diff --git a/test/external/fuzz_emulated_long.py b/test/external/fuzz_emulated_long.py
new file mode 100644
index 0000000000..e15c479e85
--- /dev/null
+++ b/test/external/fuzz_emulated_long.py
@@ -0,0 +1,25 @@
+import random
+import z3
+from tinygrad import dtypes, Device
+from tinygrad.uop.validate import uops_to_z3, z3_cdiv
+from tinygrad.uop.ops import UOp
+from tinygrad.uop import Ops
+from tinygrad.uop.decompositions import l2i
+random.seed(42)
+
+def split(v): return (v & 0xFFFFFFFF).cast(dtypes.uint), (v >> 32).cast(dtypes.uint)
+def combine(lo, hi): return lo.cast(dtypes.ulong) | (hi.cast(dtypes.ulong) << 32)
+
+if __name__ == "__main__":
+  for i in range(10_000):
+    if i % 1000 == 0:
+      print(f"Progress: {i}")
+    a = UOp.variable('a0', random.randint(dtypes.ulong.min, 0), random.randint(1, dtypes.ulong.max), dtype=dtypes.ulong)
+    b = UOp.variable('b0', random.randint(dtypes.ulong.min, 0), random.randint(1, dtypes.ulong.max), dtype=dtypes.ulong)
+    expr = combine(*l2i(Ops.IDIV, dtypes.uint, *split(a), *split(b)))
+
+    solver = z3.Solver()
+    z3_expr, x = uops_to_z3(solver, expr, a, b)
+
+    if solver.check(z3_expr != z3_cdiv(a, b)) == z3.sat:
+      assert False, f"Failed: {expr.render()} != x//{d} at x={solver.model()}\nx={u}\nd={d}\n{z3_expr=}\n{x/d=}"
diff --git a/test/test_dtype.py b/test/test_dtype.py
index 8579850e8c..e1bbe695cc 100644
--- a/test/test_dtype.py
+++ b/test/test_dtype.py
@@ -372,6 +372,17 @@ class TestBoolDType(TestDType): DTYPE = dtypes.bool
 
 class TestBFloat16Type(TestDType): DTYPE = dtypes.bfloat16
 
+@unittest.skipUnless(Ops.SHL in Device[Device.DEFAULT].renderer.code_for_op, "half decomp requires bitshift")
+class TestEmulatedFloat16(TestFloat16Type):
+  @classmethod
+  def setUpClass(cls):
+    cls.stack = contextlib.ExitStack()
+    cls.stack.enter_context(Context(EMULATED_DTYPES="half"))
+    cls.DATA = rand_for_dtype(cls.DTYPE, 10)
+
+  @classmethod
+  def tearDownClass(cls): cls.stack.close()
+
 class TestFp8e4m3(TestDType): DTYPE = dtypes.fp8e4m3
 class TestFp8e5m2(TestDType): DTYPE = dtypes.fp8e5m2