Add back a default rtol.

tests/cpp/test_multidevice_transformer.cpp

@@ -78,17 +78,21 @@ void validate(
     // BFloat16 error is quite high, but the program has been verified with
     // double precision to be logically correct.
     const double atol = atols[i];
+    constexpr double kRtol = 1.6e-2;
     auto generate_comparison_details = [](at::Tensor expected_out,
                                           at::Tensor out,
-                                          double atol) -> std::string {
+                                          double atol,
+                                          double rtol) -> std::string {
       std::ostringstream oss;
       auto error = (out - expected_out).abs();
-      auto max_absolute_error = error.max().item().to<double>();
       auto max_relative_error =
-          max_absolute_error / expected_out.abs().max().item().to<double>();
-      auto error_count = at::sum(error >= atol).item();
-      indent(oss, 1) << "max absolute error: " << max_absolute_error
-                     << std::endl;
+          (error.max() / expected_out.abs().max()).item().to<double>();
+      auto error_count =
+          at::sum(error >= atol + expected_out.abs() * rtol).item();
+      indent(oss, 1)
+          << "max absolute error under rtol: "
+          << (error - expected_out.abs() * rtol).max().item().to<double>()
+          << std::endl;
       indent(oss, 1) << "max relative error: " << max_relative_error
                      << std::endl;
       indent(oss, 1) << "failing elements: " << error_count << ", "
@@ -97,10 +101,11 @@ void validate(
       return oss.str();
     };
 
-    EXPECT_TRUE(outputs[i].allclose(expected_outputs[i], /*rtol=*/0.0, atol))
+    EXPECT_TRUE(outputs[i].allclose(expected_outputs[i], kRtol, atol))
         << "Output " << i << " mismatches with atol " << atol << ":"
         << std::endl
-        << generate_comparison_details(expected_outputs[i], outputs[i], atol);
+        << generate_comparison_details(
+               expected_outputs[i], outputs[i], atol, kRtol);
   }
 }
 
@@ -881,7 +886,7 @@ TEST_P(DistributedTransformerTest, MHA_Backward) {
   validate(
       expected_outputs,
       out,
-      {1e-5, 0.02, 1e-5, 1e-5, 1e-5, 0.1, 0.1, 0.02, 0.01});
+      {1e-5, 0.02, 1e-5, 1e-4, 1e-4, 0.1, 0.1, 0.1, 0.01});
 }
 
 TEST_P(DistributedTransformerTest, Forward) {