Increase test coverage in common/dtypes_test.py (#18618)

* Add tests in `common/dtypes_test.py`

* Add tests in `common/dtypes_test.py`

* Add more tests to `/common/dtypes_test.py`

* Add tests in `common/dtypes_test.py`

keras/backend/common/dtypes_test.py

@@ -2,6 +2,7 @@
 
 from keras import backend
 from keras import ops
+from keras.backend.common import dtypes
 from keras.backend.common.variables import ALLOWED_DTYPES
 from keras.backend.torch.core import to_torch_dtype
 from keras.testing import test_case
@@ -62,3 +63,63 @@ def test_result_type_invalid_dtypes(self):
             ValueError, "Invalid `dtypes`. At least one dtype is required."
         ):
             backend.result_type()
+
+    def test_respect_weak_type_for_bool(self):
+        self.assertEqual(dtypes._respect_weak_type("bool", True), "bool")
+
+    def test_respect_weak_type_for_int(self):
+        self.assertEqual(dtypes._respect_weak_type("int32", True), "int")
+
+    def test_respect_weak_type_for_float(self):
+        self.assertEqual(dtypes._respect_weak_type("float32", True), "float")
+
+    def test_resolve_weak_type_for_bfloat16(self):
+        self.assertEqual(dtypes._resolve_weak_type("bfloat16"), "float32")
+
+    def test_resolve_weak_type_for_bfloat16_with_precision(self):
+        self.assertEqual(
+            dtypes._resolve_weak_type("bfloat16", precision="64"), "float64"
+        )
+
+    def test_invalid_dtype_for_keras_promotion(self):
+        with self.assertRaisesRegex(
+            ValueError, "is not a valid dtype for Keras type promotion."
+        ):
+            dtypes._least_upper_bound("invalid_dtype")
+
+    def test_resolve_weak_type_for_invalid_dtype(self):
+        with self.assertRaisesRegex(
+            ValueError, "Invalid value for argument `dtype`. Expected one of"
+        ):
+            dtypes._resolve_weak_type("invalid_dtype")
+
+    def test_resolve_weak_type_for_invalid_precision(self):
+        with self.assertRaisesRegex(
+            ValueError,
+            "Invalid value for argument `precision`. Expected one of",
+        ):
+            dtypes._resolve_weak_type("int32", precision="invalid_precision")
+
+    def test_cycle_detection_in_make_lattice_upper_bounds(self):
+        original_lattice_function = dtypes._type_promotion_lattice
+
+        def mock_lattice():
+            lattice = original_lattice_function()
+            lattice["int32"].append("float32")
+            lattice["float32"].append("int32")
+            return lattice
+
+        dtypes._type_promotion_lattice = mock_lattice
+
+        with self.assertRaisesRegex(
+            ValueError, "cycle detected in type promotion lattice for node"
+        ):
+            dtypes._make_lattice_upper_bounds()
+
+        dtypes._type_promotion_lattice = original_lattice_function
+
+    def test_respect_weak_type_for_invalid_dtype(self):
+        with self.assertRaisesRegex(
+            ValueError, "Invalid value for argument `dtype`. Expected one of"
+        ):
+            dtypes._respect_weak_type("invalid_dtype", True)