From 55e3ae02ac1f13fbcc7a83f5e37a39fd2b142db1 Mon Sep 17 00:00:00 2001
From: Rasmus Munk Larsen <rmlarsen@google.com>
Date: Thu, 4 Nov 2021 18:04:04 -0700
Subject: [PATCH] Compare summation results against forward error bound.

---
 unsupported/test/cxx11_tensor_reduction.cpp | 10 ++++++----
 1 file changed, 6 insertions(+), 4 deletions(-)

diff --git a/unsupported/test/cxx11_tensor_reduction.cpp b/unsupported/test/cxx11_tensor_reduction.cpp
index afcb79570..9648b9c8b 100644
--- a/unsupported/test/cxx11_tensor_reduction.cpp
+++ b/unsupported/test/cxx11_tensor_reduction.cpp
@@ -501,14 +501,16 @@ void test_sum_accuracy() {
 
     // Compute the reference value in double precsion.
     double expected_sum = 0.0;
+    double abs_sum = 0.0;
     for (int i = 0; i < num_elements; ++i) {
       expected_sum += static_cast<double>(tensor(i));
+      abs_sum += static_cast<double>(numext::abs(tensor(i)));
     }
-    // Scale tolerance to account for # elements.  Otherwise, we periodically fail, since
-    // E[sum] == prescribed_mean == 0 for the first iteration.
+    // Test against probabilistic forward error bound. In reality, the error is much smaller
+    // when we use tree summation.
     double err = Eigen::numext::abs(static_cast<double>(sum()) - expected_sum);
-    double tol = Eigen::numext::sqrt(num_elements) * static_cast<double>(test_precision<ScalarType>()) * numext::maxi(1.0, prescribed_mean);
-    VERIFY(err < tol);
+    double tol = numext::sqrt(num_elements) * NumTraits<ScalarType>::epsilon() * static_cast<ScalarType>(abs_sum);
+    VERIFY_LE(err, tol);
   }
 }