Optimized ApplySplit, BuildHist and UpdatePredictCache functions on CPU (#5244)

* Split up sparse and dense build hist kernels.
* Add `PartitionBuilder`.

tests/cpp/common/test_partition_builder.cc

@@ -0,0 +1,76 @@
+#include <gtest/gtest.h>
+#include <vector>
+#include <string>
+#include <utility>
+
+#include "../../../src/common/row_set.h"
+#include "../helpers.h"
+
+namespace xgboost {
+namespace common {
+
+TEST(PartitionBuilder, BasicTest) {
+  constexpr size_t kBlockSize = 16;
+  constexpr size_t kNodes = 5;
+  constexpr size_t kTasks = 3 + 5 + 10 + 1 + 2;
+
+  std::vector<size_t> tasks = { 3, 5, 10, 1, 2 };
+
+  PartitionBuilder<kBlockSize> builder;
+  builder.Init(kTasks, kNodes, [&](size_t i) {
+    return tasks[i];
+  });
+
+  std::vector<size_t> rows_for_left_node = { 2, 12, 0, 16, 8 };
+
+  for(size_t nid = 0; nid < kNodes; ++nid) {
+    size_t value_left = 0;
+    size_t value_right = 0;
+
+    size_t left_total = tasks[nid] * rows_for_left_node[nid];
+
+    for(size_t j = 0; j < tasks[nid]; ++j) {
+      size_t begin = kBlockSize*j;
+      size_t end = kBlockSize*(j+1);
+
+      auto left  = builder.GetLeftBuffer(nid, begin, end);
+      auto right = builder.GetRightBuffer(nid, begin, end);
+
+      size_t n_left   = rows_for_left_node[nid];
+      size_t n_right = kBlockSize - rows_for_left_node[nid];
+
+      for(size_t i = 0; i < n_left; i++) {
+        left[i] = value_left++;
+      }
+
+      for(size_t i = 0; i < n_right; i++) {
+        right[i] = left_total + value_right++;
+      }
+
+      builder.SetNLeftElems(nid, begin, end, n_left);
+      builder.SetNRightElems(nid, begin, end, n_right);
+    }
+  }
+  builder.CalculateRowOffsets();
+
+  std::vector<size_t> v(*std::max_element(tasks.begin(), tasks.end()) * kBlockSize);
+
+  for(size_t nid = 0; nid < kNodes; ++nid) {
+
+    for(size_t j = 0; j < tasks[nid]; ++j) {
+      builder.MergeToArray(nid, kBlockSize*j, v.data());
+    }
+
+    for(size_t j = 0; j < tasks[nid] * kBlockSize; ++j) {
+      ASSERT_EQ(v[j], j);
+    }
+    size_t n_left  = builder.GetNLeftElems(nid);
+    size_t n_right = builder.GetNRightElems(nid);
+
+    ASSERT_EQ(n_left, rows_for_left_node[nid] * tasks[nid]);
+    ASSERT_EQ(n_right, (kBlockSize - rows_for_left_node[nid]) * tasks[nid]);
+  }
+}
+
+}  // namespace common
+}  // namespace xgboost