_returns_void)  // if Op does not evaluate norms, use the (scaled)
                               // norms of the first arg
@@ -324,7 +324,9 @@ inline std::
         auto result_tile =
             world.taskq.add(task, ord, detail::get_sparse_tile(ord, arg),
                             detail::get_sparse_tile(ord, args)...);
-        ++task_count;
+        ++ntask_created;
+        result_tile.register_callback(
+            new IncrementCounter<decltype(ntask_completed)>(ntask_completed));
         tiles.emplace_back(ord, std::move(result_tile));
         if (op_returns_void)  // if Op does not evaluate norms, find max
                               // (scaled) norms of all args
@@ -339,9 +341,10 @@ inline std::
   }
 
   // Wait for tile norm data to be collected.
-  if (task_count > 0)
-    world.await(
-        [&counter, task_count]() -> bool { return counter == task_count; });
+  if (ntask_created > 0)
+    world.await([&ntask_completed, ntask_created]() -> bool {
+      return ntask_created == ntask_completed;
+    });
 
   // Construct the new array
   result_array_type result(
diff --git a/src/TiledArray/conversions/make_array.h b/src/TiledArray/conversions/make_array.h
index 6f5ada0bba..1295e6f8e4 100644
--- a/src/TiledArray/conversions/make_array.h
+++ b/src/TiledArray/conversions/make_array.h
@@ -26,6 +26,7 @@
 #ifndef TILEDARRAY_CONVERSIONS_MAKE_ARRAY_H__INCLUDED
 #define TILEDARRAY_CONVERSIONS_MAKE_ARRAY_H__INCLUDED
 
+#include "TiledArray/array_impl.h"
 #include "TiledArray/external/madness.h"
 #include "TiledArray/shape.h"
 #include "TiledArray/type_traits.h"
@@ -79,6 +80,10 @@ inline Array make_array(
   // Make an empty result array
   Array result(world, trange);
 
+  // Construct the task function used to construct the result tiles.
+  std::atomic<std::int64_t> ntask_completed{0};
+  std::int64_t ntask_created{0};
+
   // Iterate over local tiles of arg
   for (const auto index : *result.pmap()) {
     // Spawn a task to evaluate the tile
@@ -89,11 +94,20 @@ inline Array make_array(
           return tile;
         },
         trange.make_tile_range(index));
-
+    ++ntask_created;
+    tile.register_callback(
+        new detail::IncrementCounter<decltype(ntask_completed)>(
+            ntask_completed));
     // Store result tile
-    result.set(index, tile);
+    result.set(index, std::move(tile));
   }
 
+  // Wait for tile tasks to complete
+  if (ntask_created > 0)
+    world.await([&ntask_completed, ntask_created]() -> bool {
+      return ntask_completed == ntask_created;
+    });
+
   return result;
 }
 
@@ -150,26 +164,28 @@ inline Array make_array(
       trange.tiles_range(), 0);
 
   // Construct the task function used to construct the result tiles.
-  madness::AtomicInt counter;
-  counter = 0;
-  int task_count = 0;
+  std::atomic<std::int64_t> ntask_completed{0};
+  std::int64_t ntask_created{0};
   auto task = [&](const ordinal_type index) -> value_type {
     value_type tile;
     tile_norms.at_ordinal(index) = op(tile, trange.make_tile_range(index));
-    ++counter;
     return tile;
   };
 
   for (const auto index : *pmap) {
     auto result_tile = world.taskq.add(task, index);
-    ++task_count;
+    ++ntask_created;
+    result_tile.register_callback(
+        new detail::IncrementCounter<decltype(ntask_completed)>(
+            ntask_completed));
     tiles.emplace_back(index, std::move(result_tile));
   }
 
   // Wait for tile norm data to be collected.
-  if (task_count > 0)
-    world.await(
-        [&counter, task_count]() -> bool { return counter == task_count; });
+  if (ntask_created > 0)
+    world.await([&ntask_completed, ntask_created]() -> bool {
+      return ntask_completed == ntask_created;
+    });
 
   // Construct the new array
   Array result(world, trange,
diff --git a/src/TiledArray/dist_array.h b/src/TiledArray/dist_array.h
index 3bc9fe3c62..1aa90ce351 100644
--- a/src/TiledArray/dist_array.h
+++ b/src/TiledArray/dist_array.h
@@ -906,23 +906,29 @@ class DistArray : public madness::archive::ParallelSerializableObject {
   ///                              guarantee.
   /// \throw TiledArray::Exception if skip_set is false and a local tile is
   ///                              already set. Weak throw guarantee.
-  void fill_local(const element_type& value = element_type(),
-                  bool skip_set = false) {
-    init_tiles(
+  template <Fence fence = Fence::No>
+  std::int64_t fill_local(const element_type& value = element_type(),
+                          bool skip_set = false) {
+    return init_tiles<HostExecutor::Default, fence>(
         [value](const range_type& range) { return value_type(range, value); },
         skip_set);
   }
 
   /// Fill all local tiles with the specified value
 
+  /// \tparam fence If Fence::No, the operation will return early,
+  ///         before the tasks have completed
   /// \param[in] value What each local tile should be filled with.
   /// \param[in] skip_set If false, will throw if any tiles are already set
+  /// \return the total number of tiles that have been (or will be) initialized
   /// \throw TiledArray::Exception if the PIMPL is uninitialized. Strong throw
   ///                              guarantee.
   /// \throw TiledArray::Exception if skip_set is false and a local tile is
   ///                              already set. Weak throw guarantee.
-  void fill(const element_type& value = numeric_type(), bool skip_set = false) {
-    fill_local(value, skip_set);
+  template <Fence fence = Fence::No>
+  std::int64_t fill(const element_type& value = numeric_type(),
+                    bool skip_set = false) {
+    return fill_local<fence>(value, skip_set);
   }
 
   /// Fill all local tiles with random values
@@ -934,18 +940,21 @@ class DistArray : public madness::archive::ParallelSerializableObject {
   /// generate random values of type T this function will be disabled via SFINAE
   /// and attempting to use it will lead to a compile-time error.
   ///
+  /// \tparam fence If Fence::No, the operation will return early,
+  ///         before the tasks have completed
   /// \tparam T The type of random value to generate. Defaults to
   ///           element_type.
   /// \param[in] skip_set If false, will throw if any tiles are already set
+  /// \return the total number of tiles that have been (or will be) initialized
   /// \throw TiledArray::Exception if the PIMPL is not initialized. Strong
   ///                              throw guarantee.
   /// \throw TiledArray::Exception if skip_set is false and a local tile is
   ///                              already initialized. Weak throw guarantee.
   template <HostExecutor Exec = HostExecutor::Default,
-            typename T = element_type,
+            typename T = element_type, Fence fence = Fence::No,
             typename = detail::enable_if_can_make_random_t<T>>
-  void fill_random(bool skip_set = false) {
-    init_elements<Exec>(
+  std::int64_t fill_random(bool skip_set = false) {
+    return init_elements<Exec, fence>(
         [](const auto&) { return detail::MakeRandom<T>::generate_value(); });
   }
 
@@ -978,6 +987,8 @@ class DistArray : public madness::archive::ParallelSerializableObject {
   ///        return tile;
   ///     });
   /// \endcode
+  /// \tparam fence If Fence::No, the operation will return early,
+  ///         before the tasks have completed
   /// \tparam Op The type of the functor/function
   /// \param[in] op The operation used to generate tiles
   /// \param[in] skip_set If false, will throw if any tiles are already set
@@ -985,9 +996,11 @@ class DistArray : public madness::archive::ParallelSerializableObject {
   ///                              guarantee.
   /// \throw TiledArray::Exception if a tile is already set and skip_set is
   ///                              false. Weak throw guarantee.
-  template <HostExecutor Exec = HostExecutor::Default, typename Op>
-  void init_tiles(Op&& op, bool skip_set = false) {
-    impl_ref().template init_tiles<Exec>(std::forward<Op>(op), skip_set);
+  template <HostExecutor Exec = HostExecutor::Default, Fence fence = Fence::No,
+            typename Op>
+  std::int64_t init_tiles(Op&& op, bool skip_set = false) {
+    return impl_ref().template init_tiles<Exec, fence>(std::forward<Op>(op),
+                                                       skip_set);
   }
 
   /// Initialize elements of local, non-zero tiles with a user provided functor
@@ -1009,15 +1022,17 @@ class DistArray : public madness::archive::ParallelSerializableObject {
   /// \tparam Op Type of the function/functor which will generate the elements.
   /// \param[in] op The operation used to generate elements
   /// \param[in] skip_set If false, will throw if any tiles are already set
+  /// \return the total number of tiles that have been (or will be) initialized
   /// \throw TiledArray::Exception if the PIMPL is not initialized. Strong
   ///                              throw guarnatee.
   /// \throw TiledArray::Exception if skip_set is false and a local, non-zero
   ///                              tile is already initialized. Weak throw
   ///                              guarantee.
-  template <HostExecutor Exec = HostExecutor::Default, typename Op>
-  void init_elements(Op&& op, bool skip_set = false) {
+  template <HostExecutor Exec = HostExecutor::Default, Fence fence = Fence::No,
+            typename Op>
+  std::int64_t init_elements(Op&& op, bool skip_set = false) {
     auto op_shared_handle = make_op_shared_handle(std::forward<Op>(op));
-    init_tiles<Exec>(
+    return init_tiles<Exec, fence>(
         [op = std::move(op_shared_handle)](
             const TiledArray::Range& range) -> value_type {
           // Initialize the tile with the given range object
diff --git a/src/TiledArray/fwd.h b/src/TiledArray/fwd.h
index 652b835fab..e33aea5c18 100644
--- a/src/TiledArray/fwd.h
+++ b/src/TiledArray/fwd.h
@@ -203,6 +203,14 @@ using Array
 
 enum class HostExecutor { Thread, MADWorld, Default = MADWorld };
 
+/// fence types
+enum class Fence {
+  Global,  //!< global fence (`world.gop.fence()`)
+  Local,   //!< local fence (all local work done, equivalent to
+           //!< `world.taskq.fence() in absence of active messages)
+  No       //!< no fence
+};
+
 namespace conversions {
 
 /// user defined conversions
diff --git a/src/TiledArray/special/diagonal_array.h b/src/TiledArray/special/diagonal_array.h
index d60b23db94..eac0c65e92 100644
--- a/src/TiledArray/special/diagonal_array.h
+++ b/src/TiledArray/special/diagonal_array.h
@@ -157,7 +157,8 @@ std::enable_if_t<is_iterator<RandomAccessIterator>::value, void>
 write_diag_tiles_to_array_rng(Array &A, RandomAccessIterator diagonals_begin) {
   using Tile = typename Array::value_type;
 
-  A.init_tiles(
+  // N.B. Fence::Local ensures lifetime of the diagonals range
+  A.template init_tiles<HostExecutor::Default, Fence::Local>(
       // Task to create each tile
       [diagonals_begin](const Range &rng) {
         // Compute range of diagonal elements in the tile
@@ -221,7 +222,6 @@ diagonal_array(World &world, TiledRange const &trange,
   if constexpr (is_dense_v<Policy>) {
     Array A(world, trange);
     detail::write_diag_tiles_to_array_rng(A, diagonals_begin);
-    A.world().taskq.fence();  // ensure tasks outlive the diagonals_begin view
     return A;
   } else {
     // Compute shape and init the Array
@@ -231,7 +231,6 @@ diagonal_array(World &world, TiledRange const &trange,
     ShapeType shape(shape_norm, trange);
     Array A(world, trange, shape);
     detail::write_diag_tiles_to_array_rng(A, diagonals_begin);
-    A.world().taskq.fence();  // ensure tasks outlive the diagonals_begin view
     return A;
   }
   abort();  // unreachable
diff --git a/src/TiledArray/util/bug.cpp b/src/TiledArray/util/bug.cpp
index 5e58ba667c..ff37f14343 100644
--- a/src/TiledArray/util/bug.cpp
+++ b/src/TiledArray/util/bug.cpp
@@ -166,7 +166,7 @@ void Debugger::set_prefix(const char *p) {
 
 void Debugger::set_prefix(int i) {
   char p[128];
-  sprintf(p, "%3d: ", i);
+  snprintf(p, sizeof(p), "%3d: ", i);
   set_prefix(p);
 }
 
diff --git a/tests/dist_array.cpp b/tests/dist_array.cpp
index 998b0d8f9f..64f69e69db 100644
--- a/tests/dist_array.cpp
+++ b/tests/dist_array.cpp
@@ -60,7 +60,7 @@ namespace {
 std::string to_parallel_archive_file_name(const char* prefix_name, int rank) {
   char buf[256];
   MADNESS_ASSERT(strlen(prefix_name) + 7 <= sizeof(buf));
-  sprintf(buf, "%s.%5.5d", prefix_name, rank);
+  snprintf(buf, sizeof(buf), "%s.%5.5d", prefix_name, rank);
   return buf;
 }
 }  // namespace
@@ -716,7 +716,7 @@ BOOST_AUTO_TEST_CASE(parallel_serialization) {
   mktemp(archive_file_prefix_name);
   madness::archive::ParallelOutputArchive<> oar(world, archive_file_prefix_name,
                                                 nio);
-  oar& a;
+  oar & a;
   oar.close();
 
   madness::archive::ParallelInputArchive<> iar(world, archive_file_prefix_name,
@@ -740,7 +740,7 @@ BOOST_AUTO_TEST_CASE(parallel_sparse_serialization) {
   mktemp(archive_file_prefix_name);
   madness::archive::ParallelOutputArchive<> oar(world, archive_file_prefix_name,
                                                 nio);
-  oar& b;
+  oar & b;
   oar.close();
 
   madness::archive::ParallelInputArchive<> iar(world, archive_file_prefix_name,
@@ -783,7 +783,7 @@ BOOST_AUTO_TEST_CASE(issue_225) {
   madness::archive::BinaryFstreamInputArchive iar(archive_file_name);
   decltype(S) S_read;
   decltype(St) St_read;
-  iar& S_read& St_read;
+  iar & S_read & St_read;
 
   BOOST_CHECK_EQUAL(S_read.trange(), S.trange());
   BOOST_REQUIRE(S_read.shape() == S.shape());