analyze-blocking-sizes.cpp
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Created: Fri, Jul 4, 16:12

analyze-blocking-sizes.cpp
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	// 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 invocation 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);
	}

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