diff --git a/src/array_api_extra/_funcs.py b/src/array_api_extra/_funcs.py
index 05a8d17..5e72d3a 100644
--- a/src/array_api_extra/_funcs.py
+++ b/src/array_api_extra/_funcs.py
@@ -367,9 +367,9 @@ def sinc(x: Array, /, *, xp: ModuleType) -> Array:
 
     Parameters
     ----------
-    x : array
+    x : array of floats
         Array (possibly multi-dimensional) of values for which to calculate
-        ``sinc(x)``.
+        ``sinc(x)``. Should have a floating point dtype.
 
     Returns
     -------
@@ -423,5 +423,8 @@ def sinc(x: Array, /, *, xp: ModuleType) -> Array:
            -3.89817183e-17], dtype=array_api_strict.float64)
 
     """
+    if not xp.isdtype(x.dtype, "real floating"):
+        err_msg = "`x` must have a real floating data type."
+        raise ValueError(err_msg)
     y = xp.pi * xp.where(x == 0, xp.asarray(1.0e-20), x)
     return xp.sin(y) / y
diff --git a/tests/test_funcs.py b/tests/test_funcs.py
index 556add1..b37d32b 100644
--- a/tests/test_funcs.py
+++ b/tests/test_funcs.py
@@ -9,7 +9,7 @@
 import pytest
 from numpy.testing import assert_allclose, assert_array_equal, assert_equal
 
-from array_api_extra import atleast_nd, cov, expand_dims, kron
+from array_api_extra import atleast_nd, cov, expand_dims, kron, sinc
 
 if TYPE_CHECKING:
     Array = Any  # To be changed to a Protocol later (see array-api#589)
@@ -224,3 +224,16 @@ def test_positive_negative_repeated(self):
         a = xp.empty((2, 3, 4, 5))
         with pytest.raises(ValueError, match="Duplicate dimensions"):
             expand_dims(a, axis=(3, -3), xp=xp)
+
+
+class TestSinc:
+    def test_simple(self):
+        assert_array_equal(sinc(xp.asarray(0.0), xp=xp), xp.asarray(1.0))
+        w = sinc(xp.linspace(-1, 1, 100), xp=xp)
+        # check symmetry
+        assert_allclose(w, xp.flip(w, axis=0))
+
+    @pytest.mark.parametrize("x", [0, 1 + 3j])
+    def test_dtype(self, x):
+        with pytest.raises(ValueError, match="real floating data type"):
+            sinc(xp.asarray(x), xp=xp)