🐎 Optimized and restructured B+-Trees

src/CMakeLists.txt

@@ -6,7 +6,7 @@ project (nvm-DS)
 ################################################################################
 
 # Set the mount path of your pmem device where the structures should be stored
-set(PMEM_MNT_PATH "/mnt/pmem/test")
+set(PMEM_MNT_PATH "/mnt/pmem0/test")
 
 # Installation path (creates include and lib within this directory)
 if(NOT PROJECT_INSTALL_DIR)
@@ -40,6 +40,10 @@ if(NOT CMAKE_BUILD_TYPE)
   message(STATUS "Setting build type to 'Release' as none was specified.")
   set(CMAKE_BUILD_TYPE Release CACHE STRING "Choose the type of build." FORCE)
 endif()
+if(CMAKE_BUILD_TYPE EQUAL "Release")
+  # this disables asserts for release builds
+  add_definitions("-DNDEBUG")
+endif()
 
 # show used compiler
 message("Using Compiler: ${CMAKE_CXX_COMPILER_ID}.")
@@ -88,9 +92,9 @@ set(PROJECT_INCLUDE_DIR ${PROJECT_INSTALL_DIR}/include)
 # Including Data Structures #
 #############################
 #
-add_subdirectory(pbptree) # Persistent version of B⁺-Tree
-add_subdirectory(fptree)  # Remake of the FPTree
-add_subdirectory(wbtree)  # Remake of the wB+Tree
+add_subdirectory(pbptrees) # Persistent versions of B⁺-Tree, contains also:
+                           # - Remake of the FPTree
+                           # - Remake of the wB+Tree
 add_subdirectory(ptable)  # BDCC-based analytical table structure
 
 #########################

src/bench/ptable/common.hpp

@@ -21,7 +21,7 @@
 #include <chrono>
 #include <unistd.h>
 #include <experimental/filesystem>
-#include "PTable.hpp"
+#include "ptable/PTable.hpp"
 
 using pmem::obj::make_persistent;
 using pmem::obj::p;
@@ -89,7 +89,7 @@ const int hibit_pos(int n) noexcept {
 
 template<size_t SIZE>
 static inline VectorVector *createPointVector(VectorVector *v) {
-  if (SIZE >= 100) {
+  if constexpr (SIZE >= 100) {
     createPointVector<SIZE / 10>(v);
     v->emplace_back(Vector{SIZE, SIZE / 2});
   }
@@ -129,8 +129,8 @@ void insert (pool<root> &pop, const std::string &path, size_t entries) {
     measures.push_back(diff);
   }
 
-  auto avg = std::accumulate(measures.begin(), measures.end(), 0) / measures.size();
-  auto minmax = std::minmax_element(std::begin(measures), std::end(measures));
+  const auto avg = std::accumulate(measures.begin(), measures.end(), 0) / measures.size();
+  const auto minmax = std::minmax_element(std::begin(measures), std::end(measures));
   LOG("\nInsert Statistics in µs: "
          << "\n\tAvg: \t" << avg
          << "\n\tMin: \t" << *minmax.first

src/bench/trees/common.hpp

@@ -32,7 +32,7 @@
 #include "benchmark/benchmark.h"
 #include "PBPTree.hpp"
 
-using namespace dbis::pbptree;
+using namespace dbis::pbptrees;
 
 using pmem::obj::delete_persistent;
 using pmem::obj::make_persistent;
@@ -45,11 +45,11 @@ using pmem::obj::transaction;
 using MyTuple = std::tuple <int, int, double>;
 using MyKey = unsigned long long;
 constexpr auto TARGET_BRANCH_SIZE = 512;
-constexpr auto TARGET_LEAF_SIZE = 512; //< 512B best performance
+constexpr auto TARGET_LEAF_SIZE = 256; //< 512B best performance
 constexpr auto TARGET_DEPTH = 1;
-constexpr auto IS_HYBRID = false;
-const std::string path = dbis::gPmemPath + "tree_bench.data";
-constexpr auto POOL_SIZE = 1024 * 1024 * 1024 * 1ull; //< 1GB
+constexpr auto IS_HYBRID = 0;
+const std::string path = dbis::gPmemPath + "tree_benchSp.data";
+constexpr auto POOL_SIZE = 1024 * 1024 * 1024 * 4ull; //< 1GB
 constexpr auto LAYOUT = "Tree";
 
 /* wBPTree pre-calculations */
@@ -58,12 +58,12 @@ constexpr unsigned int getBranchKeyswBPTree() {
   constexpr auto keys = getBranchKeyswBPTree<N-1>();
   constexpr auto CL_h = keys + ((keys + 63) / 64) * 8;
   constexpr auto CL = ((CL_h + 63) / 64) * 64;
-  constexpr auto SIZE = CL + keys * (sizeof(MyKey) + 16) + 16; //< CacheLine structure & n keys & n+1 children
-  return (SIZE <= TARGET_BRANCH_SIZE)? keys : ((TARGET_BRANCH_SIZE - CL - 16) / (sizeof(MyKey) + 16));
+  constexpr auto SIZE = CL + keys * (sizeof(MyKey) + 24) + 24; //< CacheLine structure & n keys & n+1 children
+  return (SIZE <= TARGET_BRANCH_SIZE)? keys : ((TARGET_BRANCH_SIZE - CL - 24) / (sizeof(MyKey) + 24));
 }
 template<>
 constexpr unsigned int getBranchKeyswBPTree<1>() {
-  return ((TARGET_BRANCH_SIZE - 64 - 16) / (sizeof(MyKey) + 16));
+  return ((TARGET_BRANCH_SIZE - 64 - 24) / (sizeof(MyKey) + 24));
 }
 template<unsigned int N>
 constexpr unsigned int getLeafKeyswBPTree() {
@@ -91,7 +91,7 @@ constexpr unsigned int getLeafKeysPBPTree() {
 /* FPTree pre-calculations */
 template<unsigned int N>
 constexpr unsigned int getBranchKeysFPTree() {
-  return ((TARGET_BRANCH_SIZE - 28) / (sizeof(MyKey) + 24)); //< lowest branch uses actually less space
+  return ((TARGET_BRANCH_SIZE - 28) / (sizeof(MyKey) + 24));
 }
 template<unsigned int N>
 constexpr unsigned int getLeafKeysFPTree() {
@@ -106,6 +106,33 @@ constexpr unsigned int getLeafKeysFPTree<1>() {
   return ((TARGET_LEAF_SIZE - 64 - 32) / (sizeof(MyKey) + sizeof(MyTuple)));
 }
 
+/* BitPBPTree pre-calculations */
+template<unsigned int N>
+constexpr unsigned int getBranchKeysBitPBPTree() {
+  constexpr auto keys = getBranchKeysBitPBPTree<N-1>();
+  constexpr auto word = sizeof(unsigned long) * 8;
+  constexpr auto BM = (keys + word - 1) / word * 8;
+  constexpr auto SIZE = BM + keys * (sizeof(MyKey) + 24) + 24; //< bitmap structure & n keys & n+1 children
+  return (SIZE <= TARGET_BRANCH_SIZE)? keys : ((TARGET_BRANCH_SIZE - BM - 24) / (sizeof(MyKey) + 24));
+}
+template<>
+constexpr unsigned int getBranchKeysBitPBPTree<1>() {
+  return ((TARGET_BRANCH_SIZE - sizeof(unsigned long) - 24) / (sizeof(MyKey) + 24));
+}
+
+template<unsigned int N>
+constexpr unsigned int getLeafKeysBitPBPTree() {
+  constexpr auto keys = getLeafKeysBitPBPTree<N-1>();
+  constexpr auto word = sizeof(unsigned long) * 8;
+  constexpr auto BM = (keys + word - 1) / word * 8;
+  constexpr auto SIZE = BM + 32 + keys * (sizeof(MyKey) + sizeof(MyTuple));
+  return (SIZE <= TARGET_LEAF_SIZE)? keys : ((TARGET_LEAF_SIZE - BM - 32) / (sizeof(MyKey) + sizeof(MyTuple)));
+}
+template<>
+constexpr unsigned int getLeafKeysBitPBPTree<1>() {
+  return ((TARGET_LEAF_SIZE - sizeof(unsigned long) - 32) / (sizeof(MyKey) + sizeof(MyTuple)));
+}
+
 /* Power of function */
 constexpr uint64_t ipow(uint64_t base, int exp, uint64_t result = 1) {
   return exp < 1 ? result : ipow(base*base, exp/2, (exp % 2) ? result*base : result);
@@ -115,7 +142,7 @@ constexpr uint64_t ipow(uint64_t base, int exp, uint64_t result = 1) {
 constexpr auto LEAFKEYS = getLeafKeysPBPTree<5>(); ///< 5 iterations should be enough
 constexpr auto BRANCHKEYS = getBranchKeysPBPTree<5>() & ~1; ///< make this one even
 constexpr auto ELEMENTS = LEAFKEYS*ipow(BRANCHKEYS+1, TARGET_DEPTH);
-constexpr auto KEYPOS = ELEMENTS/ELEMENTS;
+constexpr auto KEYPOS = 1;
 
 using TreeType = PBPTree<MyKey, MyTuple, BRANCHKEYS, LEAFKEYS>;
 
@@ -149,7 +176,7 @@ class HybridWrapper {
     return node.branch->children.get_ro()[pos];
   }
 
-  inline void recover(const T &tree, Int2Type<true>) const {
+  inline void recover(T &tree, Int2Type<true>) const {
     tree.recover();
   }
   inline void recover(const T &tree, Int2Type<false>) const {
@@ -169,7 +196,7 @@ class HybridWrapper {
     return getChildAt(node, pos, Int2Type<isHybrid>());
   }
 
-  inline void recover(const T &tree) const {
+  inline void recover(T &tree) const {
     recover(tree, Int2Type<isHybrid>());
   }
 };

src/bench/trees/tree_get.cpp

@@ -19,8 +19,8 @@
 
 /* Get benchmarks on Tree */
 static void BM_TreeGet(benchmark::State &state) {
-  std::cout << "BRANCHKEYS: " << BRANCHKEYS
-    << "\nLEAFKEYS: " << LEAFKEYS
+  std::cout << "BRANCHKEYS: " << BRANCHKEYS << " - " << sizeof(TreeType::BranchNode)
+    << "\nLEAFKEYS: " << LEAFKEYS << " - " << sizeof(TreeType::LeafNode)
     << "\n";
   struct root {
     persistent_ptr<TreeType> tree;
@@ -49,11 +49,11 @@ static void BM_TreeGet(benchmark::State &state) {
   auto leaf = node.leaf;
 
   /* BENCHMARKING */
-  unsigned int p;
   for (auto _ : state) {
-   benchmark::DoNotOptimize(
-        p = treeRef.lookupPositionInLeafNode(leaf, LEAFKEYS)
-   );
+    unsigned int p;
+    benchmark::DoNotOptimize(
+      p = treeRef.lookupPositionInLeafNode(leaf, KEYPOS)
+    );
   }
 
   //treeRef.printBranchNode(0, treeRef.rootNode.branch);
@@ -64,5 +64,4 @@ static void BM_TreeGet(benchmark::State &state) {
   std::experimental::filesystem::remove_all(path);
 }
 BENCHMARK(BM_TreeGet);
-
 BENCHMARK_MAIN();

src/bench/trees/tree_insert.cpp

@@ -66,7 +66,9 @@ static void BM_TreeInsert(benchmark::State &state) {
     dbis::PersistEmulation::getBytesWritten();
     state.ResumeTiming();
 
-    split = treeRef.insertInLeafNode(leaf, KEYPOS, reqTup, &splitInfo);
+    transaction::run(pop, [&] {
+      split = treeRef.insertInLeafNode(leaf, KEYPOS, reqTup, &splitInfo);
+    });
 
     state.PauseTiming();
     assert(split == false);
@@ -99,6 +101,6 @@ void prepare(const persistent_ptr<TreeType> tree) {
   switch (KEYPOS) {
     case 1 /*first*/: insertLoop(2, LEAFKEYS); break;
     case ELEMENTS /*last*/:  insertLoop(1, LEAFKEYS-1);break;
-    case ELEMENTS/2 /*middle*/: {insertLoop(1, KEYPOS-1); insertLoop(KEYPOS+1, LEAFKEYS);}
+    case (ELEMENTS+1)/2 /*middle*/: {insertLoop(1, KEYPOS-1); insertLoop(KEYPOS+1, LEAFKEYS);}
   }
 }

src/bench/trees/tree_scan.cpp

@@ -31,27 +31,27 @@ static void BM_TreeScan(benchmark::State &state) {
   if (access(path.c_str(), F_OK) != 0) {
     pop = pool<root>::create(path, LAYOUT, POOL_SIZE);
     transaction::run(pop, [&] {
-        pop.root()->tree = make_persistent<TreeType>();
-        });
-    insert(pop.root()->tree);
+      pop.root()->tree = make_persistent<TreeType>();
+      insert(pop.root()->tree);
+    });
   } else {
     LOG("Warning: " << path << " already exists");
     pop = pool<root>::open(path, LAYOUT);
-    hybridWrapper.recover(*pop.root()->tree);
+    transaction::run(pop, [&] {
+      hybridWrapper.recover(*pop.root()->tree);
+    });
   }
   auto tree = pop.root()->tree;
   auto &treeRef = *tree;
   auto node = treeRef.rootNode;
+  MyKey key;
 
   /* BENCHMARKING */
   for (auto _ : state) {
-
     //benchmark::DoNotOptimize(
-      treeRef.scan([](const auto& k, const auto& v) {
-         const auto key = k;
-        });
-    //);
-    //auto p = treeRef.lookupPositionInLeafNode(leaf, 1);
+    treeRef.scan([&key](const auto& k, const auto& v) {
+        benchmark::DoNotOptimize(key = k);
+    });
   }
   //treeRef.printBranchNode(0, treeRef.rootNode.branch);
   std::cout << "Elements:" << ELEMENTS << "\n";

src/bench/trees/tree_split.cpp

@@ -64,7 +64,9 @@ static void BM_TreeSplit(benchmark::State &state) {
     dbis::PersistEmulation::getBytesWritten();
     state.ResumeTiming();
 
-    treeRef.splitLeafNode(leaf, &splitInfo);
+    transaction::run(pop, [&] {
+      treeRef.splitLeafNode(leaf, &splitInfo);
+    });
 
     state.PauseTiming();
     //treeRef.printLeafNode(0, leaf);

src/fptree/CMakeLists.txt

-project (fptree)
-
-include_directories(${PROJECT_SOURCE_DIR})
-get_property(I_DIRS DIRECTORY ${CMAKE_CURRENT_SOURCE_DIR} PROPERTY INCLUDE_DIRECTORIES)
-set(TEST_INCLUDE_DIRS ${TEST_INCLUDE_DIRS}
-                      ${I_DIRS}
-  CACHE INTERNAL "TESTING: Include Directories" FORCE
-)
-
-set(PROJECT_INCLUDES_F ${PROJECT_INCLUDES_F}
-                       ${CMAKE_CURRENT_SOURCE_DIR}/PTree.hpp
-                       ${CMAKE_CURRENT_SOURCE_DIR}/FPTree.hpp
-                       PARENT_SCOPE)

src/pbptree/CMakeLists.txt → src/pbptrees/CMakeLists.txt

@@ -12,7 +12,11 @@ set(TEST_INCLUDE_DIRS ${TEST_INCLUDE_DIRS}
 ################
 #
 set(PROJECT_INCLUDES_F ${PROJECT_INCLUDES_F}
-                       ${CMAKE_CURRENT_SOURCE_DIR}/BitPBPTree.hpp
                        ${CMAKE_CURRENT_SOURCE_DIR}/PBPTree.hpp
                        ${CMAKE_CURRENT_SOURCE_DIR}/UnsortedPBPTree.hpp
+                       ${CMAKE_CURRENT_SOURCE_DIR}/BitPBPTree.hpp
+                       ${CMAKE_CURRENT_SOURCE_DIR}/PTree.hpp
+                       ${CMAKE_CURRENT_SOURCE_DIR}/FPTree.hpp
+                       ${CMAKE_CURRENT_SOURCE_DIR}/wBPTree.hpp
+                       ${CMAKE_CURRENT_SOURCE_DIR}/wHBPTree.hpp
                        PARENT_SCOPE)

src/pbptrees/README.md

+Persistent B<sup>+</sup>-Trees
+==============================
+

src/wbtree/wHBPTree.hpp → src/pbptrees/wHBPTree.hpp

@@ -30,9 +30,9 @@
 #include <libpmemobj++/utils.hpp>
 
 #include "config.h"
-#include "utils/ElementOfRankK.hpp"
+#include "utils/BitOperations.hpp"
 
-namespace dbis::wbptree {
+namespace dbis::pbptrees {
 
 using pmem::obj::delete_persistent;
 using pmem::obj::make_persistent;
@@ -125,17 +125,15 @@ class wHBPTree {
     std::array<uint8_t, E+1> slot; ///< slot array for indirection, first = num
     std::bitset<E> b;              ///< bitset for valid entries
 
-    unsigned int getFreeZero() const {
-      unsigned int idx = 0;
-      while (idx < E && b.test(idx)) ++idx;
-      return idx;
+    inline const auto getFreeZero() const {
+      return BitOperations::getFreeZero(b);
     }
   };
 
   /**
    * A structure for representing a leaf node of a B+ tree.
    */
-  struct LeafNode {
+  struct alignas(64) LeafNode {
     /**
      * Constructor for creating a new empty leaf node.
      */
@@ -153,7 +151,7 @@ class wHBPTree {
   /**
    * A structure for representing an branch node (branch node) of a B+ tree.
    */
-  struct BranchNode {
+  struct alignas(64) BranchNode {
     /**
      * Constructor for creating a new empty branch node.
      */
@@ -207,8 +205,8 @@ class wHBPTree {
     Node rightChild; ///< the resulting rhs child node
   };
 
-  unsigned int                depth; ///< the depth of the tree, i.e. the number of levels (0 => rootNode is LeafNode)
-  Node                     rootNode; ///< pointer to the root node
+  unsigned int      depth; ///< the depth of the tree, i.e. the number of levels (0 => rootNode is LeafNode)
+  Node           rootNode; ///< pointer to the root node
   pptr<LeafNode> leafList; ///< pointer to the most left leaf node. Necessary for recovery
 
   public:
@@ -297,34 +295,31 @@ class wHBPTree {
    * @param val the value that is associated with the key
    */
   void insert(const KeyType &key, const ValueType &val) {
-    auto pop = pmem::obj::pool_by_vptr(this);
-    transaction::run(pop, [&] {
-      SplitInfo splitInfo;
+    SplitInfo splitInfo;
 
-      bool wasSplit = false;
-      if (depth == 0) {
-        /// the root node is a leaf node
-        auto n = rootNode.leaf;
-        wasSplit = insertInLeafNode(n, key, val, &splitInfo);
-      } else {
-        /// the root node is a branch node
-        auto n = rootNode.branch;
-        wasSplit = insertInBranchNode(n, depth, key, val, &splitInfo);
-      }
-      if (wasSplit) {
-        /* we had an overflow in the node and therefore the node is split */
-        const auto root = newBranchNode();
-        auto &rootRef = *root;
-        rootRef.keys[0] = splitInfo.key;
-        rootRef.children[0] = splitInfo.leftChild;
-        rootRef.children[N] = splitInfo.rightChild;
-        rootRef.search.slot[1] = 0;
-        rootRef.search.b.set(0);
-        rootRef.search.slot[0] = 1;
-        rootNode.branch = root;
-        ++depth;
-      }
-    });
+    bool wasSplit = false;
+    if (depth == 0) {
+      /// the root node is a leaf node
+      auto n = rootNode.leaf;
+      wasSplit = insertInLeafNode(n, key, val, &splitInfo);
+    } else {
+      /// the root node is a branch node
+      auto n = rootNode.branch;
+      wasSplit = insertInBranchNode(n, depth, key, val, &splitInfo);
+    }
+    if (wasSplit) {
+      /* we had an overflow in the node and therefore the node is split */
+      const auto root = newBranchNode();
+      auto &rootRef = *root;
+      rootRef.keys[0] = splitInfo.key;
+      rootRef.children[0] = splitInfo.leftChild;
+      rootRef.children[N] = splitInfo.rightChild;
+      rootRef.search.slot[1] = 0;
+      rootRef.search.b.set(0);
+      rootRef.search.slot[0] = 1;
+      rootNode.branch = root;
+      ++depth;
+    }
   }
 
   /**
@@ -358,8 +353,6 @@ class wHBPTree {
    */
   bool erase(const KeyType &key) {
     bool deleted = false;
-    auto pop = pmem::obj::pool_by_vptr(this);
-    transaction::run(pop, [&] {
       if (depth == 0) {
         /* special case: the root node is a leaf node and there is no need to
          * handle underflow */
@@ -371,7 +364,6 @@ class wHBPTree {
         assert(node != nullptr);
         deleted = eraseFromBranchNode(node, depth, key);
       }
-    });
     return deleted;
   }
  /**
@@ -430,14 +422,14 @@ class wHBPTree {
     /// we traverse to the leftmost leaf node
     auto node = rootNode;
     auto d = depth;
-    while ( d-- > 0) node = node.branch->children[0];
+    while (d-- > 0) node = node.branch->children[0];
     auto leaf = node.leaf;
-
     while (leaf != nullptr) {
       const auto &leafRef = *leaf;
       /// for each key-value pair call func
+      const auto &bits = leafRef.search.get_ro().b;
       for (auto i = 0u; i < M; i++) {
-        if (!leafRef.search.get_ro().b.test(i)) continue;
+        if (!bits.test(i)) continue;
         const auto &key = leafRef.keys.get_ro()[i];
         const auto &val = leafRef.values.get_ro()[i];
         func(key, val);
@@ -462,8 +454,9 @@ class wHBPTree {
     while (!higherThanMax && leaf != nullptr) {
       const auto &leafRef = *leaf;
       /// for each key-value pair within the range call func
+      const auto &bits = leafRef.search.get_ro().b;
       for (auto i = 0u; i < M; i++) {
-        if (!leafRef.search.get_ro().b.test(i)) continue;
+        if (!bits.test(i)) continue;
         auto &key = leafRef.keys.get_ro()[i];
         if (key < minKey) continue;
         if (key > maxKey) { higherThanMax = true; continue; }
@@ -509,7 +502,7 @@ class wHBPTree {
 
       /// move all entries behind this position to a new sibling node
       pptr<LeafNode> sibling = newLeafNode();
-      auto &sibRef = *sibling; 
+      auto &sibRef = *sibling;
       auto &sibSlots = sibRef.search.get_rw().slot;
       sibSlots[0] = slotArray[0] - middle;
       for (auto i = 1u; i < sibSlots[0] + 1; i++) {
@@ -1351,6 +1344,6 @@ class wHBPTree {
   }
 
 }; /* end class wHBPTree */
-} /* namespace dbis::wbptree */
+} /* namespace dbis::pbptrees */
 
 #endif /* DBIS_wHBPTree_hpp_ */

src/test/BitPBPTreeTest.cpp

@@ -24,7 +24,7 @@
 #include "BitPBPTree.hpp"
 
 
-using namespace dbis::pbptree;
+using namespace dbis::pbptrees;
 
 using pmem::obj::delete_persistent_atomic;
 using pmem::obj::pool;
@@ -93,7 +93,7 @@ TEST_CASE("Finding the leaf node containing a key", "[BitPBPTree]") {
   /* -------------------------------------------------------------------------------------------- */
   SECTION("Looking up a key in a leaf node") {
     auto &btree = *rootRef.btree10;
-    const auto node = btree.newLeafNode();
+    auto node = btree.newLeafNode();
     auto &nodeRef = *node;
     for (auto i = 0; i < 10; i++) {
       nodeRef.keys.get_rw()[i] = i + 1;
@@ -346,7 +346,7 @@ TEST_CASE("Finding the leaf node containing a key", "[BitPBPTree]") {
     btree.underflowAtBranchLevel(innerNodes[0], 0, innerNodes[1]);
 
     REQUIRE(node1Ref.bits.get_ro().count() == 1);
-    REQUIRE((node1Ref.keys.get_ro())[btree.findMinKeyInNode(innerNodes[0])] == 9);
+    REQUIRE((node1Ref.keys.get_ro())[dbis::findMinKeyAtPNode(innerNodes[0], node1Ref.bits.get_ro())] == 9);
 
     REQUIRE(node2Ref.bits.get_ro().count() == 2);
     REQUIRE(node3Ref.bits.get_ro().count() == 2);
@@ -498,8 +498,8 @@ TEST_CASE("Finding the leaf node containing a key", "[BitPBPTree]") {
   SECTION("Handling of underflow at a leaf node by merge and replace the root node") {
     auto &btree = *rootRef.btree6;
 
-    const auto leaf1 = btree.newLeafNode();
-    const auto leaf2 = btree.newLeafNode();
+    auto leaf1 = btree.newLeafNode();
+    auto leaf2 = btree.newLeafNode();
     auto &leaf1Ref = *leaf1;
     auto &leaf2Ref = *leaf2;
     leaf1Ref.nextLeaf = leaf2;
@@ -517,12 +517,12 @@ TEST_CASE("Finding the leaf node containing a key", "[BitPBPTree]") {
 
     parentRef.keys.get_rw()[0] = 4;
     parentRef.children.get_rw()[0] = leaf1;
-    parentRef.children.get_rw()[1] = leaf2;
+    parentRef.children.get_rw()[6] = leaf2;
     parentRef.bits.get_rw().set(0);
     btree.rootNode = parent;
     btree.depth = 1;
 
-    btree.underflowAtLeafLevel(parent, 1, leaf2);
+    btree.underflowAtLeafLevel(parent, 6, leaf2);
     REQUIRE(leaf1Ref.bits.get_ro().count() == 5);
     REQUIRE(btree.rootNode.leaf == leaf1);
 
@@ -540,7 +540,7 @@ TEST_CASE("Finding the leaf node containing a key", "[BitPBPTree]") {
     auto &btree = *rootRef.btree6;
 
     const auto leaf1 = btree.newLeafNode();
-    const auto leaf2 = btree.newLeafNode();
+    auto leaf2 = btree.newLeafNode();
     const auto leaf3 = btree.newLeafNode();
     auto &leaf1Ref = *leaf1;
     auto &leaf2Ref = *leaf2;
@@ -573,6 +573,8 @@ TEST_CASE("Finding the leaf node containing a key", "[BitPBPTree]") {
 
     btree.underflowAtLeafLevel(parent, 1, leaf2);
     REQUIRE(leaf1Ref.bits.get_ro().count() == 5);
+    REQUIRE(leaf2 == nullptr);
+    REQUIRE(leaf3Ref.bits.get_ro().count() == 3);
     REQUIRE(btree.rootNode.branch == parent);
     REQUIRE(parentRef.bits.get_ro().count() == 1);
   }
@@ -582,7 +584,7 @@ TEST_CASE("Finding the leaf node containing a key", "[BitPBPTree]") {
     auto &btree = *rootRef.btree6;
 
     const auto leaf1 = btree.newLeafNode();
-    const auto leaf2 = btree.newLeafNode();
+    auto leaf2 = btree.newLeafNode();
     auto &leaf1Ref = *leaf1;
     auto &leaf2Ref = *leaf2;
     leaf1Ref.nextLeaf = leaf2;
@@ -784,9 +786,9 @@ TEST_CASE("Finding the leaf node containing a key", "[BitPBPTree]") {
       nodeRef.bits.get_rw().set(i);
     }
 
-    btree.insertInLeafNodeAtFreePosition(node, 5, 5000);
+    btree.insertInLeafNodeAtPosition(node, 9, 5, 5000);
     REQUIRE(nodeRef.bits.get_ro().count() == 10);
-    btree.insertInLeafNodeAtFreePosition(node, 1, 1);
+    btree.insertInLeafNodeAtPosition(node, 10, 1, 1);
     REQUIRE(nodeRef.bits.get_ro().count() == 11);
 
     std::array<int, 11> expectedKeys{{1, 2, 4, 5, 6, 8, 10, 12, 14, 16, 18}};
@@ -841,10 +843,8 @@ TEST_CASE("Finding the leaf node containing a key", "[BitPBPTree]") {
     auto &btree = *rootRef.btree4;
     PBPTreeType4::SplitInfo splitInfo;
     const auto leaf1 = btree.newLeafNode();
-    const auto leaf2 = btree.newLeafNode();
+    auto leaf2 = btree.newLeafNode();
     const auto node = btree.newBranchNode();
-    auto &leaf1Ref = *leaf1;
-    auto &leaf2Ref = *leaf2;
     auto &nodeRef = *node;
 
     btree.insertInLeafNode(leaf1, 1, 10, &splitInfo);
@@ -862,18 +862,19 @@ TEST_CASE("Finding the leaf node containing a key", "[BitPBPTree]") {
     nodeRef.bits.get_rw().set(0);
 
     btree.rootNode = node;
-    btree.depth = 2;
+    btree.depth = 1;
 
-    btree.insertInBranchNode(node, 1, 12, 112, &splitInfo);
-    REQUIRE(leaf2Ref.bits.get_ro().count() == 2);
-    REQUIRE(nodeRef.bits.get_ro().count() == 2);
+    btree.insertInBranchNode(node, 1, 12