Add test for eta and mitigate float error. (#7446)

* Add eta test.
* Don't skip test.

tests/cpp/tree/test_tree_stat.cc

@@ -56,4 +56,62 @@ TEST_F(UpdaterTreeStatTest, Exact) {
 TEST_F(UpdaterTreeStatTest, Approx) {
   this->RunTest("grow_histmaker");
 }
+
+class UpdaterEtaTest : public ::testing::Test {
+ protected:
+  std::shared_ptr<DMatrix> p_dmat_;
+  HostDeviceVector<GradientPair> gpairs_;
+  size_t constexpr static kRows = 10;
+  size_t constexpr static kCols = 10;
+  size_t constexpr static kClasses = 10;
+
+  void SetUp() override {
+    p_dmat_ = RandomDataGenerator(kRows, kCols, .5f).GenerateDMatrix(true, false, kClasses);
+    auto g = GenerateRandomGradients(kRows);
+    gpairs_.Resize(kRows);
+    gpairs_.Copy(g);
+  }
+
+  void RunTest(std::string updater) {
+    auto tparam = CreateEmptyGenericParam(0);
+    float eta = 0.4;
+    auto up_0 = std::unique_ptr<TreeUpdater>{
+        TreeUpdater::Create(updater, &tparam, ObjInfo{ObjInfo::kClassification})};
+    up_0->Configure(Args{{"eta", std::to_string(eta)}});
+
+    auto up_1 = std::unique_ptr<TreeUpdater>{
+        TreeUpdater::Create(updater, &tparam, ObjInfo{ObjInfo::kClassification})};
+    up_1->Configure(Args{{"eta", "1.0"}});
+
+    for (size_t iter = 0; iter < 4; ++iter) {
+      RegTree tree_0;
+      {
+        tree_0.param.num_feature = kCols;
+        up_0->Update(&gpairs_, p_dmat_.get(), {&tree_0});
+      }
+
+      RegTree tree_1;
+      {
+        tree_1.param.num_feature = kCols;
+        up_1->Update(&gpairs_, p_dmat_.get(), {&tree_1});
+      }
+      tree_0.WalkTree([&](bst_node_t nidx) {
+        if (tree_0[nidx].IsLeaf()) {
+          EXPECT_NEAR(tree_1[nidx].LeafValue() * eta, tree_0[nidx].LeafValue(), kRtEps);
+        }
+        return true;
+      });
+    }
+  }
+};
+
+TEST_F(UpdaterEtaTest, Hist) { this->RunTest("grow_quantile_histmaker"); }
+
+TEST_F(UpdaterEtaTest, Exact) { this->RunTest("grow_colmaker"); }
+
+TEST_F(UpdaterEtaTest, Approx) { this->RunTest("grow_histmaker"); }
+
+#if defined(XGBOOST_USE_CUDA)
+TEST_F(UpdaterEtaTest, GpuHist) { this->RunTest("grow_gpu_hist"); }
+#endif  // defined(XGBOOST_USE_CUDA)
 }  // namespace xgboost