diff --git a/src/target/llvm/intrin_rule_llvm.cc b/src/target/llvm/intrin_rule_llvm.cc
index eefa547efdee..e519c9eef397 100644
--- a/src/target/llvm/intrin_rule_llvm.cc
+++ b/src/target/llvm/intrin_rule_llvm.cc
@@ -30,6 +30,8 @@
 #include <tvm/tir/op.h>
 #include <tvm/tir/op_attr_types.h>
 
+#include <limits>
+
 #include "../intrin_rule.h"
 
 namespace tvm {
@@ -175,7 +177,15 @@ TVM_REGISTER_OP("tir.asin")
       PrimExpr term7 = term5 * x2 * make_const(x.dtype(), 25) / make_const(x.dtype(), 112);
       PrimExpr term9 = term7 * x2 * make_const(x.dtype(), 1225) / make_const(x.dtype(), 3456);
       PrimExpr term11 = term9 * x2 * make_const(x.dtype(), 3969) / make_const(x.dtype(), 28160);
-      return term1 + term3 + term5 + term7 + term9 + term11;
+      PrimExpr series = term1 + term3 + term5 + term7 + term9 + term11;
+      /* --- domain limit check --- */
+      PrimExpr lower = make_const(x.dtype(), -1.0);
+      PrimExpr upper = make_const(x.dtype(), 1.0);
+      PrimExpr out_range = tir::Or(x<lower, x> upper);
+      // Use a quiet NaN constant
+      PrimExpr nan_const = make_const(x.dtype(), std::numeric_limits<double>::quiet_NaN());
+      // select: if out of [-1,1] → NaN, else → series
+      return tir::Select(out_range, nan_const, series);
     });
 
 TVM_REGISTER_OP("tir.acos")
diff --git a/tests/python/tir-base/test_tir_intrin.py b/tests/python/tir-base/test_tir_intrin.py
index c73e9c36879c..3e731f55fb0e 100644
--- a/tests/python/tir-base/test_tir_intrin.py
+++ b/tests/python/tir-base/test_tir_intrin.py
@@ -100,6 +100,23 @@ def run_test(tvm_intrin, np_func, atol=1e-5, rtol=1e-5):
         func(a, b)
         tvm.testing.assert_allclose(b.numpy(), np_func(a.numpy()), atol=atol, rtol=rtol)
 
+        # Out‐of‐bounds test for asin/acos
+        name = tvm_intrin.__name__
+        if name in ("asin", "acos"):
+            # generate some values outside [-1, 1]
+            n = 8
+            out_np = np.concatenate(
+                [
+                    np.random.uniform(1.1, 2.0, size=n // 2),
+                    np.random.uniform(-2.0, -1.1, size=n // 2),
+                ]
+            ).astype(A.dtype)
+            a2 = tvm.nd.array(out_np, dev)
+            b2 = tvm.nd.array(np.empty_like(out_np), dev)
+            func(a2, b2)
+            # all outputs should be NaN
+            assert np.all(np.isnan(b2.numpy()))
+
     for func in test_funcs:
         atol = rtol = 1e-3 if func[0].__name__ in ["asin", "acos", "atan"] else 1e-5
         run_test(*func, atol, rtol)