diff --git a/bench/analyze-blocking-sizes.cpp b/bench/analyze-blocking-sizes.cpp
new file mode 100644
index 0000000..d563a1d
--- /dev/null
+++ b/bench/analyze-blocking-sizes.cpp
@@ -0,0 +1,876 @@
+// This file is part of Eigen, a lightweight C++ template library
+// for linear algebra.
+//
+// Copyright (C) 2015 Benoit Jacob <benoitjacob@google.com>
+//
+// This Source Code Form is subject to the terms of the Mozilla
+// Public License v. 2.0. If a copy of the MPL was not distributed
+// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
+
+#include <iostream>
+#include <cstdint>
+#include <cstdlib>
+#include <vector>
+#include <algorithm>
+#include <fstream>
+#include <string>
+#include <cmath>
+#include <cassert>
+#include <cstring>
+#include <memory>
+
+#include <Eigen/Core>
+
+using namespace std;
+
+const int default_precision = 4;
+
+// see --only-cubic-sizes
+bool only_cubic_sizes = false;
+
+// see --dump-tables
+bool dump_tables = false;
+
+uint8_t log2_pot(size_t x) {
+  size_t l = 0;
+  while (x >>= 1) l++;
+  return l;
+}
+
+uint16_t compact_size_triple(size_t k, size_t m, size_t n)
+{
+  return (log2_pot(k) << 8) | (log2_pot(m) << 4) | log2_pot(n);
+}
+
+// just a helper to store a triple of K,M,N sizes for matrix product
+struct size_triple_t
+{
+  uint16_t k, m, n;
+  size_triple_t() : k(0), m(0), n(0) {}
+  size_triple_t(size_t _k, size_t _m, size_t _n) : k(_k), m(_m), n(_n) {}
+  size_triple_t(const size_triple_t& o) : k(o.k), m(o.m), n(o.n) {}
+  size_triple_t(uint16_t compact)
+  {
+    k = 1 << ((compact & 0xf00) >> 8);
+    m = 1 << ((compact & 0x0f0) >> 4);
+    n = 1 << ((compact & 0x00f) >> 0);
+  }
+  bool is_cubic() const { return k == m && m == n; }
+};
+
+ostream& operator<<(ostream& s, const size_triple_t& t)
+{
+  return s << "(" << t.k << ", " << t.m << ", " << t.n << ")";
+}
+
+struct inputfile_entry_t
+{
+  uint16_t product_size;
+  uint16_t pot_block_size;
+  size_triple_t nonpot_block_size;
+  float gflops;
+};
+
+struct inputfile_t
+{
+  enum class type_t {
+    unknown,
+    all_pot_sizes,
+    default_sizes
+  };
+
+  string filename;
+  vector<inputfile_entry_t> entries;
+  type_t type;
+
+  inputfile_t(const string& fname)
+    : filename(fname)
+    , type(type_t::unknown)
+  {
+    ifstream stream(filename);
+    if (!stream.is_open()) {
+      cerr << "couldn't open input file: " << filename << endl;
+      exit(1);
+    }
+    string line;
+    while (getline(stream, line)) {
+      if (line.empty()) continue;
+      if (line.find("BEGIN MEASUREMENTS ALL POT SIZES") == 0) {
+        if (type != type_t::unknown) {
+          cerr << "Input file " << filename << " contains redundant BEGIN MEASUREMENTS lines";
+          exit(1);
+        }
+        type = type_t::all_pot_sizes;
+        continue;
+      }
+      if (line.find("BEGIN MEASUREMENTS DEFAULT SIZES") == 0) {
+        if (type != type_t::unknown) {
+          cerr << "Input file " << filename << " contains redundant BEGIN MEASUREMENTS lines";
+          exit(1);
+        }
+        type = type_t::default_sizes;
+        continue;
+      }
+      
+
+      if (type == type_t::unknown) {
+        continue;
+      }
+      switch(type) {
+        case type_t::all_pot_sizes: {
+          unsigned int product_size, block_size;
+          float gflops;
+          int sscanf_result =
+            sscanf(line.c_str(), "%x %x %f",
+                   &product_size,
+                   &block_size,
+                   &gflops);
+          if (3 != sscanf_result ||
+              !product_size ||
+              product_size > 0xfff ||
+              !block_size ||
+              block_size > 0xfff ||
+              !isfinite(gflops))
+          {
+            cerr << "ill-formed input file: " << filename << endl;
+            cerr << "offending line:" << endl << line << endl;
+            exit(1);
+          }
+          if (only_cubic_sizes && !size_triple_t(product_size).is_cubic()) {
+            continue;
+          }
+          inputfile_entry_t entry;
+          entry.product_size = uint16_t(product_size);
+          entry.pot_block_size = uint16_t(block_size);
+          entry.gflops = gflops;
+          entries.push_back(entry);
+          break;
+        }
+        case type_t::default_sizes: {
+          unsigned int product_size;
+          float gflops;
+          int bk, bm, bn;
+          int sscanf_result =
+            sscanf(line.c_str(), "%x default(%d, %d, %d) %f",
+                   &product_size,
+                   &bk, &bm, &bn,
+                   &gflops);
+          if (5 != sscanf_result ||
+              !product_size ||
+              product_size > 0xfff ||
+              !isfinite(gflops))
+          {
+            cerr << "ill-formed input file: " << filename << endl;
+            cerr << "offending line:" << endl << line << endl;
+            exit(1);
+          }
+          if (only_cubic_sizes && !size_triple_t(product_size).is_cubic()) {
+            continue;
+          }
+          inputfile_entry_t entry;
+          entry.product_size = uint16_t(product_size);
+          entry.pot_block_size = 0;
+          entry.nonpot_block_size = size_triple_t(bk, bm, bn);
+          entry.gflops = gflops;
+          entries.push_back(entry);
+          break;
+        }
+        
+        default:
+          break;
+      }
+    }
+    stream.close();
+    if (type == type_t::unknown) {
+      cerr << "Unrecognized input file " << filename << endl;
+      exit(1);
+    }
+    if (entries.empty()) {
+      cerr << "didn't find any measurements in input file: " << filename << endl;
+      exit(1);
+    }
+  }
+};
+
+struct preprocessed_inputfile_entry_t
+{
+  uint16_t product_size;
+  uint16_t block_size;
+
+  float efficiency;
+};
+
+bool lower_efficiency(const preprocessed_inputfile_entry_t& e1, const preprocessed_inputfile_entry_t& e2)
+{
+  return e1.efficiency < e2.efficiency;
+}
+
+struct preprocessed_inputfile_t
+{
+  string filename;
+  vector<preprocessed_inputfile_entry_t> entries;
+
+  preprocessed_inputfile_t(const inputfile_t& inputfile)
+    : filename(inputfile.filename)
+  {
+    if (inputfile.type != inputfile_t::type_t::all_pot_sizes) {
+      abort();
+    }
+    auto it = inputfile.entries.begin();
+    auto it_first_with_given_product_size = it;
+    while (it != inputfile.entries.end()) {
+      ++it;
+      if (it == inputfile.entries.end() ||
+        it->product_size != it_first_with_given_product_size->product_size)
+      {
+        import_input_file_range_one_product_size(it_first_with_given_product_size, it);
+        it_first_with_given_product_size = it;
+      }
+    }
+  }
+
+private:
+  void import_input_file_range_one_product_size(
+    const vector<inputfile_entry_t>::const_iterator& begin,
+    const vector<inputfile_entry_t>::const_iterator& end)
+  {
+    uint16_t product_size = begin->product_size;
+    float max_gflops = 0.0f;
+    for (auto it = begin; it != end; ++it) {
+      if (it->product_size != product_size) {
+        cerr << "Unexpected ordering of entries in " << filename << endl;
+        cerr << "(Expected all entries for product size " << hex << product_size << dec << " to be grouped)" << endl;
+        exit(1);
+      }
+      max_gflops = max(max_gflops, it->gflops);
+    }
+    for (auto it = begin; it != end; ++it) {
+      preprocessed_inputfile_entry_t entry;
+      entry.product_size = it->product_size;
+      entry.block_size = it->pot_block_size;
+      entry.efficiency = it->gflops / max_gflops;
+      entries.push_back(entry);
+    }
+  }
+};
+
+void check_all_files_in_same_exact_order(
+       const vector<preprocessed_inputfile_t>& preprocessed_inputfiles)
+{
+  if (preprocessed_inputfiles.empty()) {
+    return;
+  }
+
+  const preprocessed_inputfile_t& first_file = preprocessed_inputfiles[0];
+  const size_t num_entries = first_file.entries.size();
+
+  for (size_t i = 0; i < preprocessed_inputfiles.size(); i++) {
+    if (preprocessed_inputfiles[i].entries.size() != num_entries) {
+      cerr << "these files have different number of entries: "
+           << preprocessed_inputfiles[i].filename
+           << " and "
+           << first_file.filename
+           << endl;
+      exit(1);
+    }
+  }
+
+  for (size_t entry_index = 0; entry_index < num_entries; entry_index++) {
+    const uint16_t entry_product_size = first_file.entries[entry_index].product_size;
+    const uint16_t entry_block_size = first_file.entries[entry_index].block_size;
+    for (size_t file_index = 0; file_index < preprocessed_inputfiles.size(); file_index++) {
+      const preprocessed_inputfile_t& cur_file = preprocessed_inputfiles[file_index];
+      if (cur_file.entries[entry_index].product_size != entry_product_size ||
+          cur_file.entries[entry_index].block_size != entry_block_size)
+      {
+        cerr << "entries not in same order between these files: "
+             << first_file.filename
+             << " and "
+             << cur_file.filename
+             << endl;
+        exit(1);
+      }
+    }
+  }
+}
+
+float efficiency_of_subset(
+        const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,
+        const vector<size_t>& subset)
+{
+  if (subset.size() <= 1) {
+    return 1.0f;
+  }
+  const preprocessed_inputfile_t& first_file = preprocessed_inputfiles[subset[0]];
+  const size_t num_entries = first_file.entries.size();
+  float efficiency = 1.0f;
+  size_t entry_index = 0;
+  size_t first_entry_index_with_this_product_size = 0;
+  uint16_t product_size = first_file.entries[0].product_size;
+  while (entry_index < num_entries) {
+    ++entry_index;
+    if (entry_index == num_entries ||
+        first_file.entries[entry_index].product_size != product_size)
+    {
+      float efficiency_this_product_size = 0.0f;
+      for (size_t e = first_entry_index_with_this_product_size; e < entry_index; e++) {
+        float efficiency_this_entry = 1.0f;
+        for (auto i = subset.begin(); i != subset.end(); ++i) {
+          efficiency_this_entry = min(efficiency_this_entry, preprocessed_inputfiles[*i].entries[e].efficiency);
+        }
+        efficiency_this_product_size = max(efficiency_this_product_size, efficiency_this_entry);
+      }
+      efficiency = min(efficiency, efficiency_this_product_size);
+      if (entry_index < num_entries) {
+        first_entry_index_with_this_product_size = entry_index;
+        product_size = first_file.entries[entry_index].product_size;
+      }
+    }
+  }
+
+  return efficiency;
+}
+
+void dump_table_for_subset(
+        const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,
+        const vector<size_t>& subset)
+{
+  const preprocessed_inputfile_t& first_file = preprocessed_inputfiles[subset[0]];
+  const size_t num_entries = first_file.entries.size();
+  size_t entry_index = 0;
+  size_t first_entry_index_with_this_product_size = 0;
+  uint16_t product_size = first_file.entries[0].product_size;
+  size_t i = 0;
+  size_triple_t min_product_size(first_file.entries.front().product_size);
+  size_triple_t max_product_size(first_file.entries.back().product_size);
+  if (!min_product_size.is_cubic() || !max_product_size.is_cubic()) {
+    abort();
+  }
+  if (only_cubic_sizes) {
+    cerr << "Can't generate tables with --only-cubic-sizes." << endl;
+    abort();
+  }
+  cout << "struct LookupTable {" << endl;
+  cout << "  static const size_t BaseSize = " << min_product_size.k << ";" << endl;
+  const size_t NumSizes = log2_pot(max_product_size.k / min_product_size.k) + 1;
+  const size_t TableSize = NumSizes * NumSizes * NumSizes;
+  cout << "  static const size_t NumSizes = " << NumSizes << ";" << endl;
+  cout << "  static const unsigned short* Data() {" << endl;
+  cout << "    static const unsigned short data[" << TableSize << "] = {";
+  while (entry_index < num_entries) {
+    ++entry_index;
+    if (entry_index == num_entries ||
+        first_file.entries[entry_index].product_size != product_size)
+    {
+      float best_efficiency_this_product_size = 0.0f;
+      uint16_t best_block_size_this_product_size = 0;
+      for (size_t e = first_entry_index_with_this_product_size; e < entry_index; e++) {
+        float efficiency_this_entry = 1.0f;
+        for (auto i = subset.begin(); i != subset.end(); ++i) {
+          efficiency_this_entry = min(efficiency_this_entry, preprocessed_inputfiles[*i].entries[e].efficiency);
+        }
+        if (efficiency_this_entry > best_efficiency_this_product_size) {
+          best_efficiency_this_product_size = efficiency_this_entry;
+          best_block_size_this_product_size = first_file.entries[e].block_size;
+        }
+      }
+      if ((i++) % NumSizes) {
+        cout << " ";
+      } else {
+        cout << endl << "      ";
+      }
+      cout << "0x" << hex << best_block_size_this_product_size << dec;
+      if (entry_index < num_entries) {
+        cout << ",";
+        first_entry_index_with_this_product_size = entry_index;
+        product_size = first_file.entries[entry_index].product_size;
+      }
+    }
+  }
+  if (i != TableSize) {
+    cerr << endl << "Wrote " << i << " table entries, expected " << TableSize << endl;
+    abort();
+  }
+  cout << endl << "    };" << endl;
+  cout << "    return data;" << endl;
+  cout << "  }" << endl;
+  cout << "};" << endl;
+}
+
+float efficiency_of_partition(
+        const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,
+        const vector<vector<size_t>>& partition)
+{
+  float efficiency = 1.0f;
+  for (auto s = partition.begin(); s != partition.end(); ++s) {
+    efficiency = min(efficiency, efficiency_of_subset(preprocessed_inputfiles, *s));
+  }
+  return efficiency;
+}
+
+void make_first_subset(size_t subset_size, vector<size_t>& out_subset, size_t set_size)
+{
+  assert(subset_size >= 1 && subset_size <= set_size);
+  out_subset.resize(subset_size);
+  for (size_t i = 0; i < subset_size; i++) {
+    out_subset[i] = i;
+  }
+}
+
+bool is_last_subset(const vector<size_t>& subset, size_t set_size)
+{
+  return subset[0] == set_size - subset.size();
+}
+
+void next_subset(vector<size_t>& inout_subset, size_t set_size)
+{
+  if (is_last_subset(inout_subset, set_size)) {
+    cerr << "iterating past the last subset" << endl;
+    abort();
+  }
+  size_t i = 1;
+  while (inout_subset[inout_subset.size() - i] == set_size - i) {
+    i++;
+    assert(i <= inout_subset.size());
+  }
+  size_t first_index_to_change = inout_subset.size() - i;
+  inout_subset[first_index_to_change]++;
+  size_t p = inout_subset[first_index_to_change];
+  for (size_t j = first_index_to_change + 1; j < inout_subset.size(); j++) {
+    inout_subset[j] = ++p;
+  }
+}
+
+const size_t number_of_subsets_limit = 100;
+const size_t always_search_subsets_of_size_at_least = 2;
+
+bool is_number_of_subsets_feasible(size_t n, size_t p)
+{ 
+  assert(n>0 && p>0 && p<=n);
+  uint64_t numerator = 1, denominator = 1;
+  for (size_t i = 0; i < p; i++) {
+    numerator *= n - i;
+    denominator *= i + 1;
+    if (numerator > denominator * number_of_subsets_limit) {
+      return false;
+    }
+  }
+  return true;
+}
+
+size_t max_feasible_subset_size(size_t n)
+{
+  assert(n > 0);
+  const size_t minresult = min<size_t>(n-1, always_search_subsets_of_size_at_least);
+  for (size_t p = 1; p <= n - 1; p++) {
+    if (!is_number_of_subsets_feasible(n, p+1)) {
+      return max(p, minresult);
+    }
+  }
+  return n - 1;
+}
+
+void find_subset_with_efficiency_higher_than(
+       const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,
+       float required_efficiency_to_beat,
+       vector<size_t>& inout_remainder,
+       vector<size_t>& out_subset)
+{
+  out_subset.resize(0);
+
+  if (required_efficiency_to_beat >= 1.0f) {
+    cerr << "can't beat efficiency 1." << endl;
+    abort();
+  }
+
+  while (!inout_remainder.empty()) {
+
+    vector<size_t> candidate_indices(inout_remainder.size());
+    for (size_t i = 0; i < candidate_indices.size(); i++) {
+      candidate_indices[i] = i;
+    }
+
+    size_t candidate_indices_subset_size = max_feasible_subset_size(candidate_indices.size());
+    while (candidate_indices_subset_size >= 1) {
+      vector<size_t> candidate_indices_subset;
+      make_first_subset(candidate_indices_subset_size,
+                        candidate_indices_subset,
+                        candidate_indices.size());
+
+      vector<size_t> best_candidate_indices_subset;
+      float best_efficiency = 0.0f;
+      vector<size_t> trial_subset = out_subset;
+      trial_subset.resize(out_subset.size() + candidate_indices_subset_size);
+      while (true)
+      {
+        for (size_t i = 0; i < candidate_indices_subset_size; i++) {
+          trial_subset[out_subset.size() + i] = inout_remainder[candidate_indices_subset[i]];
+        }
+        
+        float trial_efficiency = efficiency_of_subset(preprocessed_inputfiles, trial_subset);
+        if (trial_efficiency > best_efficiency) {
+          best_efficiency = trial_efficiency;
+          best_candidate_indices_subset = candidate_indices_subset;
+        }
+        if (is_last_subset(candidate_indices_subset, candidate_indices.size())) {
+          break;
+        }
+        next_subset(candidate_indices_subset, candidate_indices.size());
+      }
+       
+      if (best_efficiency > required_efficiency_to_beat) {
+        for (size_t i = 0; i < best_candidate_indices_subset.size(); i++) {
+          candidate_indices[i] = candidate_indices[best_candidate_indices_subset[i]];
+        }
+        candidate_indices.resize(best_candidate_indices_subset.size());
+      }
+      candidate_indices_subset_size--;
+    }
+      
+    size_t candidate_index = candidate_indices[0];
+    auto candidate_iterator = inout_remainder.begin() + candidate_index;
+    vector<size_t> trial_subset = out_subset;
+
+    trial_subset.push_back(*candidate_iterator);
+    float trial_efficiency = efficiency_of_subset(preprocessed_inputfiles, trial_subset);
+    if (trial_efficiency > required_efficiency_to_beat) {
+      out_subset.push_back(*candidate_iterator);
+      inout_remainder.erase(candidate_iterator);
+    } else {
+      break;
+    }
+  }
+}
+
+void find_partition_with_efficiency_higher_than(
+       const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,
+       float required_efficiency_to_beat,
+       vector<vector<size_t>>& out_partition)
+{
+  out_partition.resize(0);
+
+  vector<size_t> remainder;
+  for (size_t i = 0; i < preprocessed_inputfiles.size(); i++) {
+    remainder.push_back(i);
+  }
+
+  while (!remainder.empty()) {
+    vector<size_t> new_subset;
+    find_subset_with_efficiency_higher_than(
+      preprocessed_inputfiles,
+      required_efficiency_to_beat,
+      remainder,
+      new_subset);
+    out_partition.push_back(new_subset);
+  }
+}
+
+void print_partition(
+       const vector<preprocessed_inputfile_t>& preprocessed_inputfiles,
+       const vector<vector<size_t>>& partition)
+{
+  float efficiency = efficiency_of_partition(preprocessed_inputfiles, partition);
+  cout << "Partition into " << partition.size() << " subsets for " << efficiency * 100.0f << "% efficiency"  << endl;
+  for (auto subset = partition.begin(); subset != partition.end(); ++subset) {
+    cout << "  Subset " << (subset - partition.begin())
+         << ", efficiency " << efficiency_of_subset(preprocessed_inputfiles, *subset) * 100.0f << "%:"
+         << endl;
+    for (auto file = subset->begin(); file != subset->end(); ++file) {
+      cout << "    " << preprocessed_inputfiles[*file].filename << endl;
+    }
+    if (dump_tables) {
+      cout << "  Table:" << endl;
+      dump_table_for_subset(preprocessed_inputfiles, *subset);
+    }
+  }
+  cout << endl;
+}
+
+struct action_t
+{
+  virtual const char* invokation_name() const { abort(); return nullptr; }
+  virtual void run(const vector<string>&) const { abort(); }
+  virtual ~action_t() {}
+};
+
+struct partition_action_t : action_t
+{
+  virtual const char* invokation_name() const override { return "partition"; }
+  virtual void run(const vector<string>& input_filenames) const override
+  {
+    vector<preprocessed_inputfile_t> preprocessed_inputfiles;
+
+    if (input_filenames.empty()) {
+      cerr << "The " << invokation_name() << " action needs a list of input files." << endl;
+      exit(1);
+    }
+
+    for (auto it = input_filenames.begin(); it != input_filenames.end(); ++it) {
+      inputfile_t inputfile(*it);
+      switch (inputfile.type) {
+        case inputfile_t::type_t::all_pot_sizes:
+          preprocessed_inputfiles.emplace_back(inputfile);
+          break;
+        case inputfile_t::type_t::default_sizes:
+          cerr << "The " << invokation_name() << " action only uses measurements for all pot sizes, and "
+               << "has no use for " << *it << " which contains measurements for default sizes." << endl;
+          exit(1);
+          break;
+        default:
+          cerr << "Unrecognized input file: " << *it << endl;
+          exit(1);
+      }
+    }
+
+    check_all_files_in_same_exact_order(preprocessed_inputfiles);
+
+    float required_efficiency_to_beat = 0.0f;
+    vector<vector<vector<size_t>>> partitions;
+    cerr << "searching for partitions...\r" << flush;
+    while (true)
+    {
+      vector<vector<size_t>> partition;
+      find_partition_with_efficiency_higher_than(
+        preprocessed_inputfiles,
+        required_efficiency_to_beat,
+        partition);
+      float actual_efficiency = efficiency_of_partition(preprocessed_inputfiles, partition);
+      cerr << "partition " << preprocessed_inputfiles.size() << " files into " << partition.size()
+           << " subsets for " << 100.0f * actual_efficiency
+           << " % efficiency"
+           << "                  \r" << flush;
+      partitions.push_back(partition);
+      if (partition.size() == preprocessed_inputfiles.size() || actual_efficiency == 1.0f) {
+        break;
+      }
+      required_efficiency_to_beat = actual_efficiency;
+    }
+    cerr << "                                                                  " << endl;
+    while (true) {
+      bool repeat = false;
+      for (size_t i = 0; i < partitions.size() - 1; i++) {
+        if (partitions[i].size() >= partitions[i+1].size()) {
+          partitions.erase(partitions.begin() + i);
+          repeat = true;
+          break;
+        }
+      }
+      if (!repeat) {
+        break;
+      }
+    }
+    for (auto it = partitions.begin(); it != partitions.end(); ++it) {
+      print_partition(preprocessed_inputfiles, *it);
+    }
+  }
+};
+
+struct evaluate_defaults_action_t : action_t
+{
+  struct results_entry_t {
+    uint16_t product_size;
+    size_triple_t default_block_size;
+    uint16_t best_pot_block_size;
+    float default_gflops;
+    float best_pot_gflops;
+    float default_efficiency;
+  };
+  friend ostream& operator<<(ostream& s, const results_entry_t& entry)
+  {
+    return s
+      << "Product size " << size_triple_t(entry.product_size)
+      << ": default block size " << entry.default_block_size
+      << " -> " << entry.default_gflops
+      << " GFlop/s = " << entry.default_efficiency * 100.0f << " %"
+      << " of best POT block size " << size_triple_t(entry.best_pot_block_size)
+      << " -> " << entry.best_pot_gflops
+      << " GFlop/s" << dec;
+  }
+  static bool lower_efficiency(const results_entry_t& e1, const results_entry_t& e2) {
+    return e1.default_efficiency < e2.default_efficiency;
+  }
+  virtual const char* invokation_name() const override { return "evaluate-defaults"; }
+  void show_usage_and_exit() const
+  {
+    cerr << "usage: " << invokation_name() << " default-sizes-data all-pot-sizes-data" << endl;
+    cerr << "checks how well the performance with default sizes compares to the best "
+         << "performance measured over all POT sizes." << endl;
+    exit(1);
+  }
+  virtual void run(const vector<string>& input_filenames) const override
+  {
+    if (input_filenames.size() != 2) {
+      show_usage_and_exit();
+    }
+    inputfile_t inputfile_default_sizes(input_filenames[0]);
+    inputfile_t inputfile_all_pot_sizes(input_filenames[1]);
+    if (inputfile_default_sizes.type != inputfile_t::type_t::default_sizes) {
+      cerr << inputfile_default_sizes.filename << " is not an input file with default sizes." << endl;
+      show_usage_and_exit();
+    }
+    if (inputfile_all_pot_sizes.type != inputfile_t::type_t::all_pot_sizes) {
+      cerr << inputfile_all_pot_sizes.filename << " is not an input file with all POT sizes." << endl;
+      show_usage_and_exit();
+    }
+    vector<results_entry_t> results;
+    vector<results_entry_t> cubic_results;
+    
+    uint16_t product_size = 0;
+    auto it_all_pot_sizes = inputfile_all_pot_sizes.entries.begin();
+    for (auto it_default_sizes = inputfile_default_sizes.entries.begin();
+         it_default_sizes != inputfile_default_sizes.entries.end();
+         ++it_default_sizes)
+    {
+      if (it_default_sizes->product_size == product_size) {
+        continue;
+      }
+      product_size = it_default_sizes->product_size;
+      while (it_all_pot_sizes != inputfile_all_pot_sizes.entries.end() &&
+             it_all_pot_sizes->product_size != product_size)
+      {
+        ++it_all_pot_sizes;
+      }
+      if (it_all_pot_sizes == inputfile_all_pot_sizes.entries.end()) {
+        break;
+      }
+      uint16_t best_pot_block_size = 0;
+      float best_pot_gflops = 0;
+      for (auto it = it_all_pot_sizes;
+           it != inputfile_all_pot_sizes.entries.end() && it->product_size == product_size;
+           ++it)
+      {
+        if (it->gflops > best_pot_gflops) {
+          best_pot_gflops = it->gflops;
+          best_pot_block_size = it->pot_block_size;
+        }
+      }
+      results_entry_t entry;
+      entry.product_size = product_size;
+      entry.default_block_size = it_default_sizes->nonpot_block_size;
+      entry.best_pot_block_size = best_pot_block_size;
+      entry.default_gflops = it_default_sizes->gflops;
+      entry.best_pot_gflops = best_pot_gflops;
+      entry.default_efficiency = entry.default_gflops / entry.best_pot_gflops;
+      results.push_back(entry);
+
+      size_triple_t t(product_size);
+      if (t.k == t.m && t.m == t.n) {
+        cubic_results.push_back(entry);
+      }
+    }
+
+    cout << "All results:" << endl;
+    for (auto it = results.begin(); it != results.end(); ++it) {
+      cout << *it << endl;
+    }
+    cout << endl;
+
+    sort(results.begin(), results.end(), lower_efficiency);
+    
+    const size_t n = min<size_t>(20, results.size());
+    cout << n << " worst results:" << endl;
+    for (size_t i = 0; i < n; i++) {
+      cout << results[i] << endl;
+    }
+    cout << endl;
+
+    cout << "cubic results:" << endl;
+    for (auto it = cubic_results.begin(); it != cubic_results.end(); ++it) {
+      cout << *it << endl;
+    }
+    cout << endl;
+
+    sort(cubic_results.begin(), cubic_results.end(), lower_efficiency);
+    
+    cout.precision(2);
+    vector<float> a = {0.5f, 0.20f, 0.10f, 0.05f, 0.02f, 0.01f};
+    for (auto it = a.begin(); it != a.end(); ++it) {
+      size_t n = min(results.size() - 1, size_t(*it * results.size()));
+      cout << (100.0f * n / (results.size() - 1))
+           << " % of product sizes have default efficiency <= "
+           << 100.0f * results[n].default_efficiency << " %" << endl;
+    }
+    cout.precision(default_precision);
+  }
+};
+
+
+void show_usage_and_exit(int argc, char* argv[],
+                         const vector<unique_ptr<action_t>>& available_actions)
+{
+  cerr << "usage: " << argv[0] << " <action> [options...] <input files...>" << endl;
+  cerr << "available actions:" << endl;
+  for (auto it = available_actions.begin(); it != available_actions.end(); ++it) {
+    cerr << "  " << (*it)->invokation_name() << endl;
+  } 
+  cerr << "the input files should each contain an output of benchmark-blocking-sizes" << endl;
+  exit(1);
+}
+
+int main(int argc, char* argv[])
+{
+  cout.precision(default_precision);
+  cerr.precision(default_precision);
+
+  vector<unique_ptr<action_t>> available_actions;
+  available_actions.emplace_back(new partition_action_t);
+  available_actions.emplace_back(new evaluate_defaults_action_t);
+
+  vector<string> input_filenames;
+
+  action_t* action = nullptr;
+
+  if (argc < 2) {
+    show_usage_and_exit(argc, argv, available_actions);
+  }
+  for (int i = 1; i < argc; i++) {
+    bool arg_handled = false;
+    // Step 1. Try to match action invokation names.
+    for (auto it = available_actions.begin(); it != available_actions.end(); ++it) {
+      if (!strcmp(argv[i], (*it)->invokation_name())) {
+        if (!action) {
+          action = it->get();
+          arg_handled = true;
+          break;
+        } else {
+          cerr << "can't specify more than one action!" << endl;
+          show_usage_and_exit(argc, argv, available_actions);
+        }
+      }
+    }
+    if (arg_handled) {
+      continue;
+    }
+    // Step 2. Try to match option names.
+    if (argv[i][0] == '-') {
+      if (!strcmp(argv[i], "--only-cubic-sizes")) {
+        only_cubic_sizes = true;
+        arg_handled = true;
+      }
+      if (!strcmp(argv[i], "--dump-tables")) {
+        dump_tables = true;
+        arg_handled = true;
+      }
+      if (!arg_handled) {
+        cerr << "Unrecognized option: " << argv[i] << endl;
+        show_usage_and_exit(argc, argv, available_actions);
+      }
+    }
+    if (arg_handled) {
+      continue;
+    }
+    // Step 3. Default to interpreting args as input filenames.
+    input_filenames.emplace_back(argv[i]);
+  }
+
+  if (dump_tables && only_cubic_sizes) {
+    cerr << "Incompatible options: --only-cubic-sizes and --dump-tables." << endl;
+    show_usage_and_exit(argc, argv, available_actions);
+  }
+
+  if (!action) {
+    show_usage_and_exit(argc, argv, available_actions);
+  }
+
+  action->run(input_filenames);
+}