diff --git a/src/common/span.h b/src/common/span.h
index a59c39e72..cb49b84cd 100644
--- a/src/common/span.h
+++ b/src/common/span.h
@@ -621,8 +621,8 @@ XGBOOST_DEVICE auto as_writable_bytes(Span<T, E> s) __span_noexcept ->  // NOLIN
   return {reinterpret_cast<byte*>(s.data()), s.size_bytes()};
 }
 
-}  // namespace common
-}  // namespace xgboost
+}  // namespace common NOLINT
+}  // namespace xgboost NOLINT
 
 #if defined(_MSC_VER) &&_MSC_VER < 1910
 #undef constexpr
diff --git a/src/linear/updater_gpu_coordinate.cu b/src/linear/updater_gpu_coordinate.cu
index 47c58198f..0d4cbe824 100644
--- a/src/linear/updater_gpu_coordinate.cu
+++ b/src/linear/updater_gpu_coordinate.cu
@@ -5,8 +5,10 @@
 
 #include <thrust/execution_policy.h>
 #include <thrust/inner_product.h>
+#include <xgboost/data.h>
 #include <xgboost/linear_updater.h>
 #include "../common/common.h"
+#include "../common/span.h"
 #include "../common/device_helpers.cuh"
 #include "../common/timer.h"
 #include "./param.h"
@@ -17,8 +19,8 @@ namespace linear {
 
 DMLC_REGISTRY_FILE_TAG(updater_gpu_coordinate);
 
-void RescaleIndices(size_t ridx_begin, dh::DVec<Entry> *data) {
-  auto d_data = data->Data();
+void RescaleIndices(size_t ridx_begin, dh::DVec<xgboost::Entry> *data) {
+  auto d_data = data->GetSpan();
   dh::LaunchN(data->DeviceIdx(), data->Size(),
               [=] __device__(size_t idx) { d_data[idx].index -= ridx_begin; });
 }
@@ -27,57 +29,66 @@ class DeviceShard {
   int device_id_;
   dh::BulkAllocator<dh::MemoryType::kDevice> ba_;
   std::vector<size_t> row_ptr_;
-  dh::DVec<Entry> data_;
+  dh::DVec<xgboost::Entry> data_;
   dh::DVec<GradientPair> gpair_;
   dh::CubMemory temp_;
   size_t ridx_begin_;
   size_t ridx_end_;
 
  public:
-  DeviceShard(int device_id, const SparsePage &batch,
+  DeviceShard(int device_id,
+              const SparsePage &batch,  // column batch
               bst_uint row_begin, bst_uint row_end,
               const LinearTrainParam &param,
               const gbm::GBLinearModelParam &model_param)
       : device_id_(device_id),
         ridx_begin_(row_begin),
         ridx_end_(row_end) {
+    if ( IsEmpty() ) { return; }
     dh::safe_cuda(cudaSetDevice(device_id_));
     // The begin and end indices for the section of each column associated with
     // this shard
     std::vector<std::pair<bst_uint, bst_uint>> column_segments;
     row_ptr_ = {0};
+    // iterate through columns
     for (auto fidx = 0; fidx < batch.Size(); fidx++) {
-      auto col = batch[fidx];
+      common::Span<Entry const> col = batch[fidx];
       auto cmp = [](Entry e1, Entry e2) {
         return e1.index < e2.index;
       };
       auto column_begin =
-          std::lower_bound(col.data(), col.data() + col.size(),
-                           Entry(row_begin, 0.0f), cmp);
+          std::lower_bound(col.cbegin(), col.cend(),
+                           xgboost::Entry(row_begin, 0.0f), cmp);
       auto column_end =
-          std::upper_bound(col.data(), col.data() + col.size(),
-                           Entry(row_end, 0.0f), cmp);
+          std::lower_bound(col.cbegin(), col.cend(),
+                           xgboost::Entry(row_end, 0.0f), cmp);
       column_segments.push_back(
-          std::make_pair(column_begin - col.data(), column_end - col.data()));
-      row_ptr_.push_back(row_ptr_.back() + column_end - column_begin);
+          std::make_pair(column_begin - col.cbegin(), column_end - col.cbegin()));
+      row_ptr_.push_back(row_ptr_.back() + (column_end - column_begin));
     }
     ba_.Allocate(device_id_, &data_, row_ptr_.back(), &gpair_,
-                (row_end - row_begin) * model_param.num_output_group);
+                 (row_end - row_begin) * model_param.num_output_group);
 
     for (int fidx = 0; fidx < batch.Size(); fidx++) {
       auto col = batch[fidx];
       auto seg = column_segments[fidx];
       dh::safe_cuda(cudaMemcpy(
-          data_.Data() + row_ptr_[fidx], col.data() + seg.first,
+          data_.GetSpan().subspan(row_ptr_[fidx]).data(),
+          col.data() + seg.first,
           sizeof(Entry) * (seg.second - seg.first), cudaMemcpyHostToDevice));
     }
     // Rescale indices with respect to current shard
     RescaleIndices(ridx_begin_, &data_);
   }
+
+  bool IsEmpty() {
+    return (ridx_end_ - ridx_begin_) == 0;
+  }
+
   void UpdateGpair(const std::vector<GradientPair> &host_gpair,
                    const gbm::GBLinearModelParam &model_param) {
     gpair_.copy(host_gpair.begin() + ridx_begin_ * model_param.num_output_group,
-               host_gpair.begin() + ridx_end_ * model_param.num_output_group);
+                host_gpair.begin() + ridx_end_ * model_param.num_output_group);
   }
 
   GradientPair GetBiasGradient(int group_idx, int num_group) {
@@ -95,7 +106,7 @@ class DeviceShard {
 
   void UpdateBiasResidual(float dbias, int group_idx, int num_groups) {
     if (dbias == 0.0f) return;
-    auto d_gpair = gpair_.Data();
+    auto d_gpair = gpair_.GetSpan();
     dh::LaunchN(device_id_, ridx_end_ - ridx_begin_, [=] __device__(size_t idx) {
       auto &g = d_gpair[idx * num_groups + group_idx];
       g += GradientPair(g.GetHess() * dbias, 0);
@@ -104,9 +115,9 @@ class DeviceShard {
 
   GradientPair GetGradient(int group_idx, int num_group, int fidx) {
     dh::safe_cuda(cudaSetDevice(device_id_));
-    auto d_col = data_.Data() + row_ptr_[fidx];
+    common::Span<xgboost::Entry> d_col = data_.GetSpan().subspan(row_ptr_[fidx]);
     size_t col_size = row_ptr_[fidx + 1] - row_ptr_[fidx];
-    auto d_gpair = gpair_.Data();
+    common::Span<GradientPair> d_gpair = gpair_.GetSpan();
     auto counting = thrust::make_counting_iterator(0ull);
     auto f = [=] __device__(size_t idx) {
       auto entry = d_col[idx];
@@ -120,8 +131,8 @@ class DeviceShard {
   }
 
   void UpdateResidual(float dw, int group_idx, int num_groups, int fidx) {
-    auto d_gpair = gpair_.Data();
-    auto d_col = data_.Data() + row_ptr_[fidx];
+    common::Span<GradientPair> d_gpair = gpair_.GetSpan();
+    common::Span<Entry> d_col = data_.GetSpan().subspan(row_ptr_[fidx]);
     size_t col_size = row_ptr_[fidx + 1] - row_ptr_[fidx];
     dh::LaunchN(device_id_, col_size, [=] __device__(size_t idx) {
       auto entry = d_col[idx];
@@ -158,21 +169,19 @@ class GPUCoordinateUpdater : public LinearUpdater {
     size_t n_devices = static_cast<size_t>(devices.Size());
     size_t row_begin = 0;
     size_t num_row = static_cast<size_t>(p_fmat->Info().num_row_);
-    // Use fast integer ceiling
-    // See https://stackoverflow.com/a/2745086
-    size_t shard_size = (num_row + n_devices - 1) / n_devices;
 
     // Partition input matrix into row segments
     std::vector<size_t> row_segments;
     row_segments.push_back(0);
     for (int d_idx = 0; d_idx < n_devices; ++d_idx) {
-      size_t row_end = std::min(row_begin + shard_size, num_row);
+      size_t shard_size = dist_.ShardSize(num_row, d_idx);
+      size_t row_end = row_begin + shard_size;
       row_segments.push_back(row_end);
       row_begin = row_end;
     }
 
     CHECK(p_fmat->SingleColBlock());
-    const auto &batch = *p_fmat->GetColumnBatches().begin();
+    SparsePage const& batch = *(p_fmat->GetColumnBatches().begin());
 
     shards.resize(n_devices);
     // Create device shards
@@ -194,7 +203,9 @@ class GPUCoordinateUpdater : public LinearUpdater {
     monitor.Start("UpdateGpair");
     // Update gpair
     dh::ExecuteIndexShards(&shards, [&](int idx, std::unique_ptr<DeviceShard>& shard) {
-      shard->UpdateGpair(in_gpair->ConstHostVector(), model->param);
+      if (!shard->IsEmpty()) {
+        shard->UpdateGpair(in_gpair->ConstHostVector(), model->param);
+      }
     });
     monitor.Stop("UpdateGpair");
 
@@ -225,8 +236,13 @@ class GPUCoordinateUpdater : public LinearUpdater {
       // Get gradient
       auto grad = dh::ReduceShards<GradientPair>(
           &shards, [&](std::unique_ptr<DeviceShard> &shard) {
-            return shard->GetBiasGradient(group_idx,
-                                          model->param.num_output_group);
+            if (!shard->IsEmpty()) {
+              GradientPair result =
+                  shard->GetBiasGradient(group_idx,
+                                         model->param.num_output_group);
+              return result;
+            }
+            return GradientPair(0, 0);
           });
 
       auto dbias = static_cast<float>(
@@ -236,8 +252,10 @@ class GPUCoordinateUpdater : public LinearUpdater {
 
       // Update residual
     dh::ExecuteIndexShards(&shards, [&](int idx, std::unique_ptr<DeviceShard>& shard) {
-        shard->UpdateBiasResidual(dbias, group_idx,
-                                  model->param.num_output_group);
+        if (!shard->IsEmpty()) {
+          shard->UpdateBiasResidual(dbias, group_idx,
+                                    model->param.num_output_group);
+        }
       });
     }
   }
@@ -249,8 +267,11 @@ class GPUCoordinateUpdater : public LinearUpdater {
     // Get gradient
     auto grad = dh::ReduceShards<GradientPair>(
         &shards, [&](std::unique_ptr<DeviceShard> &shard) {
-          return shard->GetGradient(group_idx, model->param.num_output_group,
-                                    fidx);
+          if (!shard->IsEmpty()) {
+            return shard->GetGradient(group_idx, model->param.num_output_group,
+                                      fidx);
+          }
+          return GradientPair(0, 0);
         });
 
     auto dw = static_cast<float>(tparam_.learning_rate *
@@ -259,8 +280,11 @@ class GPUCoordinateUpdater : public LinearUpdater {
                                                  tparam_.reg_lambda_denorm));
     w += dw;
 
-    dh::ExecuteIndexShards(&shards, [&](int idx, std::unique_ptr<DeviceShard>& shard) {
-      shard->UpdateResidual(dw, group_idx, model->param.num_output_group, fidx);
+    dh::ExecuteIndexShards(&shards, [&](int idx,
+                                        std::unique_ptr<DeviceShard> &shard) {
+      if (!shard->IsEmpty()) {
+        shard->UpdateResidual(dw, group_idx, model->param.num_output_group, fidx);
+      }
     });
   }
 
diff --git a/tests/cpp/linear/test_linear.cc b/tests/cpp/linear/test_linear.cc
index 2a479a313..4dd27e5de 100644
--- a/tests/cpp/linear/test_linear.cc
+++ b/tests/cpp/linear/test_linear.cc
@@ -1,4 +1,6 @@
-// Copyright by Contributors
+/*!
+ * Copyright 2018 by Contributors
+ */
 #include <xgboost/linear_updater.h>
 #include "../helpers.h"
 #include "xgboost/gbm.h"