diff --git a/sycl/include/CL/__spirv/spirv_ops.hpp b/sycl/include/CL/__spirv/spirv_ops.hpp
index 020441c071e0b..9cc74c2aceafc 100644
--- a/sycl/include/CL/__spirv/spirv_ops.hpp
+++ b/sycl/include/CL/__spirv/spirv_ops.hpp
@@ -22,11 +22,11 @@
 #endif
 
 #ifdef __SYCL_DEVICE_ONLY__
-template <typename T, std::size_t R, std::size_t C,
+template <typename T, typename Ts, std::size_t R, std::size_t C,
           __spv::MatrixLayout L = __spv::MatrixLayout::RowMajor,
           __spv::Scope::Flag S = __spv::Scope::Flag::Subgroup>
 extern SYCL_EXTERNAL __spv::__spirv_JointMatrixINTEL<T, R, C, L, S> *
-__spirv_JointMatrixLoadINTEL(T *Ptr, std::size_t Stride,
+__spirv_JointMatrixLoadINTEL(Ts *Ptr, std::size_t Stride,
                              __spv::MatrixLayout Layout = L,
                              __spv::Scope::Flag Sc = S, int MemOperand = 0);
 
@@ -97,16 +97,18 @@ template <typename T, std::size_t R, std::size_t C, __spv::MatrixLayout U,
 extern SYCL_EXTERNAL size_t __spirv_JointMatrixWorkItemLengthINTEL(
     __spv::__spirv_JointMatrixINTEL<T, R, C, U, S> *);
 
-template <typename T, std::size_t R, std::size_t C, __spv::MatrixLayout U,
+template <typename T, typename Ts, std::size_t R, std::size_t C,
+          __spv::MatrixLayout U,
           __spv::Scope::Flag S = __spv::Scope::Flag::Subgroup>
-extern SYCL_EXTERNAL T __spirv_VectorExtractDynamic(
+extern SYCL_EXTERNAL Ts __spirv_VectorExtractDynamic(
     __spv::__spirv_JointMatrixINTEL<T, R, C, U, S> *, size_t i);
 
-template <typename T, std::size_t R, std::size_t C, __spv::MatrixLayout U,
+template <typename T, typename Ts, std::size_t R, std::size_t C,
+          __spv::MatrixLayout U,
           __spv::Scope::Flag S = __spv::Scope::Flag::Subgroup>
 extern SYCL_EXTERNAL __spv::__spirv_JointMatrixINTEL<T, R, C, U, S> *
 __spirv_VectorInsertDynamic(__spv::__spirv_JointMatrixINTEL<T, R, C, U, S> *,
-                            T val, size_t i);
+                            Ts val, size_t i);
 
 #ifndef __SPIRV_BUILTIN_DECLARATIONS__
 #error                                                                         \
diff --git a/sycl/include/sycl/ext/oneapi/matrix/matrix-jit.hpp b/sycl/include/sycl/ext/oneapi/matrix/matrix-jit.hpp
index 3368919af9438..bfe215d06790f 100644
--- a/sycl/include/sycl/ext/oneapi/matrix/matrix-jit.hpp
+++ b/sycl/include/sycl/ext/oneapi/matrix/matrix-jit.hpp
@@ -72,42 +72,67 @@ struct joint_matrix {
   }
 };
 
-template <typename Group, typename T, size_t NumRows, size_t NumCols,
-          matrix_layout Layout = matrix_layout::row_major,
+// class tf32 should not hold actual data. It is a tag type only, an empty class
+// with no member variables. Morally, it is equivalent to an enumeration--it
+// just uses the type system to communicate the desired accuracy of arithmetic
+// computations. Users can't construct a tf32
+namespace precision {
+class tf32 {
+  tf32() = delete;
+};
+} // namespace precision
+
+// Differentiating between the "element type" and the "storage element type"
+template <typename T> struct helper_traits {
+  using element_type = T;
+  using storage_element_type = T;
+  using fill_argument_type = T;
+};
+
+template <> struct helper_traits<precision::tf32> {
+  using element_type = precision::tf32;
+  using storage_element_type = float;
+  using fill_argument_type = float;
+};
+
+template <typename Group, typename Te, size_t NumRows, size_t NumCols,
+          matrix_layout Layout = matrix_layout::row_major, typename Tm,
           access::address_space Space>
 inline __SYCL_ALWAYS_INLINE void
 joint_matrix_load(Group sg,
-                  joint_matrix<T, NumRows, NumCols, Layout, Group> &res,
-                  multi_ptr<T, Space> src, size_t stride, matrix_layout MemL) {
+                  joint_matrix<Te, NumRows, NumCols, Layout, Group> &res,
+                  multi_ptr<Tm, Space> src, size_t stride, matrix_layout MemL) {
 #ifdef __SYCL_DEVICE_ONLY__
-  T *Ptr = src.get();
+  // For non tf32 case, check that Te is the same that Tm
+  Tm *Ptr = src.get();
+  using Ts = typename helper_traits<Te>::storage_element_type;
   switch (MemL) {
   default:
     assert(false && "Invalid Memory Layout!");
   case matrix_layout::row_major:
     res.spvm =
-        __spirv_JointMatrixLoadINTEL<T, NumRows, NumCols,
+        __spirv_JointMatrixLoadINTEL<Te, Ts, NumRows, NumCols,
                                      spv_matrix_layout_traits<Layout>::value>(
             Ptr, stride, __spv::MatrixLayout::RowMajor,
             spv_scope_traits<Group>::value);
     break;
   case matrix_layout::col_major:
     res.spvm =
-        __spirv_JointMatrixLoadINTEL<T, NumRows, NumCols,
+        __spirv_JointMatrixLoadINTEL<Te, Ts, NumRows, NumCols,
                                      spv_matrix_layout_traits<Layout>::value>(
             Ptr, stride, __spv::MatrixLayout::ColumnMajor,
             spv_scope_traits<Group>::value);
     break;
   case matrix_layout::packed_a:
     res.spvm =
-        __spirv_JointMatrixLoadINTEL<T, NumRows, NumCols,
+        __spirv_JointMatrixLoadINTEL<Te, Ts, NumRows, NumCols,
                                      spv_matrix_layout_traits<Layout>::value>(
             Ptr, stride, __spv::MatrixLayout::PackedA,
             spv_scope_traits<Group>::value);
     break;
   case matrix_layout::packed_b:
     res.spvm =
-        __spirv_JointMatrixLoadINTEL<T, NumRows, NumCols,
+        __spirv_JointMatrixLoadINTEL<Te, Ts, NumRows, NumCols,
                                      spv_matrix_layout_traits<Layout>::value>(
             Ptr, stride, __spv::MatrixLayout::PackedB,
             spv_scope_traits<Group>::value);
@@ -235,12 +260,16 @@ class wi_element {
   std::size_t idx;
 
 public:
+  using storage_element_type = typename helper_traits<T>::storage_element_type;
   wi_element(joint_matrix<T, NumRows, NumCols, Layout, Group> &Mat,
              std::size_t i)
       : M(Mat), idx(i) {}
-  operator T() {
+  operator storage_element_type() {
 #ifdef __SYCL_DEVICE_ONLY__
-    return __spirv_VectorExtractDynamic(M.spvm, idx);
+    // __spirv_VectorExtractDynamic returns storage_element_type
+    storage_element_type elem =
+        __spirv_VectorExtractDynamic<T, storage_element_type>(M.spvm, idx);
+    return elem;
 #else
     throw runtime_error("joint matrix is not supported on host device.",
                         PI_ERROR_INVALID_DEVICE);
@@ -249,7 +278,10 @@ class wi_element {
 
   explicit operator bool() {
 #ifdef __SYCL_DEVICE_ONLY__
-    return __spirv_VectorExtractDynamic(M.spvm, idx) != static_cast<T>(0);
+    // __spirv_VectorExtractDynamic returns storage_element_type
+    storage_element_type elems =
+        __spirv_VectorExtractDynamic<T, storage_element_type>(M.spvm, idx);
+    return elems != static_cast<storage_element_type>(0);
 #else
     throw runtime_error("joint matrix is not supported on host device.",
                         PI_ERROR_INVALID_DEVICE);
@@ -258,7 +290,9 @@ 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);
+    // __spirv_VectorInsertDynamic takes storage_element_type as argument
+    M.spvm = __spirv_VectorInsertDynamic(
+        M.spvm, static_cast<storage_element_type>(rhs), idx);
     return *this;
 #else
     (void)rhs;
@@ -283,10 +317,12 @@ class wi_element {
 #if __SYCL_DEVICE_ONLY__
 #define OP(op)                                                                 \
   template <typename T2> wi_element &operator op##=(const T2 &rhs) {           \
+    storage_element_type elems =                                               \
+        __spirv_VectorExtractDynamic<T, storage_element_type>(M.spvm, idx);    \
     M.spvm = __spirv_VectorInsertDynamic(                                      \
         M.spvm,                                                                \
-        static_cast<T>(__spirv_VectorExtractDynamic(M.spvm, idx)               \
-                           op static_cast<T>(rhs)),                            \
+        static_cast<storage_element_type>(                                     \
+            elems op static_cast<storage_element_type>(rhs)),                  \
         idx);                                                                  \
     return *this;                                                              \
   }
diff --git a/sycl/test/matrix/matrix-tf32-test.cpp b/sycl/test/matrix/matrix-tf32-test.cpp
new file mode 100644
index 0000000000000..abc616edb2545
--- /dev/null
+++ b/sycl/test/matrix/matrix-tf32-test.cpp
@@ -0,0 +1,175 @@
+// RUN: %clangxx -fsycl -O2 %s -o %t.out
+
+#include <sycl/sycl.hpp>
+#if (SYCL_EXT_ONEAPI_MATRIX == 2)
+#include <iostream>
+
+using namespace sycl;
+using namespace sycl::ext::oneapi::experimental::matrix;
+
+auto constexpr SG_SZ = 8;
+
+#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) {}
+};
+
+// this should be replaced with a DPC++ and spirv functions
+float round_to_tf32(float a) {
+  uint32_t tmp_uint = reinterpret_cast<uint32_t &>(a);
+  tmp_uint += 0x1000u;     // Round up the 13th last bit
+  tmp_uint &= 0xFFFFE000u; // Zero out the bottom 13 bits
+  float ret = reinterpret_cast<float &>(tmp_uint);
+  return ret;
+}
+
+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> 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<precision::tf32, TM, TK> sub_a(sg);
+           joint_matrix<precision::tf32, TK, TN, matrix_layout::packed_b> sub_b(
+               sg);
+           joint_matrix<float, TM, TN> sub_c(sg);
+           joint_matrix_load(sg, sub_c,
+                             accC.get_pointer() + (sg_startx * TM) * N +
+                                 sg_starty / SG_SZ * TN,
+                             N, matrix_layout::row_major);
+           for (int k = 0; k < K; k += TK) {
+             joint_matrix_load(sg, sub_a,
+                               accA.get_pointer() + (sg_startx * TM) * K + k, K,
+                               matrix_layout::row_major);
+             // Assume we alreay in vnni format.
+             joint_matrix_load(sg, sub_b,
+                               accB.get_pointer() + (k) * (N) +
+                                   sg_starty / SG_SZ * TN,
+                               N, matrix_layout::packed_b);
+             // If no rounding to tf32 function is called, the mad function will
+             // work on truncated floats.
+             // TODO: change signature of __spirv_VectorInsertDynamic to have
+             // two types: matrix type can be different from value type
+             for (int i = 0; i < sub_a.get_wi_data().length(); i++) {
+               sub_a.get_wi_data()[i] = round_to_tf32(sub_a.get_wi_data()[i]);
+             }
+             for (int i = 0; i < sub_b.get_wi_data().length(); i++) {
+               sub_b.get_wi_data()[i] = round_to_tf32(sub_b.get_wi_data()[i]);
+             }
+             sub_c = joint_matrix_mad(sg, sub_a, sub_b, sub_c);
+           }
+           auto wi_slice_a = sub_a.get_wi_data();
+           for (int i = 0; i < wi_slice_a.length(); i++) {
+             float elem = wi_slice_a[i];
+             wi_slice_a[i] *= 2;
+           }
+           joint_matrix_store(sg, sub_c,
+                              accC.get_pointer() + (sg_startx * TM) * N +
+                                  sg_starty / SG_SZ * TN,
+                              N, matrix_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];
+        float acc = C_mem[m * 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 / 2; i++) {
+    for (int j = 0; j < MATRIX_N * 2; 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 / 2);
+
+  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";
+}
+#endif // (SYCL_EXT_ONEAPI_MATRIX == 2)