diff --git a/chromadb/test/utils/distance_functions.py b/chromadb/test/utils/distance_functions.py
new file mode 100644
index 00000000000..d8f05e8e3a5
--- /dev/null
+++ b/chromadb/test/utils/distance_functions.py
@@ -0,0 +1,7 @@
+from chromadb.utils.distance_functions import cosine
+import numpy as np
+
+
+def test_cosine_zero() -> None:
+    x = np.array([0.0, 0.0], dtype=np.float16)
+    assert cosine(x, x) == 1.0
diff --git a/chromadb/utils/distance_functions.py b/chromadb/utils/distance_functions.py
index e7e77bf7f94..e4c95f87832 100644
--- a/chromadb/utils/distance_functions.py
+++ b/chromadb/utils/distance_functions.py
@@ -1,22 +1,32 @@
 """
 These functions match what the spec of hnswlib is.
 """
+from typing import Union, cast
 import numpy as np
-from numpy.typing import ArrayLike
+from numpy.typing import NDArray
 
+Vector = NDArray[Union[np.int32, np.float32, np.int16, np.float16]]
 
-def l2(x: ArrayLike, y: ArrayLike) -> float:
-    return np.linalg.norm(x - y) ** 2
 
+def l2(x: Vector, y: Vector) -> float:
+    return (np.linalg.norm(x - y) ** 2).item()
 
-def cosine(x: ArrayLike, y: ArrayLike) -> float:
+
+def cosine(x: Vector, y: Vector) -> float:
     # This epsilon is used to prevent division by zero, and the value is the same
     # https://github.com/nmslib/hnswlib/blob/359b2ba87358224963986f709e593d799064ace6/python_bindings/bindings.cpp#L238
+
+    # We need to adapt the epsilon to the precision of the input
     NORM_EPS = 1e-30
-    return 1 - np.dot(x, y) / (
-        (np.linalg.norm(x) + NORM_EPS) * (np.linalg.norm(y) + NORM_EPS)
+    if x.dtype == np.float16 or y.dtype == np.float16:
+        NORM_EPS = 1e-7
+    return cast(
+        float,
+        (
+            1.0 - np.dot(x, y) / ((np.linalg.norm(x) * np.linalg.norm(y)) + NORM_EPS)
+        ).item(),
     )
 
 
-def ip(x: ArrayLike, y: ArrayLike) -> float:
-    return 1 - np.dot(x, y)
+def ip(x: Vector, y: Vector) -> float:
+    return cast(float, (1.0 - np.dot(x, y)).item())