diff --git a/tests/test-backend-ops.cpp b/tests/test-backend-ops.cpp
index 2f4117a627de0f..9b796c711f753a 100644
--- a/tests/test-backend-ops.cpp
+++ b/tests/test-backend-ops.cpp
@@ -2144,6 +2144,9 @@ static bool test_backend(ggml_backend_t backend, test_mode mode, const char * op
     // test cases for 1D im2col
     test_cases.emplace_back(new test_im2col(GGML_TYPE_F32, GGML_TYPE_F16, GGML_TYPE_F16, {3000, 128, 1, 1}, {3, 128, 1280, 1}, 1, 0, 1, 0, 1, 0, false));
     test_cases.emplace_back(new test_im2col(GGML_TYPE_F32, GGML_TYPE_F16, GGML_TYPE_F32, {3000, 128, 1, 1}, {3, 128, 1280, 1}, 1, 0, 1, 0, 1, 0, false));
+    // test cases for 2D im2col with large input H and W
+    test_cases.emplace_back(new test_im2col(GGML_TYPE_F32, GGML_TYPE_F16, GGML_TYPE_F16, {1024, 1024, 256, 1}, {3, 3, 256, 1}, 1, 1, 1, 1, 1, 1, true));
+    test_cases.emplace_back(new test_im2col(GGML_TYPE_F32, GGML_TYPE_F16, GGML_TYPE_F32, {1024, 1024, 256, 1}, {3, 3, 256, 1}, 1, 1, 1, 1, 1, 1, true));
 
     test_cases.emplace_back(new test_conv_transpose_1d());
     test_cases.emplace_back(new test_conv_transpose_1d({3,2,1,1}, {2,3,2,1}, 3, 0, 1));
@@ -2286,6 +2289,8 @@ static bool test_backend(ggml_backend_t backend, test_mode mode, const char * op
     test_cases.emplace_back(new test_mul_mat(GGML_TYPE_F16, GGML_TYPE_F32,  83, 2,   64, { 8,  1}, {4, 1}));
     test_cases.emplace_back(new test_mul_mat(GGML_TYPE_F16, GGML_TYPE_F32,  64, 45, 128, { 8,  1}, {4, 1}));
     test_cases.emplace_back(new test_mul_mat(GGML_TYPE_F16, GGML_TYPE_F32, 128, 45,  64, { 8,  1}, {4, 1}));
+    // test case for fp16-convert-to-fp32 kernel with large k under fp32 compute dtype
+    test_cases.emplace_back(new test_mul_mat(GGML_TYPE_F16, GGML_TYPE_F16, 512, 262144, 9216, {1, 1}, {1, 1}));
 
     for (ggml_type type_a : base_types) {
         for (ggml_type type_b : {GGML_TYPE_F32 /*, GGML_TYPE_F16 */}) {