diff --git a/folx/ad.py b/folx/ad.py
index f1dc97d..6e06fc0 100644
--- a/folx/ad.py
+++ b/folx/ad.py
@@ -94,6 +94,8 @@ def jvp_fun(s):
             return jax.jvp(f, primals, unravel(s))[1]
 
         eye = jnp.eye(flat_primals.size, dtype=flat_primals.dtype)
+        if hasattr(jax.lax, 'pvary'):
+            eye = jax.lax.pvary(eye, tuple(jax.typeof(flat_primals).vma))
         J = jax.vmap(jvp_fun, out_axes=-1)(eye)
         return J
 
diff --git a/test/test_shard_map.py b/test/test_shard_map.py
new file mode 100644
index 0000000..bd0b73f
--- /dev/null
+++ b/test/test_shard_map.py
@@ -0,0 +1,29 @@
+from functools import partial
+
+import jax
+import jax.numpy as jnp
+import pytest
+from packaging.version import Version
+
+from folx import forward_laplacian
+
+
+@pytest.mark.skipif(
+    Version(jax.__version__) < Version('0.7.1'), reason='jax version too old'
+)
+def test_shard_map_bug_integer_pow():
+    # see https://github.com/microsoft/folx/issues/38
+
+    def f(w, x):
+        return jax.lax.integer_pow(x @ w, 1)
+
+    @jax.smap(out_axes=0, in_axes=(None, 0), axis_name='i')
+    @partial(jax.vmap, in_axes=(None, 0))
+    def test(w, x):
+        return forward_laplacian(partial(f, w))(x)
+
+    x = jnp.ones((1, 16))
+    w = jnp.ones((16, 16))
+
+    with jax.set_mesh(jax.sharding.Mesh(jax.devices()[:1], 'i')):
+        test(w, x)