diff --git a/benchmarks/algorithms.bench.cpp b/benchmarks/algorithms.bench.cpp
index 8631539..eee8a4d 100644
--- a/benchmarks/algorithms.bench.cpp
+++ b/benchmarks/algorithms.bench.cpp
@@ -1,62 +1,270 @@
-#include <unordered_set>
-#include <vector>
+
+#include <algorithm>
 #include <cstdint>
+#include <map>
+#include <random>
+#include <string>
+#include <utility>
+#include <vector>
 
-#include "benchmark/benchmark.h"
+#include "CartesianBenchmarks.hpp"
 #include "GenerateInput.hpp"
+#include "benchmark/benchmark.h"
+#include "test_macros.h"
 
-constexpr std::size_t TestNumInputs = 1024;
+namespace {
 
-template <class GenInputs>
-void BM_Sort(benchmark::State& st, GenInputs gen) {
-    using ValueType = typename decltype(gen(0))::value_type;
-    const auto in = gen(st.range(0));
-    std::vector<ValueType> inputs[5];
-    auto reset_inputs = [&]() {
-        for (auto& C : inputs) {
-            C = in;
-            benchmark::DoNotOptimize(C.data());
-        }
-    };
-    reset_inputs();
-    while (st.KeepRunning()) {
-        for (auto& I : inputs) {
-            std::sort(I.data(), I.data() + I.size());
-            benchmark::DoNotOptimize(I.data());
-        }
-        st.PauseTiming();
-        reset_inputs();
-        benchmark::ClobberMemory();
-        st.ResumeTiming();
-    }
+enum class ValueType { Uint32, String };
+struct AllValueTypes : EnumValuesAsTuple<AllValueTypes, ValueType, 2> {
+  static constexpr const char* Names[] = {"uint32", "string"};
+};
+
+template <class V>
+using Value =
+    std::conditional_t<V() == ValueType::Uint32, uint32_t, std::string>;
+
+enum class Order {
+  Random,
+  Ascending,
+  Descending,
+  SingleElement,
+  PipeOrgan,
+  Heap
+};
+struct AllOrders : EnumValuesAsTuple<AllOrders, Order, 6> {
+  static constexpr const char* Names[] = {"Random",     "Ascending",
+                                          "Descending", "SingleElement",
+                                          "PipeOrgan",  "Heap"};
+};
+
+void fillValues(std::vector<uint32_t>& V, size_t N, Order O) {
+  if (O == Order::SingleElement) {
+    V.resize(N, 0);
+  } else {
+    while (V.size() < N)
+      V.push_back(V.size());
+  }
 }
 
-BENCHMARK_CAPTURE(BM_Sort, random_uint32,
-    getRandomIntegerInputs<uint32_t>)->Arg(TestNumInputs);
+void fillValues(std::vector<std::string>& V, size_t N, Order O) {
 
-BENCHMARK_CAPTURE(BM_Sort, sorted_ascending_uint32,
-    getSortedIntegerInputs<uint32_t>)->Arg(TestNumInputs);
+  if (O == Order::SingleElement) {
+    V.resize(N, getRandomString(1024));
+  } else {
+    while (V.size() < N)
+      V.push_back(getRandomString(1024));
+  }
+}
 
-BENCHMARK_CAPTURE(BM_Sort, sorted_descending_uint32,
-    getReverseSortedIntegerInputs<uint32_t>)->Arg(TestNumInputs);
+template <class T>
+void sortValues(T& V, Order O) {
+  assert(std::is_sorted(V.begin(), V.end()));
+  switch (O) {
+  case Order::Random: {
+    std::random_device R;
+    std::mt19937 M(R());
+    std::shuffle(V.begin(), V.end(), M);
+    break;
+  }
+  case Order::Ascending:
+    std::sort(V.begin(), V.end());
+    break;
+  case Order::Descending:
+    std::sort(V.begin(), V.end(), std::greater<>());
+    break;
+  case Order::SingleElement:
+    // Nothing to do
+    break;
+  case Order::PipeOrgan:
+    std::sort(V.begin(), V.end());
+    std::reverse(V.begin() + V.size() / 2, V.end());
+    break;
+  case Order::Heap:
+    std::make_heap(V.begin(), V.end());
+    break;
+  }
+}
 
-BENCHMARK_CAPTURE(BM_Sort, single_element_uint32,
-    getDuplicateIntegerInputs<uint32_t>)->Arg(TestNumInputs);
+template <class ValueType>
+std::vector<std::vector<Value<ValueType> > > makeOrderedValues(size_t N,
+                                                               Order O) {
+  // Let's make sure that all random sequences of the same size are the same.
+  // That way we can compare the different algorithms with the same input.
+  static std::map<std::pair<size_t, Order>, std::vector<Value<ValueType> > >
+      Cached;
 
-BENCHMARK_CAPTURE(BM_Sort, pipe_organ_uint32,
-    getPipeOrganIntegerInputs<uint32_t>)->Arg(TestNumInputs);
+  auto& Values = Cached[{N, O}];
+  if (Values.empty()) {
+    fillValues(Values, N, O);
+    sortValues(Values, O);
+  };
+  const size_t NumCopies = std::max(size_t{1}, 1000 / N);
+  return { NumCopies, Values };
+}
 
-BENCHMARK_CAPTURE(BM_Sort, random_strings,
-    getRandomStringInputs)->Arg(TestNumInputs);
+template <class T, class U>
+TEST_ALWAYS_INLINE void resetCopies(benchmark::State& state, T& Copies,
+                                    U& Orig) {
+  state.PauseTiming();
+  for (auto& Copy : Copies)
+    Copy = Orig;
+  state.ResumeTiming();
+}
 
-BENCHMARK_CAPTURE(BM_Sort, sorted_ascending_strings,
-    getSortedStringInputs)->Arg(TestNumInputs);
+template <class ValueType, class F>
+void runOpOnCopies(benchmark::State& state, size_t Quantity, Order O,
+                   bool CountElements, F f) {
+  auto Copies = makeOrderedValues<ValueType>(Quantity, O);
+  const auto Orig = Copies[0];
 
-BENCHMARK_CAPTURE(BM_Sort, sorted_descending_strings,
-    getReverseSortedStringInputs)->Arg(TestNumInputs);
+  const size_t Batch = CountElements ? Copies.size() * Quantity : Copies.size();
+  while (state.KeepRunningBatch(Batch)) {
+    for (auto& Copy : Copies) {
+      f(Copy);
+      benchmark::DoNotOptimize(Copy);
+    }
+    resetCopies(state, Copies, Orig);
+  }
+}
 
-BENCHMARK_CAPTURE(BM_Sort, single_element_strings,
-    getDuplicateStringInputs)->Arg(TestNumInputs);
+template <class ValueType, class Order>
+struct Sort {
+  size_t Quantity;
 
+  void run(benchmark::State& state) const {
+    runOpOnCopies<ValueType>(state, Quantity, Order(), false, [](auto& Copy) {
+      std::sort(Copy.begin(), Copy.end());
+    });
+  }
 
-BENCHMARK_MAIN();
+  bool skip() const { return Order() == ::Order::Heap; }
+
+  std::string name() const {
+    return "BM_Sort" + ValueType::name() + Order::name() + "_" +
+           std::to_string(Quantity);
+  };
+};
+
+template <class ValueType, class Order>
+struct StableSort {
+  size_t Quantity;
+
+  void run(benchmark::State& state) const {
+    runOpOnCopies<ValueType>(state, Quantity, Order(), false, [](auto& Copy) {
+      std::stable_sort(Copy.begin(), Copy.end());
+    });
+  }
+
+  bool skip() const { return Order() == ::Order::Heap; }
+
+  std::string name() const {
+    return "BM_StableSort" + ValueType::name() + Order::name() + "_" +
+           std::to_string(Quantity);
+  };
+};
+
+template <class ValueType, class Order>
+struct MakeHeap {
+  size_t Quantity;
+
+  void run(benchmark::State& state) const {
+    runOpOnCopies<ValueType>(state, Quantity, Order(), false, [](auto& Copy) {
+      std::make_heap(Copy.begin(), Copy.end());
+    });
+  }
+
+  std::string name() const {
+    return "BM_MakeHeap" + ValueType::name() + Order::name() + "_" +
+           std::to_string(Quantity);
+  };
+};
+
+template <class ValueType>
+struct SortHeap {
+  size_t Quantity;
+
+  void run(benchmark::State& state) const {
+    runOpOnCopies<ValueType>(
+        state, Quantity, Order::Heap, false,
+        [](auto& Copy) { std::sort_heap(Copy.begin(), Copy.end()); });
+  }
+
+  std::string name() const {
+    return "BM_SortHeap" + ValueType::name() + "_" + std::to_string(Quantity);
+  };
+};
+
+template <class ValueType, class Order>
+struct MakeThenSortHeap {
+  size_t Quantity;
+
+  void run(benchmark::State& state) const {
+    runOpOnCopies<ValueType>(state, Quantity, Order(), false, [](auto& Copy) {
+      std::make_heap(Copy.begin(), Copy.end());
+      std::sort_heap(Copy.begin(), Copy.end());
+    });
+  }
+
+  std::string name() const {
+    return "BM_MakeThenSortHeap" + ValueType::name() + Order::name() + "_" +
+           std::to_string(Quantity);
+  };
+};
+
+template <class ValueType, class Order>
+struct PushHeap {
+  size_t Quantity;
+
+  void run(benchmark::State& state) const {
+    runOpOnCopies<ValueType>(state, Quantity, Order(), true, [](auto& Copy) {
+      for (auto I = Copy.begin(), E = Copy.end(); I != E; ++I) {
+        std::push_heap(Copy.begin(), I + 1);
+      }
+    });
+  }
+
+  bool skip() const { return Order() == ::Order::Heap; }
+
+  std::string name() const {
+    return "BM_PushHeap" + ValueType::name() + Order::name() + "_" +
+           std::to_string(Quantity);
+  };
+};
+
+template <class ValueType>
+struct PopHeap {
+  size_t Quantity;
+
+  void run(benchmark::State& state) const {
+    runOpOnCopies<ValueType>(state, Quantity, Order(), true, [](auto& Copy) {
+      for (auto B = Copy.begin(), I = Copy.end(); I != B; --I) {
+        std::pop_heap(B, I);
+      }
+    });
+  }
+
+  std::string name() const {
+    return "BM_PopHeap" + ValueType::name() + "_" + std::to_string(Quantity);
+  };
+};
+
+} // namespace
+
+int main(int argc, char** argv) {
+  benchmark::Initialize(&argc, argv);
+  if (benchmark::ReportUnrecognizedArguments(argc, argv))
+    return 1;
+
+  const std::vector<size_t> Quantities = {1 << 0, 1 << 2,  1 << 4,  1 << 6,
+                                          1 << 8, 1 << 10, 1 << 14, 1 << 18};
+  makeCartesianProductBenchmark<Sort, AllValueTypes, AllOrders>(Quantities);
+  makeCartesianProductBenchmark<StableSort, AllValueTypes, AllOrders>(
+      Quantities);
+  makeCartesianProductBenchmark<MakeHeap, AllValueTypes, AllOrders>(Quantities);
+  makeCartesianProductBenchmark<SortHeap, AllValueTypes>(Quantities);
+  makeCartesianProductBenchmark<MakeThenSortHeap, AllValueTypes, AllOrders>(
+      Quantities);
+  makeCartesianProductBenchmark<PushHeap, AllValueTypes, AllOrders>(Quantities);
+  makeCartesianProductBenchmark<PopHeap, AllValueTypes>(Quantities);
+  benchmark::RunSpecifiedBenchmarks();
+}