diff --git a/sycl/include/CL/__spirv/spirv_ops.hpp b/sycl/include/CL/__spirv/spirv_ops.hpp
index df1cd55cab0a2..5832a3a79610a 100644
--- a/sycl/include/CL/__spirv/spirv_ops.hpp
+++ b/sycl/include/CL/__spirv/spirv_ops.hpp
@@ -25,19 +25,23 @@
 #ifdef __SYCL_DEVICE_ONLY__
 
 #if (SYCL_EXT_ONEAPI_MATRIX_VERSION > 1)
-template <typename T, std::size_t R, std::size_t C, __spv::MatrixUse U,
+extern __DPCPP_SYCL_EXTERNAL float __spirv_RoundFToTF32INTEL(float a);
+template <typename T, typename Tp, std::size_t R, std::size_t C,
+          __spv::MatrixUse U,
           __spv::MatrixLayout L = __spv::MatrixLayout::RowMajor,
           __spv::Scope::Flag S = __spv::Scope::Flag::Subgroup>
-extern __DPCPP_SYCL_EXTERNAL __spv::__spirv_JointMatrixINTEL<T, R, C, L, S, U> *
-__spirv_JointMatrixLoadINTEL(T *Ptr, std::size_t Stride,
-                             __spv::MatrixLayout Layout = L,
-                             __spv::Scope::Flag Sc = S, int MemOperand = 0);
+extern __DPCPP_SYCL_EXTERNAL
+    __spv::__spirv_JointMatrixINTEL<Tp, R, C, L, S, U> *
+    __spirv_JointMatrixLoadINTEL(T *Ptr, std::size_t Stride,
+                                 __spv::MatrixLayout Layout = L,
+                                 __spv::Scope::Flag Sc = S, int MemOperand = 0);
 
-template <typename T, std::size_t R, std::size_t C, __spv::MatrixUse U,
+template <typename T, typename Tp, std::size_t R, std::size_t C,
+          __spv::MatrixUse U,
           __spv::MatrixLayout L = __spv::MatrixLayout::RowMajor,
           __spv::Scope::Flag S = __spv::Scope::Flag::Subgroup>
 extern __DPCPP_SYCL_EXTERNAL void __spirv_JointMatrixStoreINTEL(
-    T *Ptr, __spv::__spirv_JointMatrixINTEL<T, R, C, L, S, U> *Object,
+    T *Ptr, __spv::__spirv_JointMatrixINTEL<Tp, R, C, L, S, U> *Object,
     std::size_t Stride, __spv::MatrixLayout Layout = L,
     __spv::Scope::Flag Sc = S, int MemOperand = 0);
 
@@ -100,11 +104,13 @@ extern __DPCPP_SYCL_EXTERNAL
         __spv::__spirv_JointMatrixINTEL<T3, M, N, LC, S, UC> *C,
         __spv::Scope::Flag Sc = __spv::Scope::Flag::Subgroup);
 
-template <typename T, std::size_t R, std::size_t C, __spv::MatrixUse U,
+template <typename T, typename Tp, std::size_t R, std::size_t C,
+          __spv::MatrixUse U,
           __spv::MatrixLayout L = __spv::MatrixLayout::RowMajor,
           __spv::Scope::Flag S = __spv::Scope::Flag::Subgroup>
-extern __DPCPP_SYCL_EXTERNAL __spv::__spirv_JointMatrixINTEL<T, R, C, L, S, U> *
-__spirv_CompositeConstruct(const T v);
+extern __DPCPP_SYCL_EXTERNAL
+    __spv::__spirv_JointMatrixINTEL<Tp, R, C, L, S, U> *
+    __spirv_CompositeConstruct(const T v);
 
 template <typename T, std::size_t R, std::size_t C, __spv::MatrixUse U,
           __spv::MatrixLayout L = __spv::MatrixLayout::RowMajor,
@@ -119,18 +125,20 @@ template <typename T, std::size_t R, std::size_t C, __spv::MatrixUse U,
 extern __DPCPP_SYCL_EXTERNAL size_t __spirv_JointMatrixWorkItemLengthINTEL(
     __spv::__spirv_JointMatrixINTEL<T, R, C, L, S, U> *);
 
-template <typename T, std::size_t R, std::size_t C, __spv::MatrixUse U,
+template <typename Ts, typename T, std::size_t R, std::size_t C,
+          __spv::MatrixUse U,
           __spv::MatrixLayout L = __spv::MatrixLayout::RowMajor,
           __spv::Scope::Flag S = __spv::Scope::Flag::Subgroup>
-extern __DPCPP_SYCL_EXTERNAL T __spirv_VectorExtractDynamic(
+extern __DPCPP_SYCL_EXTERNAL Ts __spirv_VectorExtractDynamic(
     __spv::__spirv_JointMatrixINTEL<T, R, C, L, S, U> *, size_t i);
 
-template <typename T, std::size_t R, std::size_t C, __spv::MatrixUse U,
+template <typename Ts, typename T, std::size_t R, std::size_t C,
+          __spv::MatrixUse U,
           __spv::MatrixLayout L = __spv::MatrixLayout::RowMajor,
           __spv::Scope::Flag S = __spv::Scope::Flag::Subgroup>
 extern __DPCPP_SYCL_EXTERNAL __spv::__spirv_JointMatrixINTEL<T, R, C, L, S, U> *
 __spirv_VectorInsertDynamic(__spv::__spirv_JointMatrixINTEL<T, R, C, L, S, U> *,
-                            T val, size_t i);
+                            Ts val, size_t i);
 #else
 template <typename T, std::size_t R, std::size_t C,
           __spv::MatrixLayout L = __spv::MatrixLayout::RowMajor,
diff --git a/sycl/include/sycl/ext/oneapi/matrix/matrix-intel.hpp b/sycl/include/sycl/ext/oneapi/matrix/matrix-intel.hpp
index ba11632f5d371..cb827d9839a6e 100644
--- a/sycl/include/sycl/ext/oneapi/matrix/matrix-intel.hpp
+++ b/sycl/include/sycl/ext/oneapi/matrix/matrix-intel.hpp
@@ -67,10 +67,26 @@ struct joint_matrix;
 
 } // namespace matrix
 } // namespace experimental
+
+namespace detail {
+// Differentiating between the "element type" and the "storage element type"
+template <typename T> struct jm_type_interpretation_helper_trait {
+  using element_type = T;
+  using storage_element_type = T;
+};
+
+template <>
+struct jm_type_interpretation_helper_trait<
+    sycl::ext::oneapi::experimental::matrix::precision::tf32> {
+  using element_type = sycl::ext::oneapi::experimental::matrix::precision::tf32;
+  using storage_element_type = float;
+};
+} // namespace detail
 } // namespace oneapi
 
 namespace intel::experimental::matrix {
 
+using namespace sycl::ext::oneapi::experimental::matrix;
 // Begin wi_element definition
 
 template <typename T, size_t NumRows, size_t NumCols,
@@ -84,6 +100,9 @@ class wi_element {
   std::size_t idx;
 
 public:
+  using storage_element_type =
+      typename oneapi::detail::jm_type_interpretation_helper_trait<
+          T>::storage_element_type;
   wi_element(sycl::ext::oneapi::experimental::matrix::joint_matrix<
                  Group, T, Use, NumRows, NumCols, Layout> &Mat,
              std::size_t i)
@@ -102,9 +121,15 @@ class wi_element {
 #endif // __SYCL_DEVICE_ONLY__
   }
 
-  operator T() {
+  operator storage_element_type() {
 #ifdef __SYCL_DEVICE_ONLY__
-    return __spirv_VectorExtractDynamic(M.spvm, idx);
+    storage_element_type elem =
+        __spirv_VectorExtractDynamic<storage_element_type, T, NumRows, NumCols,
+                                     spv_matrix_use_traits<Use>::value,
+                                     spv_matrix_layout_traits<Layout>::value,
+                                     spv_scope_traits<Group>::value>(M.spvm,
+                                                                     idx);
+    return elem;
 #else
     throw runtime_error("joint matrix is not supported on host device.",
                         PI_ERROR_INVALID_DEVICE);
@@ -113,7 +138,12 @@ class wi_element {
 
   explicit operator bool() {
 #ifdef __SYCL_DEVICE_ONLY__
-    return __spirv_VectorExtractDynamic(M.spvm, idx) != static_cast<T>(0);
+    return __spirv_VectorExtractDynamic<storage_element_type, T, NumRows,
+                                        NumCols,
+                                        spv_matrix_use_traits<Use>::value,
+                                        spv_matrix_layout_traits<Layout>::value,
+                                        spv_scope_traits<Group>::value>(
+               M.spvm, idx) != static_cast<storage_element_type>(0);
 #else
     throw runtime_error("joint matrix is not supported on host device.",
                         PI_ERROR_INVALID_DEVICE);
@@ -122,7 +152,8 @@ class wi_element {
 
   template <typename T2> wi_element &operator=(const T2 &rhs) {
 #ifdef __SYCL_DEVICE_ONLY__
-    M.spvm = __spirv_VectorInsertDynamic(M.spvm, static_cast<T>(rhs), idx);
+    M.spvm = __spirv_VectorInsertDynamic(
+        M.spvm, static_cast<storage_element_type>(rhs), idx);
     return *this;
 #else
     (void)rhs;
@@ -135,7 +166,13 @@ class wi_element {
   operator=(const wi_element<T, NumRows, NumCols, Use, Layout, Group> &rhs) {
 #ifdef __SYCL_DEVICE_ONLY__
     M.spvm = __spirv_VectorInsertDynamic(
-        M.spvm, __spirv_VectorExtractDynamic(rhs.M.spvm, rhs.idx), idx);
+        M.spvm,
+        __spirv_VectorExtractDynamic<storage_element_type, T, NumRows, NumCols,
+                                     spv_matrix_use_traits<Use>::value,
+                                     spv_matrix_layout_traits<Layout>::value,
+                                     spv_scope_traits<Group>::value>(rhs.M.spvm,
+                                                                     rhs.idx),
+        idx);
     return *this;
 #else
     (void)rhs;
@@ -149,8 +186,13 @@ class wi_element {
   template <typename T2> wi_element &operator op##=(const T2 &rhs) {           \
     M.spvm = __spirv_VectorInsertDynamic(                                      \
         M.spvm,                                                                \
-        static_cast<T>(__spirv_VectorExtractDynamic(M.spvm, idx)               \
-                           op static_cast<T>(rhs)),                            \
+        static_cast<storage_element_type>(                                     \
+            __spirv_VectorExtractDynamic<                                      \
+                storage_element_type, T, NumRows, NumCols,                     \
+                spv_matrix_use_traits<Use>::value,                             \
+                spv_matrix_layout_traits<Layout>::value,                       \
+                spv_scope_traits<Group>::value>(M.spvm, idx)                   \
+                op static_cast<storage_element_type>(rhs)),                    \
         idx);                                                                  \
     return *this;                                                              \
   }
@@ -201,7 +243,11 @@ class wi_element<sycl::ext::oneapi::bfloat16, NumRows, NumCols, Use, Layout,
 
   operator sycl::ext::oneapi::bfloat16() {
 #ifdef __SYCL_DEVICE_ONLY__
-    return __spirv_VectorExtractDynamic(M.spvm, idx);
+    return __spirv_VectorExtractDynamic<
+        sycl::ext::oneapi::bfloat16, sycl::ext::oneapi::bfloat16, NumRows,
+        NumCols, spv_matrix_use_traits<Use>::value,
+        spv_matrix_layout_traits<Layout>::value,
+        spv_scope_traits<Group>::value>(M.spvm, idx);
 #else
     throw runtime_error("joint matrix is not supported on host device.",
                         PI_ERROR_INVALID_DEVICE);
@@ -210,8 +256,13 @@ class wi_element<sycl::ext::oneapi::bfloat16, NumRows, NumCols, Use, Layout,
 
   explicit operator bool() {
 #ifdef __SYCL_DEVICE_ONLY__
-    return std::fabs(static_cast<float>(__spirv_VectorExtractDynamic(
-               M.spvm, idx))) >= std::numeric_limits<float>::epsilon();
+    return std::fabs(static_cast<float>(
+               __spirv_VectorExtractDynamic<
+                   sycl::ext::oneapi::bfloat16, sycl::ext::oneapi::bfloat16,
+                   NumRows, NumCols, spv_matrix_use_traits<Use>::value,
+                   spv_matrix_layout_traits<Layout>::value,
+                   spv_scope_traits<Group>::value>(M.spvm, idx))) >=
+           std::numeric_limits<float>::epsilon();
 #else
     throw runtime_error("joint matrix is not supported on host device.",
                         PI_ERROR_INVALID_DEVICE);
@@ -233,7 +284,14 @@ class wi_element<sycl::ext::oneapi::bfloat16, NumRows, NumCols, Use, Layout,
                                          NumCols, Use, Layout, Group> &rhs) {
 #ifdef __SYCL_DEVICE_ONLY__
     M.spvm = __spirv_VectorInsertDynamic(
-        M.spvm, __spirv_VectorExtractDynamic(rhs.M.spvm, rhs.idx), idx);
+        M.spvm,
+        __spirv_VectorExtractDynamic<sycl::ext::oneapi::bfloat16,
+                                     sycl::ext::oneapi::bfloat16, NumRows,
+                                     NumCols, spv_matrix_use_traits<Use>::value,
+                                     spv_matrix_layout_traits<Layout>::value,
+                                     spv_scope_traits<Group>::value>(rhs.M.spvm,
+                                                                     rhs.idx),
+        idx);
     return *this;
 #else
     (void)rhs;
@@ -246,7 +304,13 @@ class wi_element<sycl::ext::oneapi::bfloat16, NumRows, NumCols, Use, Layout,
 #define OP(opassign, op)                                                       \
   wi_element &operator opassign(const sycl::ext::oneapi::bfloat16 &rhs) {      \
     M.spvm = __spirv_VectorInsertDynamic(                                      \
-        M.spvm, __spirv_VectorExtractDynamic(M.spvm, idx) op rhs, idx);        \
+        M.spvm,                                                                \
+        __spirv_VectorExtractDynamic<                                          \
+            sycl::ext::oneapi::bfloat16, sycl::ext::oneapi::bfloat16, NumRows, \
+            NumCols, spv_matrix_use_traits<Use>::value,                        \
+            spv_matrix_layout_traits<Layout>::value,                           \
+            spv_scope_traits<Group>::value>(M.spvm, idx) op rhs,               \
+        idx);                                                                  \
     return *this;                                                              \
   }
 #else // __SYCL_DEVICE_ONLY__
@@ -269,13 +333,21 @@ class wi_element<sycl::ext::oneapi::bfloat16, NumRows, NumCols, Use, Layout,
       const wi_element<sycl::ext::oneapi::bfloat16, NumRows, NumCols, Use,     \
                        Layout, Group> &lhs,                                    \
       const sycl::ext::oneapi::bfloat16 &rhs) {                                \
-    return __spirv_VectorExtractDynamic(lhs.M.spvm, lhs.idx) op rhs;           \
+    return __spirv_VectorExtractDynamic<                                       \
+        sycl::ext::oneapi::bfloat16, sycl::ext::oneapi::bfloat16, NumRows,     \
+        NumCols, spv_matrix_use_traits<Use>::value,                            \
+        spv_matrix_layout_traits<Layout>::value,                               \
+        spv_scope_traits<Group>::value>(lhs.M.spvm, lhs.idx) op rhs;           \
   }                                                                            \
   friend type operator op(                                                     \
       const sycl::ext::oneapi::bfloat16 &lhs,                                  \
       const wi_element<sycl::ext::oneapi::bfloat16, NumRows, NumCols, Use,     \
                        Layout, Group> &rhs) {                                  \
-    return __spirv_VectorExtractDynamic(rhs.M.spvm, rhs.idx) op lhs;           \
+    return __spirv_VectorExtractDynamic<                                       \
+        sycl::ext::oneapi::bfloat16, sycl::ext::oneapi::bfloat16, NumRows,     \
+        NumCols, spv_matrix_use_traits<Use>::value,                            \
+        spv_matrix_layout_traits<Layout>::value,                               \
+        spv_scope_traits<Group>::value>(rhs.M.spvm, rhs.idx) op lhs;           \
   }
   OP(sycl::ext::oneapi::bfloat16, +)
   OP(sycl::ext::oneapi::bfloat16, -)
@@ -287,15 +359,25 @@ class wi_element<sycl::ext::oneapi::bfloat16, NumRows, NumCols, Use, Layout,
       const wi_element<sycl::ext::oneapi::bfloat16, NumRows, NumCols, Use,     \
                        Layout, Group> &lhs,                                    \
       const sycl::ext::oneapi::bfloat16 &rhs) {                                \
-    return type{static_cast<float>(__spirv_VectorExtractDynamic(               \
-        lhs.M.spvm, lhs.idx)) op static_cast<float>(rhs)};                     \
+    return type{static_cast<float>(                                            \
+        __spirv_VectorExtractDynamic<                                          \
+            sycl::ext::oneapi::bfloat16, sycl::ext::oneapi::bfloat16, NumRows, \
+            NumCols, spv_matrix_use_traits<Use>::value,                        \
+            spv_matrix_layout_traits<Layout>::value,                           \
+            spv_scope_traits<Group>::value>(lhs.M.spvm, lhs.idx))              \
+                    op static_cast<float>(rhs)};                               \
   }                                                                            \
   friend type operator op(                                                     \
       const sycl::ext::oneapi::bfloat16 &lhs,                                  \
       const wi_element<sycl::ext::oneapi::bfloat16, NumRows, NumCols, Use,     \
                        Layout, Group> &rhs) {                                  \
-    return type{static_cast<float>(__spirv_VectorExtractDynamic(               \
-        rhs.M.spvm, rhs.idx)) op static_cast<float>(lhs)};                     \
+    return type{static_cast<float>(                                            \
+        __spirv_VectorExtractDynamic<                                          \
+            sycl::ext::oneapi::bfloat16, sycl::ext::oneapi::bfloat16, NumRows, \
+            NumCols, spv_matrix_use_traits<Use>::value,                        \
+            spv_matrix_layout_traits<Layout>::value,                           \
+            spv_scope_traits<Group>::value>(rhs.M.spvm, rhs.idx))              \
+                    op static_cast<float>(lhs)};                               \
   }
   OP(bool, ==)
   OP(bool, !=)
@@ -386,7 +468,7 @@ get_wi_data(Group sg, sycl::ext::oneapi::experimental::matrix::joint_matrix<
 // End wi_data definition
 
 template <
-    typename Group, typename T,
+    typename Group, typename T, typename Tp,
     sycl::ext::oneapi::experimental::matrix::use Use, size_t NumRows,
     size_t NumCols, sycl::ext::oneapi::experimental::matrix::layout Layout,
     access::address_space Space, access::decorated IsDecorated,
@@ -396,7 +478,7 @@ template <
 inline __SYCL_ALWAYS_INLINE void
 joint_matrix_store(Group sg,
                    sycl::ext::oneapi::experimental::matrix::joint_matrix<
-                       Group, T, Use, NumRows, NumCols, Layout> &src,
+                       Group, Tp, Use, NumRows, NumCols, Layout> &src,
                    multi_ptr<T, Space, IsDecorated> dst, size_t stride) {
 #if defined(__SYCL_DEVICE_ONLY__)
 #if defined(__NVPTX__)
@@ -411,7 +493,7 @@ joint_matrix_store(Group sg,
 #else
   // intel's impl
   T *Ptr = dst.get();
-  __spirv_JointMatrixStoreINTEL<T, NumRows, NumCols,
+  __spirv_JointMatrixStoreINTEL<T, Tp, NumRows, NumCols,
                                 sycl::ext::oneapi::experimental::matrix::
                                     spv_matrix_use_traits<Use>::value,
                                 sycl::ext::oneapi::experimental::matrix::
diff --git a/sycl/include/sycl/ext/oneapi/matrix/matrix-tensorcores.hpp b/sycl/include/sycl/ext/oneapi/matrix/matrix-tensorcores.hpp
index a871b9709ae66..018c66cf5213d 100644
--- a/sycl/include/sycl/ext/oneapi/matrix/matrix-tensorcores.hpp
+++ b/sycl/include/sycl/ext/oneapi/matrix/matrix-tensorcores.hpp
@@ -18,12 +18,6 @@ namespace oneapi {
 namespace experimental {
 namespace matrix {
 
-namespace precision {
-class tf32 {
-  tf32() = delete;
-};
-} // namespace precision
-
 template <typename Group, typename T, use Use, size_t Rows, size_t Cols,
           layout Layout = layout::dynamic>
 struct joint_matrix;
diff --git a/sycl/include/sycl/ext/oneapi/matrix/matrix-unified-utils.hpp b/sycl/include/sycl/ext/oneapi/matrix/matrix-unified-utils.hpp
index 718411b22ddbb..6f820fb82575a 100644
--- a/sycl/include/sycl/ext/oneapi/matrix/matrix-unified-utils.hpp
+++ b/sycl/include/sycl/ext/oneapi/matrix/matrix-unified-utils.hpp
@@ -18,6 +18,12 @@ enum class use { a, b, accumulator };
 
 enum class layout { row_major = 0, col_major = 1, dynamic = 3 };
 
+namespace precision {
+class tf32 {
+  tf32() = delete;
+};
+} // namespace precision
+
 } // namespace matrix
 } // namespace experimental
 } // namespace oneapi
diff --git a/sycl/include/sycl/ext/oneapi/matrix/matrix-unified.hpp b/sycl/include/sycl/ext/oneapi/matrix/matrix-unified.hpp
index 7e5f4df979741..13326bac83182 100644
--- a/sycl/include/sycl/ext/oneapi/matrix/matrix-unified.hpp
+++ b/sycl/include/sycl/ext/oneapi/matrix/matrix-unified.hpp
@@ -138,9 +138,12 @@ joint_matrix_apply(Group sg, joint_matrix<Group, T, Use, M, N, Layout> &jm,
     lambda(jm.cuda_impl.wi_marray[i]);
   }
 #else // NVPTX
+  using storage_element_type =
+      typename oneapi::detail::jm_type_interpretation_helper_trait<
+          T>::storage_element_type;
   auto wi_data_c = sycl::ext::intel::experimental::matrix::get_wi_data(sg, jm);
   for (int i = 0; i < wi_data_c.length(); i++) {
-    T element = wi_data_c[i];
+    storage_element_type element = wi_data_c[i];
     lambda(element);
     wi_data_c[i] = element;
   }
@@ -166,11 +169,14 @@ joint_matrix_fill(Group sg,
   std::ignore = sg;
   res.cuda_impl.wi_marray = v;
 #else
+  using storage_element_type =
+      typename oneapi::detail::jm_type_interpretation_helper_trait<
+          T>::storage_element_type;
   res.spvm =
-      __spirv_CompositeConstruct<T, NumRows, NumCols,
+      __spirv_CompositeConstruct<storage_element_type, T, NumRows, NumCols,
                                  spv_matrix_use_traits<Use>::value,
                                  spv_matrix_layout_traits<Layout>::value>(
-          static_cast<T>(v));
+          static_cast<storage_element_type>(v));
 #endif // defined(__NVPTX__)
 #else
   std::ignore = sg;
@@ -204,21 +210,21 @@ inline __SYCL_ALWAYS_INLINE void joint_matrix_load(
     assert(false && "Invalid Memory Layout!");
   case layout::row_major:
     res.spvm = __spirv_JointMatrixLoadINTEL<
-        T, NumRows, NumCols, spv_matrix_use_traits<use::accumulator>::value,
+        T, S, NumRows, NumCols, spv_matrix_use_traits<use::accumulator>::value,
         spv_matrix_layout_traits<layout::dynamic>::value>(
         Ptr, stride, __spv::MatrixLayout::RowMajor,
         spv_scope_traits<Group>::value);
     break;
   case layout::col_major:
     res.spvm = __spirv_JointMatrixLoadINTEL<
-        T, NumRows, NumCols, spv_matrix_use_traits<use::accumulator>::value,
+        T, S, NumRows, NumCols, spv_matrix_use_traits<use::accumulator>::value,
         spv_matrix_layout_traits<layout::dynamic>::value>(
         Ptr, stride, __spv::MatrixLayout::ColumnMajor,
         spv_scope_traits<Group>::value);
     break;
   case sycl::ext::intel::experimental::matrix::layout::packed:
     res.spvm = __spirv_JointMatrixLoadINTEL<
-        T, NumRows, NumCols, spv_matrix_use_traits<use::accumulator>::value,
+        T, S, NumRows, NumCols, spv_matrix_use_traits<use::accumulator>::value,
         spv_matrix_layout_traits<layout::dynamic>::value>(
         Ptr, stride, __spv::MatrixLayout::Packed,
         spv_scope_traits<Group>::value);
@@ -257,7 +263,7 @@ joint_matrix_load(Group sg,
 #else
   T *Ptr = src.get();
   res.spvm =
-      __spirv_JointMatrixLoadINTEL<T, NumRows, NumCols,
+      __spirv_JointMatrixLoadINTEL<T, S, NumRows, NumCols,
                                    spv_matrix_use_traits<Use>::value,
                                    spv_matrix_layout_traits<Layout>::value>(
           Ptr, stride, spv_matrix_layout_traits<Layout>::value,
@@ -294,21 +300,21 @@ inline __SYCL_ALWAYS_INLINE void joint_matrix_store(
     assert(false && "Invalid Memory Layout!");
   case layout::row_major:
     __spirv_JointMatrixStoreINTEL<
-        T, NumRows, NumCols, spv_matrix_use_traits<use::accumulator>::value,
+        T, T, NumRows, NumCols, spv_matrix_use_traits<use::accumulator>::value,
         spv_matrix_layout_traits<layout::dynamic>::value>(
         Ptr, src.spvm, stride, __spv::MatrixLayout::RowMajor,
         spv_scope_traits<Group>::value);
     break;
   case layout::col_major:
     __spirv_JointMatrixStoreINTEL<
-        T, NumRows, NumCols, spv_matrix_use_traits<use::accumulator>::value,
+        T, T, NumRows, NumCols, spv_matrix_use_traits<use::accumulator>::value,
         spv_matrix_layout_traits<layout::dynamic>::value>(
         Ptr, src.spvm, stride, __spv::MatrixLayout::ColumnMajor,
         spv_scope_traits<Group>::value);
     break;
   case sycl::ext::intel::experimental::matrix::layout::packed:
     __spirv_JointMatrixStoreINTEL<
-        T, NumRows, NumCols, spv_matrix_use_traits<use::accumulator>::value,
+        T, T, NumRows, NumCols, spv_matrix_use_traits<use::accumulator>::value,
         spv_matrix_layout_traits<layout::dynamic>::value>(
         Ptr, src.spvm, stride, __spv::MatrixLayout::Packed,
         spv_scope_traits<Group>::value);
@@ -380,20 +386,23 @@ inline __SYCL_ALWAYS_INLINE
 
 // This function rounds the bottom 13 bits up or down, and then zeros out the
 // bottom bits
-inline __SYCL_ALWAYS_INLINE float round_to_tf32(float &a) {
-#if defined(__SYCL_DEVICE_ONLY__) && defined(__NVPTX__)
+inline __SYCL_ALWAYS_INLINE float round_to_tf32(const float &a) {
+#if defined(__SYCL_DEVICE_ONLY__)
+#if defined(__NVPTX__)
   int32_t tmp_int = __nvvm_f2tf32_rna(a);
   return __nvvm_bitcast_i2f(tmp_int);
 #else
-  uint32_t tmp_uint = reinterpret_cast<uint32_t &>(a);
+  return __spirv_RoundFToTF32INTEL(a);
+#endif // defined(__NVPTX__)
+#else
+  uint32_t tmp_uint = reinterpret_cast<const uint32_t &>(a);
   tmp_uint += 0x1000u;
   tmp_uint &= 0xFFFFE000u;
   float ret = 0;
   std::memcpy(&ret, &tmp_uint, sizeof(float));
   return ret;
-#endif // defined(__SYCL_DEVICE_ONLY__) && defined(__NVPTX__)
+#endif // defined(__SYCL_DEVICE_ONLY__)
 }
-
 } // namespace matrix
 } // namespace experimental
 } // namespace oneapi
diff --git a/sycl/test-e2e/Matrix/XMX8/element_wise_all_ops_tf32.cpp b/sycl/test-e2e/Matrix/XMX8/element_wise_all_ops_tf32.cpp
new file mode 100644
index 0000000000000..2af9d9176548b
--- /dev/null
+++ b/sycl/test-e2e/Matrix/XMX8/element_wise_all_ops_tf32.cpp
@@ -0,0 +1,27 @@
+//==----------- element_wise_all_ops_tf32.cpp  - DPC++ joint_matrix---------==//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+// REQUIRES: matrix-xmx8
+
+// RUN: %clangxx -fsycl %s -o %t.out -Dsycl/test-e2e_EXT_ONEAPI_MATRIX_VERSION=4
+// RUN: %CPU_RUN_PLACEHOLDER %t.out
+// RUN: %GPU_RUN_PLACEHOLDER %t.out
+
+// XFAIL:*
+
+#include <iostream>
+#include <random>
+#include <sycl/sycl.hpp>
+
+using namespace sycl;
+using namespace sycl::ext::intel;
+using namespace sycl::ext::oneapi;
+using namespace sycl::ext::oneapi::experimental::matrix;
+
+#define SG_SZ 8
+
+#include "../element_wise_all_ops_tf32_impl.hpp"
diff --git a/sycl/test-e2e/Matrix/XMX8/joint_matrix_tf32.cpp b/sycl/test-e2e/Matrix/XMX8/joint_matrix_tf32.cpp
new file mode 100644
index 0000000000000..c35a69f05f460
--- /dev/null
+++ b/sycl/test-e2e/Matrix/XMX8/joint_matrix_tf32.cpp
@@ -0,0 +1,27 @@
+//==---------------- joint_matrix_tf32.cpp  - DPC++ joint_matrix------------==//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+// REQUIRES: matrix-xmx8
+
+// RUN: %clangxx -fsycl %s -o %t.out -Dsycl/test-e2e_EXT_ONEAPI_MATRIX_VERSION=4
+// RUN: %CPU_RUN_PLACEHOLDER %t.out
+// RUN: %GPU_RUN_PLACEHOLDER %t.out
+
+// XFAIL:*
+
+#include <iostream>
+#include <random>
+#include <sycl/sycl.hpp>
+
+using namespace sycl;
+using namespace sycl::ext::intel;
+using namespace sycl::ext::oneapi;
+using namespace sycl::ext::oneapi::experimental::matrix;
+
+#define SG_SZ 8
+
+#include "../joint_matrix_tf32_impl.hpp"
diff --git a/sycl/test-e2e/Matrix/element_wise_all_ops_tf32.cpp b/sycl/test-e2e/Matrix/element_wise_all_ops_tf32.cpp
new file mode 100644
index 0000000000000..c693a186be970
--- /dev/null
+++ b/sycl/test-e2e/Matrix/element_wise_all_ops_tf32.cpp
@@ -0,0 +1,27 @@
+//==----------- element_wise_all_ops_tf32.cpp  - DPC++ joint_matrix---------==//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+// REQUIRES: matrix
+
+// RUN: %clangxx -fsycl %s -o %t.out -Dsycl/test-e2e_EXT_ONEAPI_MATRIX_VERSION=4
+// RUN: %CPU_RUN_PLACEHOLDER %t.out
+// RUN: %GPU_RUN_PLACEHOLDER %t.out
+
+// XFAIL:*
+
+#include <iostream>
+#include <random>
+#include <sycl/sycl.hpp>
+
+using namespace sycl;
+using namespace sycl::ext::intel;
+using namespace sycl::ext::oneapi;
+using namespace sycl::ext::oneapi::experimental::matrix;
+
+#define SG_SZ 16
+
+#include "element_wise_all_ops_tf32_impl.hpp"
diff --git a/sycl/test-e2e/Matrix/element_wise_all_ops_tf32_impl.hpp b/sycl/test-e2e/Matrix/element_wise_all_ops_tf32_impl.hpp
new file mode 100644
index 0000000000000..77a84c6533b23
--- /dev/null
+++ b/sycl/test-e2e/Matrix/element_wise_all_ops_tf32_impl.hpp
@@ -0,0 +1,239 @@
+
+#define TM 8
+#define TN SG_SZ
+#define TK 16
+
+template <typename T, size_t NUM_ROWS, size_t NUM_COLS> struct big_matrix {
+public:
+  T *mat;
+
+public:
+  T *get_data() { return mat; }
+  void set_data(T *data) { mat = data; }
+  big_matrix(T *data) : mat(data) {}
+};
+
+template <typename T, size_t M, size_t N>
+void assert_ops_ref(host_accessor<T, 2, access::mode::read> C,
+                    const float ref) {
+  for (size_t i = 0; i < M; i++)
+    for (size_t j = 0; j < N; j++) {
+      auto diff = C[i][j] - ref;
+      assert(std::fabs(static_cast<float>(diff)) <
+             std::numeric_limits<float>::epsilon());
+    }
+}
+template <typename T, typename Ts, size_t M, size_t N>
+void matrix_verify_add(queue q, big_matrix<Ts, M, N> &A, nd_range<2> &r,
+                       const float ref) {
+  buffer<Ts, 2> bufA(A.get_data(), range<2>(M, N));
+
+  q.submit([&](handler &cgh) {
+     sycl::accessor accA{bufA, cgh, sycl::read_write};
+
+     cgh.parallel_for<class add_matrix>(
+         r, [accA](nd_item<2> spmd_item) [[intel::reqd_sub_group_size(SG_SZ)]] {
+           const auto global_idx = spmd_item.get_global_id(0);
+           const auto global_idy = spmd_item.get_global_id(1);
+           const auto sg_startx = global_idx - spmd_item.get_local_id(0);
+           const auto sg_starty = global_idy - spmd_item.get_local_id(1);
+
+           sub_group sg = spmd_item.get_sub_group();
+           joint_matrix<sub_group, T, use::a, TM, TK, layout::row_major> sub_a;
+
+           joint_matrix_fill(sg, sub_a, round_to_tf32(5.0));
+
+           auto wi_slice_a =
+               ext::intel::experimental::matrix::get_wi_data(sg, sub_a);
+           for (int i = 0; i < wi_slice_a.length(); i++) {
+             wi_slice_a[i] = wi_slice_a[i] + 2;
+           }
+
+           ext::intel::experimental::matrix::joint_matrix_store(
+               sg, sub_a,
+               accA.get_pointer() + (sg_startx * TM) * N +
+                   sg_starty / SG_SZ * TN,
+               N);
+         }); // parallel for
+   }).wait();
+  assert_ops_ref<Ts, M, N>(bufA.get_host_access(sycl::read_only), ref);
+}
+
+template <typename T, typename Ts, size_t M, size_t N>
+void matrix_verify_sub(queue q, big_matrix<Ts, M, N> &A, nd_range<2> &r,
+                       const float ref) {
+  buffer<Ts, 2> bufA(A.get_data(), range<2>(M, N));
+
+  q.submit([&](handler &cgh) {
+     sycl::accessor accA{bufA, cgh, sycl::read_write};
+
+     cgh.parallel_for<class sub_matrix>(
+         r, [accA](nd_item<2> spmd_item) [[intel::reqd_sub_group_size(SG_SZ)]] {
+           const auto global_idx = spmd_item.get_global_id(0);
+           const auto global_idy = spmd_item.get_global_id(1);
+           const auto sg_startx = global_idx - spmd_item.get_local_id(0);
+           const auto sg_starty = global_idy - spmd_item.get_local_id(1);
+
+           sub_group sg = spmd_item.get_sub_group();
+           joint_matrix<sub_group, T, use::a, TM, TK, layout::row_major> sub_a;
+
+           joint_matrix_fill(sg, sub_a, round_to_tf32(5.0));
+
+           auto wi_slice_a =
+               ext::intel::experimental::matrix::get_wi_data(sg, sub_a);
+           for (int i = 0; i < wi_slice_a.length(); i++) {
+             wi_slice_a[i] = wi_slice_a[i] - round_to_tf32(2);
+           }
+           ext::intel::experimental::matrix::joint_matrix_store(
+               sg, sub_a,
+               accA.get_pointer() + (sg_startx * TM) * N +
+                   sg_starty / SG_SZ * TN,
+               N);
+         }); // parallel for
+   }).wait();
+  assert_ops_ref<Ts, M, N>(bufA.get_host_access(sycl::read_only), ref);
+}
+
+template <typename T, typename Ts, size_t M, size_t N>
+void matrix_verify_mul(queue q, big_matrix<Ts, M, N> &A, nd_range<2> &r,
+                       const float ref) {
+  buffer<Ts, 2> bufA(A.get_data(), range<2>(M, N));
+
+  q.submit([&](handler &cgh) {
+     sycl::accessor accA{bufA, cgh, sycl::read_write};
+
+     cgh.parallel_for<class mul_matrix>(
+         r, [accA](nd_item<2> spmd_item) [[intel::reqd_sub_group_size(SG_SZ)]] {
+           const auto global_idx = spmd_item.get_global_id(0);
+           const auto global_idy = spmd_item.get_global_id(1);
+           const auto sg_startx = global_idx - spmd_item.get_local_id(0);
+           const auto sg_starty = global_idy - spmd_item.get_local_id(1);
+
+           sub_group sg = spmd_item.get_sub_group();
+           joint_matrix<sub_group, T, use::a, TM, TK, layout::row_major> sub_a;
+           joint_matrix_fill(sg, sub_a, round_to_tf32(5.0));
+
+           auto wi_slice_a =
+               ext::intel::experimental::matrix::get_wi_data(sg, sub_a);
+           for (int i = 0; i < wi_slice_a.length(); i++) {
+             wi_slice_a[i] = wi_slice_a[i] * round_to_tf32(3.0);
+           }
+           ext::intel::experimental::matrix::joint_matrix_store(
+               sg, sub_a,
+               accA.get_pointer() + (sg_startx * TM) * N +
+                   sg_starty / SG_SZ * TN,
+               N);
+         }); // parallel for
+   }).wait();
+  assert_ops_ref<Ts, M, N>(bufA.get_host_access(sycl::read_only), ref);
+}
+
+template <typename T, typename Ts, size_t M, size_t N>
+void matrix_verify_div(queue q, big_matrix<Ts, M, N> &A, nd_range<2> &r,
+                       const float ref) {
+  buffer<Ts, 2> bufA(A.get_data(), range<2>(M, N));
+
+  q.submit([&](handler &cgh) {
+     sycl::accessor accA{bufA, cgh, sycl::read_write};
+
+     cgh.parallel_for<class div_matrix>(
+         r, [accA](nd_item<2> spmd_item) [[intel::reqd_sub_group_size(SG_SZ)]] {
+           const auto global_idx = spmd_item.get_global_id(0);
+           const auto global_idy = spmd_item.get_global_id(1);
+           const auto sg_startx = global_idx - spmd_item.get_local_id(0);
+           const auto sg_starty = global_idy - spmd_item.get_local_id(1);
+
+           sub_group sg = spmd_item.get_sub_group();
+           joint_matrix<sub_group, T, use::a, TM, TK, layout::row_major> sub_a;
+
+           joint_matrix_fill(sg, sub_a, round_to_tf32(4.0));
+
+           auto wi_slice_a =
+               ext::intel::experimental::matrix::get_wi_data(sg, sub_a);
+           for (int i = 0; i < wi_slice_a.length(); i++) {
+             wi_slice_a[i] = wi_slice_a[i] / round_to_tf32(2.0);
+           }
+           ext::intel::experimental::matrix::joint_matrix_store(
+               sg, sub_a,
+               accA.get_pointer() + (sg_startx * TM) * N +
+                   sg_starty / SG_SZ * TN,
+               N);
+         }); // parallel for
+   }).wait();
+  assert_ops_ref<Ts, M, N>(bufA.get_host_access(sycl::read_only), ref);
+}
+
+template <typename T, typename Ts, size_t M, size_t N>
+void matrix_verify_logic(queue q, big_matrix<Ts, M, N> &A, nd_range<2> &r,
+                         const float ref) {
+  buffer<Ts, 2> bufA(A.get_data(), range<2>(M, N));
+
+  q.submit([&](handler &cgh) {
+     sycl::accessor accA{bufA, cgh, sycl::read_write};
+     cgh.parallel_for<class logic_matrix>(
+         r, [accA](nd_item<2> spmd_item) [[intel::reqd_sub_group_size(SG_SZ)]] {
+           const auto global_idx = spmd_item.get_global_id(0);
+           const auto global_idy = spmd_item.get_global_id(1);
+           const auto sg_startx = global_idx - spmd_item.get_local_id(0);
+           const auto sg_starty = global_idy - spmd_item.get_local_id(1);
+
+           sub_group sg = spmd_item.get_sub_group();
+           joint_matrix<sub_group, T, use::a, TM, TK, layout::row_major> sub_a;
+
+           joint_matrix_fill(sg, sub_a, round_to_tf32(5.0));
+
+           auto wi_slice_a =
+               ext::intel::experimental::matrix::get_wi_data(sg, sub_a);
+           for (int i = 0; i < wi_slice_a.length(); i++) {
+             if (wi_slice_a[i]) {
+               if (wi_slice_a[i] > 2.0 || wi_slice_a[i] >= 2.0 ||
+                   wi_slice_a[i] < 2.0 || wi_slice_a[i] <= 2.0) {
+                 Ts val = (wi_slice_a[i] != 2.0) ? wi_slice_a[i] : 2.0;
+                 val = val - static_cast<float>(1);
+                 val = val + static_cast<float>(1);
+                 if (wi_slice_a[i] == 2.0) {
+                   val = val - static_cast<float>(2);
+                   val = val * static_cast<float>(3);
+                   val = val / static_cast<float>(2);
+
+                 } else {
+                   val = val + static_cast<float>(2);
+                 }
+                 wi_slice_a[i] = val;
+               }
+             }
+           }
+           ext::intel::experimental::matrix::joint_matrix_store(
+               sg, sub_a,
+               accA.get_pointer() + (sg_startx * TM) * N +
+                   sg_starty / SG_SZ * TN,
+               N);
+         }); // parallel for
+   }).wait();
+  assert_ops_ref<Ts, M, N>(bufA.get_host_access(sycl::read_only), ref);
+}
+
+static constexpr size_t MATRIX_M = TM * 2;
+static constexpr size_t MATRIX_N = TN * 2;
+float A[MATRIX_M][MATRIX_N];
+float D[MATRIX_M][MATRIX_N];
+
+int main() {
+
+  big_matrix<float, MATRIX_M, MATRIX_N> MD((float *)&D);
+  big_matrix<float, MATRIX_M, MATRIX_N> MA((float *)&A);
+
+  size_t NDRangeM = MATRIX_M / TM;
+  size_t NDRangeN = MATRIX_N / TN;
+  queue q;
+  nd_range<2> r({NDRangeM, NDRangeN * SG_SZ}, {1, 1 * SG_SZ});
+
+  matrix_verify_add<precision::tf32, float, MATRIX_M, MATRIX_N>(q, MA, r, 7.0);
+  matrix_verify_sub<precision::tf32, float, MATRIX_M, MATRIX_N>(q, MA, r, 3.0);
+  matrix_verify_mul<precision::tf32, float, MATRIX_M, MATRIX_N>(q, MA, r, 15.0);
+  matrix_verify_div<precision::tf32, float, MATRIX_M, MATRIX_N>(q, MA, r, 2.0);
+  matrix_verify_logic<precision::tf32, float, MATRIX_M, MATRIX_N>(q, MA, r,
+                                                                  7.0);
+
+  return 0;
+}
diff --git a/sycl/test-e2e/Matrix/joint_matrix_tf32.cpp b/sycl/test-e2e/Matrix/joint_matrix_tf32.cpp
new file mode 100644
index 0000000000000..f50ac79bd0a46
--- /dev/null
+++ b/sycl/test-e2e/Matrix/joint_matrix_tf32.cpp
@@ -0,0 +1,27 @@
+//==---------------- joint_matrix_tf32.cpp  - DPC++ joint_matrix------------==//
+//
+// Part of the LLVM Project, under the Apache License v2.0 with LLVM Exceptions.
+// See https://llvm.org/LICENSE.txt for license information.
+// SPDX-License-Identifier: Apache-2.0 WITH LLVM-exception
+//
+//===----------------------------------------------------------------------===//
+// REQUIRES: matrix
+
+// RUN: %clangxx -fsycl %s -o %t.out -Dsycl/test-e2e_EXT_ONEAPI_MATRIX_VERSION=4
+// RUN: %CPU_RUN_PLACEHOLDER %t.out
+// RUN: %GPU_RUN_PLACEHOLDER %t.out
+
+// XFAIL:*
+
+#include <iostream>
+#include <random>
+#include <sycl/sycl.hpp>
+
+using namespace sycl;
+using namespace sycl::ext::intel;
+using namespace sycl::ext::oneapi;
+using namespace sycl::ext::oneapi::experimental::matrix;
+
+#define SG_SZ 16
+
+#include "joint_matrix_tf32_impl.hpp"
diff --git a/sycl/test-e2e/Matrix/joint_matrix_tf32_impl.hpp b/sycl/test-e2e/Matrix/joint_matrix_tf32_impl.hpp
new file mode 100644
index 0000000000000..0c6787ecd0ba9
--- /dev/null
+++ b/sycl/test-e2e/Matrix/joint_matrix_tf32_impl.hpp
@@ -0,0 +1,147 @@
+#define TM 8
+#define TN SG_SZ
+#define TK 16
+
+template <typename T, size_t NUM_ROWS, size_t NUM_COLS> struct big_matrix {
+public:
+  T *mat;
+
+public:
+  T *get_data() { return mat; }
+  void set_data(T *data) { mat = data; }
+  big_matrix(T *data) : mat(data) {}
+};
+
+template <typename T1, typename T2, size_t NUM_ROWS_A, size_t NUM_COLS_A,
+          size_t NUM_ROWS_B, size_t NUM_COLS_B, size_t NUM_ROWS_C,
+          size_t NUM_COLS_C>
+void matrix_multiply(big_matrix<T1, NUM_ROWS_C, NUM_COLS_C> &C,
+                     big_matrix<T2, NUM_ROWS_A, NUM_COLS_A> &A,
+                     big_matrix<T2, NUM_ROWS_B, NUM_COLS_B> &B) {
+  size_t M = NUM_ROWS_C;
+  size_t N = NUM_COLS_C;
+  size_t K = NUM_COLS_A;
+
+  assert(NUM_ROWS_C == NUM_ROWS_A && NUM_COLS_A == NUM_ROWS_B);
+  size_t NDRangeM = M / TM;
+  size_t NDRangeN = N / TN;
+  buffer<float, 2> bufA(A.get_data(), range<2>(M, K));
+  buffer<float, 2> bufB(B.get_data(), range<2>(K, N));
+  buffer<float, 2> bufC((float *)C.get_data(), range<2>(M, N));
+
+  queue q;
+  q.submit([&](handler &cgh) {
+     auto accC = bufC.get_access<access::mode::read_write>(cgh);
+     auto accA = bufA.get_access<access::mode::read_write>(cgh);
+     auto accB = bufB.get_access<access::mode::read_write>(cgh);
+
+     cgh.parallel_for<class imatrix>(
+         nd_range<2>({NDRangeM, NDRangeN * SG_SZ}, {1, 1 * SG_SZ}),
+         [=](nd_item<2> spmd_item) [[intel::reqd_sub_group_size(SG_SZ)]]
+
+         {
+           // The matrix API has to be accessed by all the workitems in a
+           // subgroup these functions will be called once by the subgroup no
+           // code divergence between the workitems
+           const auto global_idx = spmd_item.get_global_id(0);
+           const auto global_idy = spmd_item.get_global_id(1);
+           const auto sg_startx = global_idx - spmd_item.get_local_id(0);
+           const auto sg_starty = global_idy - spmd_item.get_local_id(1);
+
+           sub_group sg = spmd_item.get_sub_group();
+           joint_matrix<sub_group, precision::tf32, use::a, TM, TK,
+                        layout::row_major>
+               sub_a;
+           joint_matrix<sub_group, precision::tf32, use::b, TK, TN,
+                        layout::row_major>
+               sub_b;
+           joint_matrix<sub_group, float, use::accumulator, TM, TN> sub_c;
+           joint_matrix_load(sg, sub_c,
+                             accC.get_pointer() + (sg_startx * TM) * N +
+                                 sg_starty / SG_SZ * TN,
+                             N, layout::row_major);
+           joint_matrix_fill(sg, sub_a, 42);
+           for (int k = 0; k < K; k += TK) {
+             joint_matrix_load(
+                 sg, sub_a, accA.get_pointer() + (sg_startx * TM) * K + k, K);
+             joint_matrix_load(
+                 sg, sub_b,
+                 accB.get_pointer() + (k) * (N) + sg_starty / SG_SZ * TN, N);
+             // If no rounding to tf32 function is called, joint_matrix_mad
+             // function will work on truncated floats.
+             joint_matrix_apply(sg, sub_a,
+                                [=](float x) { x = round_to_tf32(x); });
+             auto wi_data_b =
+                 sycl::ext::intel::experimental::matrix::get_wi_data(sg, sub_b);
+             for (int i = 0; i < wi_data_b.length(); i++) {
+               wi_data_b[i] = round_to_tf32(wi_data_b[i]);
+             }
+             sub_c = joint_matrix_mad(sg, sub_a, sub_b, sub_c);
+           }
+           auto wi_slice_a =
+               sycl::ext::intel::experimental::matrix::get_wi_data(sg, sub_a);
+           joint_matrix_apply(sg, sub_a, [=](float x) { x *= 2; });
+           joint_matrix_store(sg, sub_c,
+                              accC.get_pointer() + (sg_startx * TM) * N +
+                                  sg_starty / SG_SZ * TN,
+                              N, layout::row_major);
+         }); // parallel for
+   }).wait();
+}
+
+static constexpr size_t MATRIX_M = TM * 2;
+static constexpr size_t MATRIX_N = TN * 2;
+static constexpr size_t MATRIX_K = TK * 2;
+float A[MATRIX_M][MATRIX_K];
+float B[MATRIX_K][MATRIX_N];
+float C[MATRIX_M][MATRIX_N];
+float D[MATRIX_M][MATRIX_N];
+
+void matrix_multiply_ref(float *A_mem, float *B_mem, float *C_mem, int M, int N,
+                         int K) {
+  for (int m = 0; m < M; m++)
+    for (int n = 0; n < N; n++) {
+      for (int k = 0; k < K; k++) {
+        float va = A_mem[m * K + k];
+        float vb = B_mem[k * N + n];
+        C_mem[m * N + n] += va * vb;
+      }
+    }
+}
+
+int main() {
+  for (int i = 0; i < MATRIX_M; i++) {
+    for (int j = 0; j < MATRIX_K; j++) {
+      A[i][j] = 1.0f * (i + j);
+    }
+  }
+  for (int i = 0; i < MATRIX_K; i++) {
+    for (int j = 0; j < MATRIX_N; j++) {
+      B[i][j] = 2.0f * i + 3.0f * j;
+    }
+  }
+  for (int i = 0; i < MATRIX_M; i++) {
+    for (int j = 0; j < MATRIX_N; j++) {
+      C[i][j] = 1.0;
+      D[i][j] = 1.0;
+    }
+  }
+
+  big_matrix<float, MATRIX_M, MATRIX_N> MC((float *)&C);
+  big_matrix<float, MATRIX_M, MATRIX_N> MD((float *)&D);
+  big_matrix<float, MATRIX_M, MATRIX_K> MA((float *)&A);
+  big_matrix<float, MATRIX_K, MATRIX_N> MB((float *)&B);
+  matrix_multiply(MC, MA, MB);
+  matrix_multiply_ref((float *)A, (float *)B, (float *)D, MATRIX_M, MATRIX_N,
+                      MATRIX_K);
+
+  bool res = true;
+  for (int i = 0; i < MATRIX_M; i++) {
+    for (int j = 0; j < MATRIX_N; j++) {
+      if (C[i][j] != D[i][j])
+        res = false;
+    }
+  }
+  std::cout << (res ? "passed" : "failed") << std::endl;
+  return !res;
+}
diff --git a/sycl/test/matrix/matrix-tf32-test.cpp b/sycl/test/matrix/matrix-tf32-test.cpp
new file mode 100644
index 0000000000000..bfea2e4c9a698
--- /dev/null
+++ b/sycl/test/matrix/matrix-tf32-test.cpp
@@ -0,0 +1,156 @@
+// RUN: %clangxx -fsycl -O2 -DSYCL_EXT_ONEAPI_MATRIX_VERSION=4 %s -o %t.out
+
+#include <iostream>
+#include <sycl/sycl.hpp>
+
+using namespace sycl;
+using namespace sycl::ext::oneapi::experimental::matrix;
+
+auto constexpr SG_SZ = 16;
+
+#define TM 8
+#define TN SG_SZ
+#define TK 16
+
+template <typename T, size_t NUM_ROWS, size_t NUM_COLS> struct big_matrix {
+public:
+  T *mat;
+
+public:
+  T *get_data() { return mat; }
+  void set_data(T *data) { mat = data; }
+  big_matrix(T *data) : mat(data) {}
+};
+
+template <typename T1, typename T2, size_t NUM_ROWS_A, size_t NUM_COLS_A,
+          size_t NUM_ROWS_B, size_t NUM_COLS_B, size_t NUM_ROWS_C,
+          size_t NUM_COLS_C>
+void matrix_multiply(big_matrix<T1, NUM_ROWS_C, NUM_COLS_C> &C,
+                     big_matrix<T2, NUM_ROWS_A, NUM_COLS_A> &A,
+                     big_matrix<T2, NUM_ROWS_B, NUM_COLS_B> &B) {
+  size_t M = NUM_ROWS_C;
+  size_t N = NUM_COLS_C;
+  size_t K = NUM_COLS_A;
+
+  assert(NUM_ROWS_C == NUM_ROWS_A && NUM_COLS_A == NUM_ROWS_B);
+  size_t NDRangeM = M / TM;
+  size_t NDRangeN = N / TN;
+  buffer<float, 2> bufA(A.get_data(), range<2>(M, K));
+  buffer<float, 2> bufB(B.get_data(), range<2>(K, N));
+  buffer<float, 2> bufC((float *)C.get_data(), range<2>(M, N));
+
+  queue q;
+  q.submit([&](handler &cgh) {
+     auto accC = bufC.get_access<access::mode::read_write>(cgh);
+     auto accA = bufA.get_access<access::mode::read_write>(cgh);
+     auto accB = bufB.get_access<access::mode::read_write>(cgh);
+
+     cgh.parallel_for<class imatrix>(
+         nd_range<2>({NDRangeM, NDRangeN * SG_SZ}, {1, 1 * SG_SZ}),
+         [=](nd_item<2> spmd_item) [[intel::reqd_sub_group_size(SG_SZ)]]
+
+         {
+           // The matrix API has to be accessed by all the workitems in a
+           // subgroup these functions will be called once by the subgroup no
+           // code divergence between the workitems
+           const auto global_idx = spmd_item.get_global_id(0);
+           const auto global_idy = spmd_item.get_global_id(1);
+           const auto sg_startx = global_idx - spmd_item.get_local_id(0);
+           const auto sg_starty = global_idy - spmd_item.get_local_id(1);
+
+           sub_group sg = spmd_item.get_sub_group();
+           joint_matrix<sub_group, precision::tf32, use::a, TM, TK,
+                        layout::row_major>
+               sub_a;
+           joint_matrix<sub_group, precision::tf32, use::b, TK, TN,
+                        layout::row_major>
+               sub_b;
+           joint_matrix<sub_group, float, use::accumulator, TM, TN> sub_c;
+           joint_matrix_load(sg, sub_c,
+                             accC.get_pointer() + (sg_startx * TM) * N +
+                                 sg_starty / SG_SZ * TN,
+                             N, layout::row_major);
+           joint_matrix_fill(sg, sub_a, 42);
+           for (int k = 0; k < K; k += TK) {
+             joint_matrix_load(
+                 sg, sub_a, accA.get_pointer() + (sg_startx * TM) * K + k, K);
+             joint_matrix_load(
+                 sg, sub_b,
+                 accB.get_pointer() + (k) * (N) + sg_starty / SG_SZ * TN, N);
+             // If no rounding to tf32 function is called, joint_matrix_mad
+             // function will work on truncated floats.
+             joint_matrix_apply(sg, sub_a,
+                                [=](float x) { x = round_to_tf32(x); });
+             auto wi_data_b =
+                 sycl::ext::intel::experimental::matrix::get_wi_data(sg, sub_b);
+             for (int i = 0; i < wi_data_b.length(); i++) {
+               wi_data_b[i] = round_to_tf32(wi_data_b[i]);
+             }
+             sub_c = joint_matrix_mad(sg, sub_a, sub_b, sub_c);
+           }
+           joint_matrix_store(sg, sub_c,
+                              accC.get_pointer() + (sg_startx * TM) * N +
+                                  sg_starty / SG_SZ * TN,
+                              N, layout::row_major);
+         }); // parallel for
+   }).wait();
+}
+
+static constexpr size_t MATRIX_M = TM * 2;
+static constexpr size_t MATRIX_N = TN * 2;
+static constexpr size_t MATRIX_K = TK * 2;
+float A[MATRIX_M][MATRIX_K];
+float B[MATRIX_K][MATRIX_N];
+float C[MATRIX_M][MATRIX_N];
+float D[MATRIX_M][MATRIX_N];
+
+void matrix_multiply_ref(float *A_mem, float *B_mem, float *C_mem, int M, int N,
+                         int K) {
+  for (int m = 0; m < M; m++)
+    for (int n = 0; n < N; n++) {
+      for (int k = 0; k < K; k++) {
+        float va = A_mem[m * K + k];
+        float vb = B_mem[k * N + n];
+        C_mem[m * N + n] += va * vb;
+      }
+    }
+}
+
+int main() {
+  for (int i = 0; i < MATRIX_M; i++) {
+    for (int j = 0; j < MATRIX_K; j++) {
+      A[i][j] = 1.0f * (i + j);
+    }
+  }
+  for (int i = 0; i < MATRIX_K; i++) {
+    for (int j = 0; j < MATRIX_N; j++) {
+      B[i][j] = 2.0f * i + 3.0f * j;
+    }
+  }
+  for (int i = 0; i < MATRIX_M; i++) {
+    for (int j = 0; j < MATRIX_N; j++) {
+      C[i][j] = 1.0;
+      D[i][j] = 1.0;
+    }
+  }
+
+  big_matrix<float, MATRIX_M, MATRIX_N> MC((float *)&C);
+  big_matrix<float, MATRIX_M, MATRIX_N> MD((float *)&D);
+  big_matrix<float, MATRIX_M, MATRIX_K> MA((float *)&A);
+  big_matrix<float, MATRIX_K, MATRIX_N> MB((float *)&B);
+  matrix_multiply(MC, MA, MB);
+  matrix_multiply_ref((float *)A, (float *)B, (float *)D, MATRIX_M, MATRIX_N,
+                      MATRIX_K);
+
+  bool res = true;
+  for (int i = 0; i < MATRIX_M; i++) {
+    for (int j = 0; j < MATRIX_N; j++) {
+      if (C[i][j] != D[i][j])
+        res = false;
+    }
+  }
+  if (res)
+    std::cout << "passed\n";
+  else
+    std::cout << "failed\n";
+}