diff --git a/tensorflow/compiler/xla/client/lib/math.cc b/tensorflow/compiler/xla/client/lib/math.cc
index f0b4057e039..ee70adc6e7d 100644
--- a/tensorflow/compiler/xla/client/lib/math.cc
+++ b/tensorflow/compiler/xla/client/lib/math.cc
@@ -612,10 +612,28 @@ XlaOp Asinh(XlaOp x) {
   });
 }
 
-// atanh(x) = 0.5 * log((1 + x) / (1 - x))
+// atanh(x) = 0.5 * log((1 + x) / (1 - x)) if abs(x) <= 1
+// atanh(x) = nan                          otherwise
 XlaOp Atanh(XlaOp x) {
-  return Log((ScalarLike(x, 1.0) + x) / (ScalarLike(x, 1.0) - x)) *
-         ScalarLike(x, 0.5);
+  XlaBuilder* b = x.builder();
+  auto do_it = [&](XlaOp x) -> StatusOr<XlaOp> {
+    TF_ASSIGN_OR_RETURN(auto shape, b->GetShape(x));
+    auto naive_result =
+        Log((ScalarLike(x, 1.0) + x) / (ScalarLike(x, 1.0) - x)) *
+        ScalarLike(x, 0.5);
+
+    // TODO(jlebar): For now, we ignore the nan edge case for complex inputs,
+    // because we don't yet have exhaustive tests for complex trig functions.
+    if (primitive_util::IsComplexType(shape.element_type())) {
+      return naive_result;
+    }
+
+    auto nan = FullLike(x, std::numeric_limits<float>::quiet_NaN());
+    return Select(Gt(Abs(x), ScalarLike(x, 1)), nan, naive_result);
+  };
+  return DoWithUpcastToF32(x, {BF16}, [&](XlaOp x) {  //
+    return b->ReportErrorOrReturn(do_it(x));
+  });
 }
 
 XlaOp Cosh(XlaOp x) { return (Exp(x) + Exp(-x)) * ScalarLike(x, 0.5); }
diff --git a/tensorflow/compiler/xla/tests/exhaustive_op_test.cc b/tensorflow/compiler/xla/tests/exhaustive_op_test.cc
index 9f0d6053da4..7f35a61ba33 100644
--- a/tensorflow/compiler/xla/tests/exhaustive_op_test.cc
+++ b/tensorflow/compiler/xla/tests/exhaustive_op_test.cc
@@ -571,11 +571,11 @@ XLA_TEST_P(ExhaustiveOpTest, Asinh) {
   }
   Run(Asinh, std::asinh);
 }
+XLA_TEST_P(ExhaustiveOpTest, Atanh) { Run(Atanh, std::atanh); }
 
 // TODO(jlebar): Enable these.
 // XLA_TEST_P(ExhaustiveOpTest, Acos) { Run(Acos, std::acos); }
 // XLA_TEST_P(ExhaustiveOpTest, Asin) { Run(Asin, std::asin); }
-// XLA_TEST_P(ExhaustiveOpTest, Atanh) { Run(Atanh, std::atanh); }
 // XLA_TEST_P(ExhaustiveOpTest, Atan) { Run(Atan, std::atan); }
 // XLA_TEST_P(ExhaustiveOpTest, Cosh) { Run(Cosh, std::cosh); }
 // XLA_TEST_P(ExhaustiveOpTest, Cos) { Run(Cos, std::cos); }