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\chapter{Technology Mapping}
\label{chapter:techmap}

Previous chapters outlined how HDL code is transformed into an RTL netlist. The
RTL netlist is still based on abstract coarse-grain cell types like arbitrary
width adders and even multipliers. This chapter covers how an RTL netlist is
transformed into a functionally equivalent netlist utilizing the cell types
available in the target architecture.

Technology mapping is often performed in two phases. In the first phase RTL cells
are mapped to an internal library of single-bit cells (see Sec.~\ref{sec:celllib_gates}).
In the second phase this netlist of internal gate types is transformed to a netlist
of gates from the target technology library.

When the target architecture provides coarse-grain cells (such as block ram
or ALUs), these must be mapped to directly form the RTL netlist, as information
on the coarse-grain structure of the design is lost when it is mapped to
bit-width gate types.

\section{Cell Substitution}

The simplest form of technology mapping is cell substitution, as performed by
the {\tt techmap} pass. This pass, when provided with a Verilog file that
implements the RTL cell types using simpler cells, simply replaces the RTL
cells with the provided implementation.

When no map file is provided, {\tt techmap} uses a built-in map file that
maps the Yosys RTL cell types to the internal gate library used by Yosys.
The curious reader may find this map file as {\tt techlibs/common/techmap.v} in
the Yosys source tree.

Additional features have been added to {\tt techmap} to allow for conditional
mapping of cells (see {\tt help techmap} or Sec.~\ref{cmd:techmap}). This can
for example be useful if the target architecture supports hardware multipliers for
certain bit-widths but not for others.

A usual synthesis flow would first use the {\tt techmap} pass to directly map
some RTL cells to coarse-grain cells provided by the target architecture (if
any) and then use techmap with the built-in default file to map the remaining
RTL cells to gate logic.

\section{Subcircuit Substitution}

Sometimes the target architecture provides cells that are more powerful than
the RTL cells used by Yosys. For example a cell in the target architecture that can
calculate the absolute-difference of two numbers does not match any single
RTL cell type but only combinations of cells.

For these cases Yosys provides the {\tt extract} pass that can match a given set
of modules against a design and identify the portions of the design that are
identical (i.e.~isomorphic subcircuits) to any of the given modules. These
matched subcircuits are then replaced by instances of the given modules.

The {\tt extract} pass also finds basic variations of the given modules,
such as swapped inputs on commutative cell types.

In addition to this the {\tt extract} pass also has limited support for
frequent subcircuit mining, i.e.~the process of finding recurring subcircuits
in the design. This has a few applications, including the design of new
coarse-grain architectures \cite{intersynthFdlBookChapter}.

The hard algorithmic work done by the {\tt extract} pass (solving the
isomorphic subcircuit problem and frequent subcircuit mining) is performed
using the SubCircuit library that can also be used stand-alone without Yosys
(see Sec.~\ref{sec:SubCircuit}).

\section{Gate-Level Technology Mapping}
\label{sec:techmap_extern}

On the gate-level the target architecture is usually described by a ``Liberty
file''. The Liberty file format is an industry standard format that can be
used to describe the behaviour and other properties of standard library cells
\citeweblink{LibertyFormat}.

Mapping a design utilizing the Yosys internal gate library (e.g.~as a result
of mapping it to this representation using the {\tt techmap} pass) is
performed in two phases.

First the register cells must be mapped to the registers that are available
on the target architectures. The target architecture might not provide all
variations of d-type flip-flops with positive and negative clock edge,
high-active and low-active asynchronous set and/or reset, etc. Therefore the
process of mapping the registers might add additional inverters to the design
and thus it is important to map the register cells first.

Mapping of the register cells may be performed by using the {\tt dfflibmap}
pass. This pass expects a Liberty file as argument (using the {\tt -liberty}
option) and only uses the register cells from the Liberty file.

Secondly the combinational logic must be mapped to the target architecture.
This is done using the external program ABC \citeweblink{ABC} via the
{\tt abc} pass by using the {\tt -liberty} option to the pass. Note that
in this case only the combinatorial cells are used from the cell library.

Occasionally Liberty files contain trade secrets (such as sensitive timing
information) that cannot be shared freely. This complicates processes such as
reporting bugs in the tools involved. When the information in the Liberty file
used by Yosys and ABC are not part of the sensitive information, the additional
tool {\tt yosys-filterlib} (see Sec.~\ref{sec:filterlib}) can be used to strip
the sensitive information from the Liberty file.
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// This is free and unencumbered software released into the public domain.
//
// Anyone is free to copy, modify, publish, use, compile, sell, or
// distribute this software, either in source code form or as a compiled
// binary, for any purpose, commercial or non-commercial, and by any
// means.

// -------------------------------------------------------
// Written by Clifford Wolf <clifford@clifford.at> in 2014
// -------------------------------------------------------

#ifndef HASHLIB_H
#define HASHLIB_H

#include <stdexcept>
#include <algorithm>
#include <string>
#include <vector>

namespace hashlib {

const int hashtable_size_trigger = 2;
const int hashtable_size_factor = 3;

// The XOR version of DJB2
inline unsigned int mkhash(unsigned int a, unsigned int b) {
	return ((a << 5) + a) ^ b;
}

// traditionally 5381 is used as starting value for the djb2 hash
const unsigned int mkhash_init = 5381;

// The ADD version of DJB2
// (use this version for cache locality in b)
inline unsigned int mkhash_add(unsigned int a, unsigned int b) {
	return ((a << 5) + a) + b;
}

inline unsigned int mkhash_xorshift(unsigned int a) {
	if (sizeof(a) == 4) {
		a ^= a << 13;
		a ^= a >> 17;
		a ^= a << 5;
	} else if (sizeof(a) == 8) {
		a ^= a << 13;
		a ^= a >> 7;
		a ^= a << 17;
	} else
		throw std::runtime_error("mkhash_xorshift() only implemented for 32 bit and 64 bit ints");
	return a;
}

template<typename T> struct hash_ops {
	static inline bool cmp(const T &a, const T &b) {
		return a == b;
	}
	static inline unsigned int hash(const T &a) {
		return a.hash();
	}
};

struct hash_int_ops {
	template<typename T>
	static inline bool cmp(T a, T b) {
		return a == b;
	}
};

template<> struct hash_ops<int32_t> : hash_int_ops
{
	static inline unsigned int hash(int32_t a) {
		return a;
	}
};
template<> struct hash_ops<int64_t> : hash_int_ops
{
	static inline unsigned int hash(int64_t a) {
		return mkhash((unsigned int)(a), (unsigned int)(a >> 32));
	}
};

template<> struct hash_ops<std::string> {
	static inline bool cmp(const std::string &a, const std::string &b) {
		return a == b;
	}
	static inline unsigned int hash(const std::string &a) {
		unsigned int v = 0;
		for (auto c : a)
			v = mkhash(v, c);
		return v;
	}
};

template<typename P, typename Q> struct hash_ops<std::pair<P, Q>> {
	static inline bool cmp(std::pair<P, Q> a, std::pair<P, Q> b) {
		return a == b;
	}
	static inline unsigned int hash(std::pair<P, Q> a) {
		return mkhash(hash_ops<P>::hash(a.first), hash_ops<Q>::hash(a.second));
	}
};

template<typename... T> struct hash_ops<std::tuple<T...>> {
	static inline bool cmp(std::tuple<T...> a, std::tuple<T...> b) {
		return a == b;
	}
	template<size_t I = 0>
	static inline typename std::enable_if<I == sizeof...(T), unsigned int>::type hash(std::tuple<T...>) {
		return mkhash_init;
	}
	template<size_t I = 0>
	static inline typename std::enable_if<I != sizeof...(T), unsigned int>::type hash(std::tuple<T...> a) {
		typedef hash_ops<typename std::tuple_element<I, std::tuple<T...>>::type> element_ops_t;
		return mkhash(hash<I+1>(a), element_ops_t::hash(std::get<I>(a)));
	}
};

template<typename T> struct hash_ops<std::vector<T>> {
	static inline bool cmp(std::vector<T> a, std::vector<T> b) {
		return a == b;
	}
	static inline unsigned int hash(std::vector<T> a) {
		unsigned int h = mkhash_init;
		for (auto k : a)
			h = mkhash(h, hash_ops<T>::hash(k));
		return h;
	}
};

struct hash_cstr_ops {
	static inline bool cmp(const char *a, const char *b) {
		for (int i = 0; a[i] || b[i]; i++)
			if (a[i] != b[i])
				return false;
		return true;
	}
	static inline unsigned int hash(const char *a) {
		unsigned int hash = mkhash_init;
		while (*a)
			hash = mkhash(hash, *(a++));
		return hash;
	}
};

struct hash_ptr_ops {
	static inline bool cmp(const void *a, const void *b) {
		return a == b;
	}
	static inline unsigned int hash(const void *a) {
		return (uintptr_t)a;
	}
};

struct hash_obj_ops {
	static inline bool cmp(const void *a, const void *b) {
		return a == b;
	}
	template<typename T>
	static inline unsigned int hash(const T *a) {
		return a ? a->hash() : 0;
	}
};

template<typename T>
inline unsigned int mkhash(const T &v) {
	return hash_ops<T>().hash(v);
}

inline int hashtable_size(int min_size)
{
	static std::vector<int> zero_and_some_primes = {
		0, 23, 29, 37, 47, 59, 79, 101, 127, 163, 211, 269, 337, 431, 541, 677,
		853, 1069, 1361, 1709, 2137, 2677, 3347, 4201, 5261, 6577, 8231, 10289,
		12889, 16127, 20161, 25219, 31531, 39419, 49277, 61603, 77017, 96281,
		120371, 150473, 188107, 235159, 293957, 367453, 459317, 574157, 717697,
		897133, 1121423, 1401791, 1752239, 2190299, 2737937, 3422429, 4278037,
		5347553, 6684443, 8355563, 10444457, 13055587, 16319519, 20399411,
		25499291, 31874149, 39842687, 49803361, 62254207, 77817767, 97272239,
		121590311, 151987889, 189984863, 237481091, 296851369, 371064217
	};

	for (auto p : zero_and_some_primes)
		if (p >= min_size) return p;

	if (sizeof(int) == 4)
		throw std::length_error("hash table exceeded maximum size. use a ILP64 abi for larger tables.");

	for (auto p : zero_and_some_primes)
		if (100129 * p > min_size) return 100129 * p;

	throw std::length_error("hash table exceeded maximum size.");
}

template<typename K, typename T, typename OPS = hash_ops<K>> class dict;
template<typename K, int offset = 0, typename OPS = hash_ops<K>> class idict;
template<typename K, typename OPS = hash_ops<K>> class pool;
template<typename K, typename OPS = hash_ops<K>> class mfp;

template<typename K, typename T, typename OPS>
class dict
{
	struct entry_t
	{
		std::pair<K, T> udata;
		int next;

		entry_t() { }
		entry_t(const std::pair<K, T> &udata, int next) : udata(udata), next(next) { }
		entry_t(std::pair<K, T> &&udata, int next) : udata(std::move(udata)), next(next) { }
	};

	std::vector<int> hashtable;
	std::vector<entry_t> entries;
	OPS ops;

#ifdef NDEBUG
	static inline void do_assert(bool) { }
#else
	static inline void do_assert(bool cond) {
		if (!cond) throw std::runtime_error("dict<> assert failed.");
	}
#endif

	int do_hash(const K &key) const
	{
		unsigned int hash = 0;
		if (!hashtable.empty())
			hash = ops.hash(key) % (unsigned int)(hashtable.size());
		return hash;
	}

	void do_rehash()
	{
		hashtable.clear();
		hashtable.resize(hashtable_size(entries.capacity() * hashtable_size_factor), -1);

		for (int i = 0; i < int(entries.size()); i++) {
			do_assert(-1 <= entries[i].next && entries[i].next < int(entries.size()));
			int hash = do_hash(entries[i].udata.first);
			entries[i].next = hashtable[hash];
			hashtable[hash] = i;
		}
	}

	int do_erase(int index, int hash)
	{
		do_assert(index < int(entries.size()));
		if (hashtable.empty() || index < 0)
			return 0;

		int k = hashtable[hash];
		do_assert(0 <= k && k < int(entries.size()));

		if (k == index) {
			hashtable[hash] = entries[index].next;
		} else {
			while (entries[k].next != index) {
				k = entries[k].next;
				do_assert(0 <= k && k < int(entries.size()));
			}
			entries[k].next = entries[index].next;
		}

		int back_idx = entries.size()-1;

		if (index != back_idx)
		{
			int back_hash = do_hash(entries[back_idx].udata.first);

			k = hashtable[back_hash];
			do_assert(0 <= k && k < int(entries.size()));

			if (k == back_idx) {
				hashtable[back_hash] = index;
			} else {
				while (entries[k].next != back_idx) {
					k = entries[k].next;
					do_assert(0 <= k && k < int(entries.size()));
				}
				entries[k].next = index;
			}

			entries[index] = std::move(entries[back_idx]);
		}

		entries.pop_back();

		if (entries.empty())
			hashtable.clear();

		return 1;
	}

	int do_lookup(const K &key, int &hash) const
	{
		if (hashtable.empty())
			return -1;

		if (entries.size() * hashtable_size_trigger > hashtable.size()) {
			((dict*)this)->do_rehash();
			hash = do_hash(key);
		}

		int index = hashtable[hash];

		while (index >= 0 && !ops.cmp(entries[index].udata.first, key)) {
			index = entries[index].next;
			do_assert(-1 <= index && index < int(entries.size()));
		}

		return index;
	}

	int do_insert(const K &key, int &hash)
	{
		if (hashtable.empty()) {
			entries.push_back(entry_t(std::pair<K, T>(key, T()), -1));
			do_rehash();
			hash = do_hash(key);
		} else {
			entries.push_back(entry_t(std::pair<K, T>(key, T()), hashtable[hash]));
			hashtable[hash] = entries.size() - 1;
		}
		return entries.size() - 1;
	}

	int do_insert(const std::pair<K, T> &value, int &hash)
	{
		if (hashtable.empty()) {
			entries.push_back(entry_t(value, -1));
			do_rehash();
			hash = do_hash(value.first);
		} else {
			entries.push_back(entry_t(value, hashtable[hash]));
			hashtable[hash] = entries.size() - 1;
		}
		return entries.size() - 1;
	}

public:
	class const_iterator : public std::iterator<std::forward_iterator_tag, std::pair<K, T>>
	{
		friend class dict;
	protected:
		const dict *ptr;
		int index;
		const_iterator(const dict *ptr, int index) : ptr(ptr), index(index) { }
	public:
		const_iterator() { }
		const_iterator operator++() { index--; return *this; }
		bool operator<(const const_iterator &other) const { return index > other.index; }
		bool operator==(const const_iterator &other) const { return index == other.index; }
		bool operator!=(const const_iterator &other) const { return index != other.index; }
		const std::pair<K, T> &operator*() const { return ptr->entries[index].udata; }
		const std::pair<K, T> *operator->() const { return &ptr->entries[index].udata; }
	};

	class iterator : public std::iterator<std::forward_iterator_tag, std::pair<K, T>>
	{
		friend class dict;
	protected:
		dict *ptr;
		int index;
		iterator(dict *ptr, int index) : ptr(ptr), index(index) { }
	public:
		iterator() { }
		iterator operator++() { index--; return *this; }
		bool operator<(const iterator &other) const { return index > other.index; }
		bool operator==(const iterator &other) const { return index == other.index; }
		bool operator!=(const iterator &other) const { return index != other.index; }
		std::pair<K, T> &operator*() { return ptr->entries[index].udata; }
		std::pair<K, T> *operator->() { return &ptr->entries[index].udata; }
		const std::pair<K, T> &operator*() const { return ptr->entries[index].udata; }
		const std::pair<K, T> *operator->() const { return &ptr->entries[index].udata; }
		operator const_iterator() const { return const_iterator(ptr, index); }
	};

	dict()
	{
	}

	dict(const dict &other)
	{
		entries = other.entries;
		do_rehash();
	}

	dict(dict &&other)
	{
		swap(other);
	}

	dict &operator=(const dict &other) {
		entries = other.entries;
		do_rehash();
		return *this;
	}

	dict &operator=(dict &&other) {
		clear();
		swap(other);
		return *this;
	}

	dict(const std::initializer_list<std::pair<K, T>> &list)
	{
		for (auto &it : list)
			insert(it);
	}

	template<class InputIterator>
	dict(InputIterator first, InputIterator last)
	{
		insert(first, last);
	}

	template<class InputIterator>
	void insert(InputIterator first, InputIterator last)
	{
		for (; first != last; ++first)
			insert(*first);
	}

	std::pair<iterator, bool> insert(const K &key)
	{
		int hash = do_hash(key);
		int i = do_lookup(key, hash);
		if (i >= 0)
			return std::pair<iterator, bool>(iterator(this, i), false);
		i = do_insert(key, hash);
		return std::pair<iterator, bool>(iterator(this, i), true);
	}

	std::pair<iterator, bool> insert(const std::pair<K, T> &value)
	{
		int hash = do_hash(value.first);
		int i = do_lookup(value.first, hash);
		if (i >= 0)
			return std::pair<iterator, bool>(iterator(this, i), false);
		i = do_insert(value, hash);
		return std::pair<iterator, bool>(iterator(this, i), true);
	}

	int erase(const K &key)
	{
		int hash = do_hash(key);
		int index = do_lookup(key, hash);
		return do_erase(index, hash);
	}

	iterator erase(iterator it)
	{
		int hash = do_hash(it->first);
		do_erase(it.index, hash);
		return ++it;
	}

	int count(const K &key) const
	{
		int hash = do_hash(key);
		int i = do_lookup(key, hash);
		return i < 0 ? 0 : 1;
	}

	int count(const K &key, const_iterator it) const
	{
		int hash = do_hash(key);
		int i = do_lookup(key, hash);
		return i < 0 || i > it.index ? 0 : 1;
	}

	iterator find(const K &key)
	{
		int hash = do_hash(key);
		int i = do_lookup(key, hash);
		if (i < 0)
			return end();
		return iterator(this, i);
	}

	const_iterator find(const K &key) const
	{
		int hash = do_hash(key);
		int i = do_lookup(key, hash);
		if (i < 0)
			return end();
		return const_iterator(this, i);
	}

	T& at(const K &key)
	{
		int hash = do_hash(key);
		int i = do_lookup(key, hash);
		if (i < 0)
			throw std::out_of_range("dict::at()");
		return entries[i].udata.second;
	}

	const T& at(const K &key) const
	{
		int hash = do_hash(key);
		int i = do_lookup(key, hash);
		if (i < 0)
			throw std::out_of_range("dict::at()");
		return entries[i].udata.second;
	}

	T at(const K &key, const T &defval) const
	{
		int hash = do_hash(key);
		int i = do_lookup(key, hash);
		if (i < 0)
			return defval;
		return entries[i].udata.second;
	}

	T& operator[](const K &key)
	{
		int hash = do_hash(key);
		int i = do_lookup(key, hash);
		if (i < 0)
			i = do_insert(std::pair<K, T>(key, T()), hash);
		return entries[i].udata.second;
	}

	template<typename Compare = std::less<K>>
	void sort(Compare comp = Compare())
	{
		std::sort(entries.begin(), entries.end(), [comp](const entry_t &a, const entry_t &b){ return comp(b.udata.first, a.udata.first); });
		do_rehash();
	}

	void swap(dict &other)
	{
		hashtable.swap(other.hashtable);
		entries.swap(other.entries);
	}

	bool operator==(const dict &other) const {
		if (size() != other.size())
			return false;
		for (auto &it : entries) {
			auto oit = other.find(it.udata.first);
			if (oit == other.end() || !(oit->second == it.udata.second))
				return false;
		}
		return true;
	}

	bool operator!=(const dict &other) const {
		return !operator==(other);
	}

	void reserve(size_t n) { entries.reserve(n); }
	size_t size() const { return entries.size(); }
	bool empty() const { return entries.empty(); }
	void clear() { hashtable.clear(); entries.clear(); }

	iterator begin() { return iterator(this, int(entries.size())-1); }
	iterator end() { return iterator(nullptr, -1); }

	const_iterator begin() const { return const_iterator(this, int(entries.size())-1); }
	const_iterator end() const { return const_iterator(nullptr, -1); }
};

template<typename K, typename OPS>
class pool
{
	template<typename, int, typename> friend class idict;

protected:
	struct entry_t
	{
		K udata;
		int next;

		entry_t() { }
		entry_t(const K &udata, int next) : udata(udata), next(next) { }
	};

	std::vector<int> hashtable;
	std::vector<entry_t> entries;
	OPS ops;

#ifdef NDEBUG
	static inline void do_assert(bool) { }
#else
	static inline void do_assert(bool cond) {
		if (!cond) throw std::runtime_error("pool<> assert failed.");
	}
#endif

	int do_hash(const K &key) const
	{
		unsigned int hash = 0;
		if (!hashtable.empty())
			hash = ops.hash(key) % (unsigned int)(hashtable.size());
		return hash;
	}

	void do_rehash()
	{
		hashtable.clear();
		hashtable.resize(hashtable_size(entries.capacity() * hashtable_size_factor), -1);

		for (int i = 0; i < int(entries.size()); i++) {
			do_assert(-1 <= entries[i].next && entries[i].next < int(entries.size()));
			int hash = do_hash(entries[i].udata);
			entries[i].next = hashtable[hash];
			hashtable[hash] = i;
		}
	}

	int do_erase(int index, int hash)
	{
		do_assert(index < int(entries.size()));
		if (hashtable.empty() || index < 0)
			return 0;

		int k = hashtable[hash];
		if (k == index) {
			hashtable[hash] = entries[index].next;
		} else {
			while (entries[k].next != index) {
				k = entries[k].next;
				do_assert(0 <= k && k < int(entries.size()));
			}
			entries[k].next = entries[index].next;
		}

		int back_idx = entries.size()-1;

		if (index != back_idx)
		{
			int back_hash = do_hash(entries[back_idx].udata);

			k = hashtable[back_hash];
			if (k == back_idx) {
				hashtable[back_hash] = index;
			} else {
				while (entries[k].next != back_idx) {
					k = entries[k].next;
					do_assert(0 <= k && k < int(entries.size()));
				}
				entries[k].next = index;
			}

			entries[index] = std::move(entries[back_idx]);
		}

		entries.pop_back();

		if (entries.empty())
			hashtable.clear();

		return 1;
	}

	int do_lookup(const K &key, int &hash) const
	{
		if (hashtable.empty())
			return -1;

		if (entries.size() * hashtable_size_trigger > hashtable.size()) {
			((pool*)this)->do_rehash();
			hash = do_hash(key);
		}

		int index = hashtable[hash];

		while (index >= 0 && !ops.cmp(entries[index].udata, key)) {
			index = entries[index].next;
			do_assert(-1 <= index && index < int(entries.size()));
		}

		return index;
	}

	int do_insert(const K &value, int &hash)
	{
		if (hashtable.empty()) {
			entries.push_back(entry_t(value, -1));
			do_rehash();
			hash = do_hash(value);
		} else {
			entries.push_back(entry_t(value, hashtable[hash]));
			hashtable[hash] = entries.size() - 1;
		}
		return entries.size() - 1;
	}

public:
	class const_iterator : public std::iterator<std::forward_iterator_tag, K>
	{
		friend class pool;
	protected:
		const pool *ptr;
		int index;
		const_iterator(const pool *ptr, int index) : ptr(ptr), index(index) { }
	public:
		const_iterator() { }
		const_iterator operator++() { index--; return *this; }
		bool operator==(const const_iterator &other) const { return index == other.index; }
		bool operator!=(const const_iterator &other) const { return index != other.index; }
		const K &operator*() const { return ptr->entries[index].udata; }
		const K *operator->() const { return &ptr->entries[index].udata; }
	};

	class iterator : public std::iterator<std::forward_iterator_tag, K>
	{
		friend class pool;
	protected:
		pool *ptr;
		int index;
		iterator(pool *ptr, int index) : ptr(ptr), index(index) { }
	public:
		iterator() { }
		iterator operator++() { index--; return *this; }
		bool operator==(const iterator &other) const { return index == other.index; }
		bool operator!=(const iterator &other) const { return index != other.index; }
		K &operator*() { return ptr->entries[index].udata; }
		K *operator->() { return &ptr->entries[index].udata; }
		const K &operator*() const { return ptr->entries[index].udata; }
		const K *operator->() const { return &ptr->entries[index].udata; }
		operator const_iterator() const { return const_iterator(ptr, index); }
	};

	pool()
	{
	}

	pool(const pool &other)
	{
		entries = other.entries;
		do_rehash();
	}

	pool(pool &&other)
	{
		swap(other);
	}

	pool &operator=(const pool &other) {
		entries = other.entries;
		do_rehash();
		return *this;
	}

	pool &operator=(pool &&other) {
		clear();
		swap(other);
		return *this;
	}

	pool(const std::initializer_list<K> &list)
	{
		for (auto &it : list)
			insert(it);
	}

	template<class InputIterator>
	pool(InputIterator first, InputIterator last)
	{
		insert(first, last);
	}

	template<class InputIterator>
	void insert(InputIterator first, InputIterator last)
	{
		for (; first != last; ++first)
			insert(*first);
	}

	std::pair<iterator, bool> insert(const K &value)
	{
		int hash = do_hash(value);
		int i = do_lookup(value, hash);
		if (i >= 0)
			return std::pair<iterator, bool>(iterator(this, i), false);
		i = do_insert(value, hash);
		return std::pair<iterator, bool>(iterator(this, i), true);
	}

	int erase(const K &key)
	{
		int hash = do_hash(key);
		int index = do_lookup(key, hash);
		return do_erase(index, hash);
	}

	iterator erase(iterator it)
	{
		int hash = do_hash(*it);
		do_erase(it.index, hash);
		return ++it;
	}

	int count(const K &key) const
	{
		int hash = do_hash(key);
		int i = do_lookup(key, hash);
		return i < 0 ? 0 : 1;
	}

	int count(const K &key, const_iterator it) const
	{
		int hash = do_hash(key);
		int i = do_lookup(key, hash);
		return i < 0 || i > it.index ? 0 : 1;
	}

	iterator find(const K &key)
	{
		int hash = do_hash(key);
		int i = do_lookup(key, hash);
		if (i < 0)
			return end();
		return iterator(this, i);
	}

	const_iterator find(const K &key) const
	{
		int hash = do_hash(key);
		int i = do_lookup(key, hash);
		if (i < 0)
			return end();
		return const_iterator(this, i);
	}

	bool operator[](const K &key)
	{
		int hash = do_hash(key);
		int i = do_lookup(key, hash);
		return i >= 0;
	}

	template<typename Compare = std::less<K>>
	void sort(Compare comp = Compare())
	{
		std::sort(entries.begin(), entries.end(), [comp](const entry_t &a, const entry_t &b){ return comp(b.udata, a.udata); });
		do_rehash();
	}

	K pop()
	{
		iterator it = begin();
		K ret = *it;
		erase(it);
		return ret;
	}

	void swap(pool &other)
	{
		hashtable.swap(other.hashtable);
		entries.swap(other.entries);
	}

	bool operator==(const pool &other) const {
		if (size() != other.size())
			return false;
		for (auto &it : entries)
			if (!other.count(it.udata))
				return false;
		return true;
	}

	bool operator!=(const pool &other) const {
		return !operator==(other);
	}

	bool hash() const {
		unsigned int hashval = mkhash_init;
		for (auto &it : entries)
			hashval ^= ops.hash(it.udata);
		return hashval;
	}

	void reserve(size_t n) { entries.reserve(n); }
	size_t size() const { return entries.size(); }
	bool empty() const { return entries.empty(); }
	void clear() { hashtable.clear(); entries.clear(); }

	iterator begin() { return iterator(this, int(entries.size())-1); }
	iterator end() { return iterator(nullptr, -1); }

	const_iterator begin() const { return const_iterator(this, int(entries.size())-1); }
	const_iterator end() const { return const_iterator(nullptr, -1); }
};

template<typename K, int offset, typename OPS>
class idict
{
	pool<K, OPS> database;

public:
	typedef typename pool<K, OPS>::const_iterator const_iterator;

	int operator()(const K &key)
	{
		int hash = database.do_hash(key);
		int i = database.do_lookup(key, hash);
		if (i < 0)
			i = database.do_insert(key, hash);
		return i + offset;
	}

	int at(const K &key) const
	{
		int hash = database.do_hash(key);
		int i = database.do_lookup(key, hash);
		if (i < 0)
			throw std::out_of_range("idict::at()");
		return i + offset;
	}

	int at(const K &key, int defval) const
	{
		int hash = database.do_hash(key);
		int i = database.do_lookup(key, hash);
		if (i < 0)
			return defval;
		return i + offset;
	}

	int count(const K &key) const
	{
		int hash = database.do_hash(key);
		int i = database.do_lookup(key, hash);
		return i < 0 ? 0 : 1;
	}

	void expect(const K &key, int i)
	{
		int j = (*this)(key);
		if (i != j)
			throw std::out_of_range("idict::expect()");
	}

	const K &operator[](int index) const
	{
		return database.entries.at(index - offset).udata;
	}

	void swap(idict &other)
	{
		database.swap(other.database);
	}

	void reserve(size_t n) { database.reserve(n); }
	size_t size() const { return database.size(); }
	bool empty() const { return database.empty(); }
	void clear() { database.clear(); }

	const_iterator begin() const { return database.begin(); }
	const_iterator end() const { return database.end(); }
};

template<typename K, typename OPS>
class mfp
{
	mutable idict<K, 0, OPS> database;
	mutable std::vector<int> parents;

public:
	typedef typename idict<K, 0, OPS>::const_iterator const_iterator;

	int operator()(const K &key) const
	{
		int i = database(key);
		parents.resize(database.size(), -1);
		return i;
	}

	const K &operator[](int index) const
	{
		return database[index];
	}

	int ifind(int i) const
	{
		int p = i, k = i;

		while (parents[p] != -1)
			p = parents[p];

		while (k != p) {
			int next_k = parents[k];
			parents[k] = p;
			k = next_k;
		}

		return p;
	}

	void imerge(int i, int j)
	{
		i = ifind(i);
		j = ifind(j);

		if (i != j)
			parents[i] = j;
	}

	void ipromote(int i)
	{
		int k = i;

		while (k != -1) {
			int next_k = parents[k];
			parents[k] = i;
			k = next_k;
		}

		parents[i] = -1;
	}

	int lookup(const K &a) const
	{
		return ifind((*this)(a));
	}

	const K &find(const K &a) const
	{
		int i = database.at(a, -1);
		if (i < 0)
			return a;
		return (*this)[ifind(i)];
	}

	void merge(const K &a, const K &b)
	{
		imerge((*this)(a), (*this)(b));
	}

	void promote(const K &a)
	{
		int i = database.at(a, -1);
		if (i >= 0)
			ipromote(i);
	}

	void swap(mfp &other)
	{
		database.swap(other.database);
		parents.swap(other.parents);
	}

	void reserve(size_t n) { database.reserve(n); }
	size_t size() const { return database.size(); }
	bool empty() const { return database.empty(); }
	void clear() { database.clear(); parents.clear(); }

	const_iterator begin() const { return database.begin(); }
	const_iterator end() const { return database.end(); }
};

} /* namespace hashlib */

#endif