docs/community.rst


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Community
=========

You can find ``cryptography`` all over the web:

* `Mailing list`_
* `Source code`_
* `Issue tracker`_
* `Documentation`_
* IRC: ``#cryptography-dev`` on ``irc.freenode.net``

Wherever we interact, we strive to follow the `Python Community Code of
Conduct`_.


.. _`Mailing list`: https://mail.python.org/mailman/listinfo/cryptography-dev
.. _`Source code`: https://github.com/pyca/cryptography
.. _`Issue tracker`: https://github.com/pyca/cryptography/issues
.. _`Documentation`: https://cryptography.io/
.. _`Python Community Code of Conduct`: http://www.python.org/psf/codeofconduct/
/*
 *  yosys -- Yosys Open SYnthesis Suite
 *
 *  Copyright (C) 2019-2020  whitequark <whitequark@whitequark.org>
 *
 *  Permission to use, copy, modify, and/or distribute this software for any
 *  purpose with or without fee is hereby granted.
 *
 *  THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 *  WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 *  MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 *  ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 *  WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 *  ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 *  OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 *
 */

// This file is included by the designs generated with `write_cxxrtl`. It is not used in Yosys itself.
//
// The CXXRTL support library implements compile time specialized arbitrary width arithmetics, as well as provides
// composite lvalues made out of bit slices and concatenations of lvalues. This allows the `write_cxxrtl` pass
// to perform a straightforward translation of RTLIL structures to readable C++, relying on the C++ compiler
// to unwrap the abstraction and generate efficient code.

#ifndef CXXRTL_H
#define CXXRTL_H

#include <cstddef>
#include <cstdint>
#include <cassert>
#include <limits>
#include <type_traits>
#include <tuple>
#include <vector>
#include <map>
#include <algorithm>
#include <memory>
#include <functional>
#include <sstream>

#include <backends/cxxrtl/cxxrtl_capi.h>

#ifndef __has_attribute
#	define __has_attribute(x) 0
#endif

// CXXRTL essentially uses the C++ compiler as a hygienic macro engine that feeds an instruction selector.
// It generates a lot of specialized template functions with relatively large bodies that, when inlined
// into the caller and (for those with loops) unrolled, often expose many new optimization opportunities.
// Because of this, most of the CXXRTL runtime must be always inlined for best performance.
#if __has_attribute(always_inline)
#define CXXRTL_ALWAYS_INLINE inline __attribute__((__always_inline__))
#else
#define CXXRTL_ALWAYS_INLINE inline
#endif
// Conversely, some functions in the generated code are extremely large yet very cold, with both of these
// properties being extreme enough to confuse C++ compilers into spending pathological amounts of time
// on a futile (the code becomes worse) attempt to optimize the least important parts of code.
#if __has_attribute(optnone)
#define CXXRTL_EXTREMELY_COLD __attribute__((__optnone__))
#elif __has_attribute(optimize)
#define CXXRTL_EXTREMELY_COLD __attribute__((__optimize__(0)))
#else
#define CXXRTL_EXTREMELY_COLD
#endif

// CXXRTL uses assert() to check for C++ contract violations (which may result in e.g. undefined behavior
// of the simulation code itself), and CXXRTL_ASSERT to check for RTL contract violations (which may at
// most result in undefined simulation results).
//
// Though by default, CXXRTL_ASSERT() expands to assert(), it may be overridden e.g. when integrating
// the simulation into another process that should survive violating RTL contracts.
#ifndef CXXRTL_ASSERT
#ifndef CXXRTL_NDEBUG
#define CXXRTL_ASSERT(x) assert(x)
#else
#define CXXRTL_ASSERT(x)
#endif
#endif

namespace cxxrtl {

// All arbitrary-width values in CXXRTL are backed by arrays of unsigned integers called chunks. The chunk size
// is the same regardless of the value width to simplify manipulating values via FFI interfaces, e.g. driving
// and introspecting the simulation in Python.
//
// It is practical to use chunk sizes between 32 bits and platform register size because when arithmetics on
// narrower integer types is legalized by the C++ compiler, it inserts code to clear the high bits of the register.
// However, (a) most of our operations do not change those bits in the first place because of invariants that are
// invisible to the compiler, (b) we often operate on non-power-of-2 values and have to clear the high bits anyway.
// Therefore, using relatively wide chunks and clearing the high bits explicitly and only when we know they may be
// clobbered results in simpler generated code.
typedef uint32_t chunk_t;
typedef uint64_t wide_chunk_t;

template<typename T>
struct chunk_traits {
	static_assert(std::is_integral<T>::value && std::is_unsigned<T>::value,
	              "chunk type must be an unsigned integral type");
	using type = T;
	static constexpr size_t bits = std::numeric_limits<T>::digits;
	static constexpr T mask = std::numeric_limits<T>::max();
};

template<class T>
struct expr_base;

template<size_t Bits>
struct value : public expr_base<value<Bits>> {
	static constexpr size_t bits = Bits;

	using chunk = chunk_traits<chunk_t>;
	static constexpr chunk::type msb_mask = (Bits % chunk::bits == 0) ? chunk::mask
		: chunk::mask >> (chunk::bits - (Bits % chunk::bits));

	static constexpr size_t chunks = (Bits + chunk::bits - 1) / chunk::bits;
	chunk::type data[chunks] = {};

	value() = default;
	template<typename... Init>
	explicit constexpr value(Init ...init) : data{init...} {}

	value(const value<Bits> &) = default;
	value<Bits> &operator=(const value<Bits> &) = default;

	value(value<Bits> &&) = default;
	value<Bits> &operator=(value<Bits> &&) = default;

	// A (no-op) helper that forces the cast to value<>.
	CXXRTL_ALWAYS_INLINE
	const value<Bits> &val() const {
		return *this;
	}

	std::string str() const {
		std::stringstream ss;
		ss << *this;
		return ss.str();
	}

	// Conversion operations.
	//
	// These functions ensure that a conversion is never out of range, and should be always used, if at all
	// possible, instead of direct manipulation of the `data` member. For very large types, .slice() and
	// .concat() can be used to split them into more manageable parts.
	template<class IntegerT>
	CXXRTL_ALWAYS_INLINE
	IntegerT get() const {
		static_assert(std::numeric_limits<IntegerT>::is_integer && !std::numeric_limits<IntegerT>::is_signed,
		              "get<T>() requires T to be an unsigned integral type");
		static_assert(std::numeric_limits<IntegerT>::digits >= Bits,
		              "get<T>() requires T to be at least as wide as the value is");
		IntegerT result = 0;
		for (size_t n = 0; n < chunks; n++)
			result |= IntegerT(data[n]) << (n * chunk::bits);
		return result;
	}

	template<class IntegerT>
	CXXRTL_ALWAYS_INLINE
	void set(IntegerT other) {
		static_assert(std::numeric_limits<IntegerT>::is_integer && !std::numeric_limits<IntegerT>::is_signed,
		              "set<T>() requires T to be an unsigned integral type");
		static_assert(std::numeric_limits<IntegerT>::digits >= Bits,
		              "set<T>() requires the value to be at least as wide as T is");
		for (size_t n = 0; n < chunks; n++)
			data[n] = (other >> (n * chunk::bits)) & chunk::mask;
	}

	// Operations with compile-time parameters.
	//
	// These operations are used to implement slicing, concatenation, and blitting.
	// The trunc, zext and sext operations add or remove most significant bits (i.e. on the left);
	// the rtrunc and rzext operations add or remove least significant bits (i.e. on the right).
	template<size_t NewBits>
	CXXRTL_ALWAYS_INLINE
	value<NewBits> trunc() const {
		static_assert(NewBits <= Bits, "trunc() may not increase width");
		value<NewBits> result;
		for (size_t n = 0; n < result.chunks; n++)
			result.data[n] = data[n];
		result.data[result.chunks - 1] &= result.msb_mask;
		return result;
	}

	template<size_t NewBits>
	CXXRTL_ALWAYS_INLINE
	value<NewBits> zext() const {
		static_assert(NewBits >= Bits, "zext() may not decrease width");
		value<NewBits> result;
		for (size_t n = 0; n < chunks; n++)
			result.data[n] = data[n];
		return result;
	}

	template<size_t NewBits>
	CXXRTL_ALWAYS_INLINE
	value<NewBits> sext() const {
		static_assert(NewBits >= Bits, "sext() may not decrease width");
		value<NewBits> result;
		for (size_t n = 0; n < chunks; n++)
			result.data[n] = data[n];
		if (is_neg()) {
			result.data[chunks - 1] |= ~msb_mask;
			for (size_t n = chunks; n < result.chunks; n++)
				result.data[n] = chunk::mask;
			result.data[result.chunks - 1] &= result.msb_mask;
		}
		return result;
	}

	template<size_t NewBits>
	CXXRTL_ALWAYS_INLINE
	value<NewBits> rtrunc() const {
		static_assert(NewBits <= Bits, "rtrunc() may not increase width");
		value<NewBits> result;
		constexpr size_t shift_chunks = (Bits - NewBits) / chunk::bits;
		constexpr size_t shift_bits   = (Bits - NewBits) % chunk::bits;
		chunk::type carry = 0;
		if (shift_chunks + result.chunks < chunks) {
			carry = (shift_bits == 0) ? 0
				: data[shift_chunks + result.chunks] << (chunk::bits - shift_bits);
		}
		for (size_t n = result.chunks; n > 0; n--) {
			result.data[n - 1] = carry | (data[shift_chunks + n - 1] >> shift_bits);
			carry = (shift_bits == 0) ? 0
				: data[shift_chunks + n - 1] << (chunk::bits - shift_bits);
		}
		return result;
	}

	template<size_t NewBits>
	CXXRTL_ALWAYS_INLINE
	value<NewBits> rzext() const {
		static_assert(NewBits >= Bits, "rzext() may not decrease width");
		value<NewBits> result;
		constexpr size_t shift_chunks = (NewBits - Bits) / chunk::bits;
		constexpr size_t shift_bits   = (NewBits - Bits) % chunk::bits;
		chunk::type carry = 0;
		for (size_t n = 0; n < chunks; n++) {
			result.data[shift_chunks + n] = (data[n] << shift_bits) | carry;
			carry = (shift_bits == 0) ? 0
				: data[n] >> (chunk::bits - shift_bits);
		}
		if (shift_chunks + chunks < result.chunks)
			result.data[shift_chunks + chunks] = carry;
		return result;
	}

	// Bit blit operation, i.e. a partial read-modify-write.
	template<size_t Stop, size_t Start>
	CXXRTL_ALWAYS_INLINE
	value<Bits> blit(const value<Stop - Start + 1> &source) const {
		static_assert(Stop >= Start, "blit() may not reverse bit order");
		constexpr chunk::type start_mask = ~(chunk::mask << (Start % chunk::bits));
		constexpr chunk::type stop_mask = (Stop % chunk::bits + 1 == chunk::bits) ? 0
			: (chunk::mask << (Stop % chunk::bits + 1));
		value<Bits> masked = *this;
		if (Start / chunk::bits == Stop / chunk::bits) {
			masked.data[Start / chunk::bits] &= stop_mask | start_mask;
		} else {
			masked.data[Start / chunk::bits] &= start_mask;
			for (size_t n = Start / chunk::bits + 1; n < Stop / chunk::bits; n++)
				masked.data[n] = 0;
			masked.data[Stop / chunk::bits] &= stop_mask;
		}
		value<Bits> shifted = source
			.template rzext<Stop + 1>()
			.template zext<Bits>();
		return masked.bit_or(shifted);
	}

	// Helpers for selecting extending or truncating operation depending on whether the result is wider or narrower
	// than the operand. In C++17 these can be replaced with `if constexpr`.
	template<size_t NewBits, typename = void>
	struct zext_cast {
		CXXRTL_ALWAYS_INLINE
		value<NewBits> operator()(const value<Bits> &val) {
			return val.template zext<NewBits>();
		}
	};

	template<size_t NewBits>
	struct zext_cast<NewBits, typename std::enable_if<(NewBits < Bits)>::type> {
		CXXRTL_ALWAYS_INLINE
		value<NewBits> operator()(const value<Bits> &val) {
			return val.template trunc<NewBits>();
		}
	};

	template<size_t NewBits, typename = void>
	struct sext_cast {
		CXXRTL_ALWAYS_INLINE
		value<NewBits> operator()(const value<Bits> &val) {
			return val.template sext<NewBits>();
		}
	};

	template<size_t NewBits>
	struct sext_cast<NewBits, typename std::enable_if<(NewBits < Bits)>::type> {
		CXXRTL_ALWAYS_INLINE
		value<NewBits> operator()(const value<Bits> &val) {
			return val.template trunc<NewBits>();
		}
	};

	template<size_t NewBits>
	CXXRTL_ALWAYS_INLINE
	value<NewBits> zcast() const {
		return zext_cast<NewBits>()(*this);
	}

	template<size_t NewBits>
	CXXRTL_ALWAYS_INLINE
	value<NewBits> scast() const {
		return sext_cast<NewBits>()(*this);
	}

	// Bit replication is far more efficient than the equivalent concatenation.
	template<size_t Count>
	CXXRTL_ALWAYS_INLINE
	value<Bits * Count> repeat() const {
		static_assert(Bits == 1, "repeat() is implemented only for 1-bit values");
		return *this ? value<Bits * Count>().bit_not() : value<Bits * Count>();
	}

	// Operations with run-time parameters (offsets, amounts, etc).
	//
	// These operations are used for computations.
	bool bit(size_t offset) const {
		return data[offset / chunk::bits] & (1 << (offset % chunk::bits));
	}

	void set_bit(size_t offset, bool value = true) {
		size_t offset_chunks = offset / chunk::bits;
		size_t offset_bits = offset % chunk::bits;
		data[offset_chunks] &= ~(1 << offset_bits);
		data[offset_chunks] |= value ? 1 << offset_bits : 0;
	}

	explicit operator bool() const {
		return !is_zero();
	}

	bool is_zero() const {
		for (size_t n = 0; n < chunks; n++)
			if (data[n] != 0)
				return false;
		return true;
	}

	bool is_neg() const {
		return data[chunks - 1] & (1 << ((Bits - 1) % chunk::bits));
	}

	bool operator ==(const value<Bits> &other) const {
		for (size_t n = 0; n < chunks; n++)
			if (data[n] != other.data[n])
				return false;
		return true;
	}

	bool operator !=(const value<Bits> &other) const {
		return !(*this == other);
	}

	value<Bits> bit_not() const {
		value<Bits> result;
		for (size_t n = 0; n < chunks; n++)
			result.data[n] = ~data[n];
		result.data[chunks - 1] &= msb_mask;
		return result;
	}

	value<Bits> bit_and(const value<Bits> &other) const {
		value<Bits> result;
		for (size_t n = 0; n < chunks; n++)
			result.data[n] = data[n] & other.data[n];
		return result;
	}

	value<Bits> bit_or(const value<Bits> &other) const {
		value<Bits> result;
		for (size_t n = 0; n < chunks; n++)
			result.data[n] = data[n] | other.data[n];
		return result;
	}

	value<Bits> bit_xor(const value<Bits> &other) const {
		value<Bits> result;
		for (size_t n = 0; n < chunks; n++)
			result.data[n] = data[n] ^ other.data[n];
		return result;
	}

	value<Bits> update(const value<Bits> &val, const value<Bits> &mask) const {
		return bit_and(mask.bit_not()).bit_or(val.bit_and(mask));
	}

	template<size_t AmountBits>
	value<Bits> shl(const value<AmountBits> &amount) const {
		// Ensure our early return is correct by prohibiting values larger than 4 Gbit.
		static_assert(Bits <= chunk::mask, "shl() of unreasonably large values is not supported");
		// Detect shifts definitely large than Bits early.
		for (size_t n = 1; n < amount.chunks; n++)
			if (amount.data[n] != 0)
				return {};
		// Past this point we can use the least significant chunk as the shift size.
		size_t shift_chunks = amount.data[0] / chunk::bits;
		size_t shift_bits   = amount.data[0] % chunk::bits;
		if (shift_chunks >= chunks)
			return {};
		value<Bits> result;
		chunk::type carry = 0;
		for (size_t n = 0; n < chunks - shift_chunks; n++) {
			result.data[shift_chunks + n] = (data[n] << shift_bits) | carry;
			carry = (shift_bits == 0) ? 0
				: data[n] >> (chunk::bits - shift_bits);
		}
		return result;
	}

	template<size_t AmountBits, bool Signed = false>
	value<Bits> shr(const value<AmountBits> &amount) const {
		// Ensure our early return is correct by prohibiting values larger than 4 Gbit.
		static_assert(Bits <= chunk::mask, "shr() of unreasonably large values is not supported");
		// Detect shifts definitely large than Bits early.
		for (size_t n = 1; n < amount.chunks; n++)
			if (amount.data[n] != 0)
				return {};
		// Past this point we can use the least significant chunk as the shift size.
		size_t shift_chunks = amount.data[0] / chunk::bits;
		size_t shift_bits   = amount.data[0] % chunk::bits;
		if (shift_chunks >= chunks)
			return {};
		value<Bits> result;
		chunk::type carry = 0;
		for (size_t n = 0; n < chunks - shift_chunks; n++) {
			result.data[chunks - shift_chunks - 1 - n] = carry | (data[chunks - 1 - n] >> shift_bits);
			carry = (shift_bits == 0) ? 0
				: data[chunks - 1 - n] << (chunk::bits - shift_bits);
		}
		if (Signed && is_neg()) {
			size_t top_chunk_idx  = (Bits - shift_bits) / chunk::bits;
			size_t top_chunk_bits = (Bits - shift_bits) % chunk::bits;
			for (size_t n = top_chunk_idx + 1; n < chunks; n++)
				result.data[n] = chunk::mask;
			if (shift_bits != 0)
				result.data[top_chunk_idx] |= chunk::mask << top_chunk_bits;
		}
		return result;
	}

	template<size_t AmountBits>
	value<Bits> sshr(const value<AmountBits> &amount) const {
		return shr<AmountBits, /*Signed=*/true>(amount);
	}

	size_t ctpop() const {
		size_t count = 0;
		for (size_t n = 0; n < chunks; n++) {
			// This loop implements the population count idiom as recognized by LLVM and GCC.
			for (chunk::type x = data[n]; x != 0; count++)
				x = x & (x - 1);
		}
		return count;
	}

	size_t ctlz() const {
		size_t count = 0;
		for (size_t n = 0; n < chunks; n++) {
			chunk::type x = data[chunks - 1 - n];
			if (x == 0) {
				count += (n == 0 ? Bits % chunk::bits : chunk::bits);
			} else {
				// This loop implements the find first set idiom as recognized by LLVM.
				for (; x != 0; count++)
					x >>= 1;
			}
		}
		return count;
	}

	template<bool Invert, bool CarryIn>
	std::pair<value<Bits>, bool /*CarryOut*/> alu(const value<Bits> &other) const {
		value<Bits> result;
		bool carry = CarryIn;
		for (size_t n = 0; n < result.chunks; n++) {
			result.data[n] = data[n] + (Invert ? ~other.data[n] : other.data[n]) + carry;
			if (result.chunks - 1 == n)
				result.data[result.chunks - 1] &= result.msb_mask;
			carry = (result.data[n] <  data[n]) ||
			        (result.data[n] == data[n] && carry);
		}
		return {result, carry};
	}

	value<Bits> add(const value<Bits> &other) const {
		return alu</*Invert=*/false, /*CarryIn=*/false>(other).first;
	}

	value<Bits> sub(const value<Bits> &other) const {
		return alu</*Invert=*/true, /*CarryIn=*/true>(other).first;
	}

	value<Bits> neg() const {
		return value<Bits> { 0u }.sub(*this);
	}

	bool ucmp(const value<Bits> &other) const {
		bool carry;
		std::tie(std::ignore, carry) = alu</*Invert=*/true, /*CarryIn=*/true>(other);
		return !carry; // a.ucmp(b) ≡ a u< b
	}

	bool scmp(const value<Bits> &other) const {
		value<Bits> result;
		bool carry;
		std::tie(result, carry) = alu</*Invert=*/true, /*CarryIn=*/true>(other);
		bool overflow = (is_neg() == !other.is_neg()) && (is_neg() != result.is_neg());
		return result.is_neg() ^ overflow; // a.scmp(b) ≡ a s< b
	}

	template<size_t ResultBits>
	value<ResultBits> mul(const value<Bits> &other) const {
		value<ResultBits> result;
		wide_chunk_t wide_result[result.chunks + 1] = {};
		for (size_t n = 0; n < chunks; n++) {
			for (size_t m = 0; m < chunks && n + m < result.chunks; m++) {
				wide_result[n + m] += wide_chunk_t(data[n]) * wide_chunk_t(other.data[m]);
				wide_result[n + m + 1] += wide_result[n + m] >> chunk::bits;
				wide_result[n + m] &= chunk::mask;
			}
		}
		for (size_t n = 0; n < result.chunks; n++) {
			result.data[n] = wide_result[n];
		}
		result.data[result.chunks - 1] &= result.msb_mask;
		return result;
	}
};

// Expression template for a slice, usable as lvalue or rvalue, and composable with other expression templates here.
template<class T, size_t Stop, size_t Start>
struct slice_expr : public expr_base<slice_expr<T, Stop, Start>> {
	static_assert(Stop >= Start, "slice_expr() may not reverse bit order");
	static_assert(Start < T::bits && Stop < T::bits, "slice_expr() must be within bounds");
	static constexpr size_t bits = Stop - Start + 1;

	T &expr;

	slice_expr(T &expr) : expr(expr) {}
	slice_expr(const slice_expr<T, Stop, Start> &) = delete;

	CXXRTL_ALWAYS_INLINE
	operator value<bits>() const {
		return static_cast<const value<T::bits> &>(expr)
			.template rtrunc<T::bits - Start>()
			.template trunc<bits>();
	}

	CXXRTL_ALWAYS_INLINE
	slice_expr<T, Stop, Start> &operator=(const value<bits> &rhs) {
		// Generic partial assignment implemented using a read-modify-write operation on the sliced expression.
		expr = static_cast<const value<T::bits> &>(expr)
			.template blit<Stop, Start>(rhs);
		return *this;
	}

	// A helper that forces the cast to value<>, which allows deduction to work.
	CXXRTL_ALWAYS_INLINE
	value<bits> val() const {
		return static_cast<const value<bits> &>(*this);
	}
};

// Expression template for a concatenation, usable as lvalue or rvalue, and composable with other expression templates here.
template<class T, class U>
struct concat_expr : public expr_base<concat_expr<T, U>> {
	static constexpr size_t bits = T::bits + U::bits;

	T &ms_expr;
	U &ls_expr;

	concat_expr(T &ms_expr, U &ls_expr) : ms_expr(ms_expr), ls_expr(ls_expr) {}
	concat_expr(const concat_expr<T, U> &) = delete;

	CXXRTL_ALWAYS_INLINE
	operator value<bits>() const {
		value<bits> ms_shifted = static_cast<const value<T::bits> &>(ms_expr)
			.template rzext<bits>();
		value<bits> ls_extended = static_cast<const value<U::bits> &>(ls_expr)
			.template zext<bits>();
		return ms_shifted.bit_or(ls_extended);
	}

	CXXRTL_ALWAYS_INLINE
	concat_expr<T, U> &operator=(const value<bits> &rhs) {
		ms_expr = rhs.template rtrunc<T::bits>();
		ls_expr = rhs.template trunc<U::bits>();
		return *this;
	}

	// A helper that forces the cast to value<>, which allows deduction to work.
	CXXRTL_ALWAYS_INLINE
	value<bits> val() const {
		return static_cast<const value<bits> &>(*this);
	}
};

// Base class for expression templates, providing helper methods for operations that are valid on both rvalues and lvalues.
//
// Note that expression objects (slices and concatenations) constructed in this way should NEVER be captured because
// they refer to temporaries that will, in general, only live until the end of the statement. For example, both of
// these snippets perform use-after-free:
//
//    const auto &a = val.slice<7,0>().slice<1>();
//    value<1> b = a;
//
//    auto &&c = val.slice<7,0>().slice<1>();
//    c = value<1>{1u};
//
// An easy way to write code using slices and concatenations safely is to follow two simple rules:
//   * Never explicitly name any type except `value<W>` or `const value<W> &`.
//   * Never use a `const auto &` or `auto &&` in any such expression.
// Then, any code that compiles will be well-defined.
template<class T>
struct expr_base {
	template<size_t Stop, size_t Start = Stop>
	CXXRTL_ALWAYS_INLINE
	slice_expr<const T, Stop, Start> slice() const {
		return {*static_cast<const T *>(this)};
	}

	template<size_t Stop, size_t Start = Stop>
	CXXRTL_ALWAYS_INLINE
	slice_expr<T, Stop, Start> slice() {
		return {*static_cast<T *>(this)};
	}

	template<class U>
	CXXRTL_ALWAYS_INLINE
	concat_expr<const T, typename std::remove_reference<const U>::type> concat(const U &other) const {
		return {*static_cast<const T *>(this), other};
	}

	template<class U>
	CXXRTL_ALWAYS_INLINE
	concat_expr<T, typename std::remove_reference<U>::type> concat(U &&other) {
		return {*static_cast<T *>(this), other};
	}
};

template<size_t Bits>
std::ostream &operator<<(std::ostream &os, const value<Bits> &val) {
	auto old_flags = os.flags(std::ios::right);
	auto old_width = os.width(0);
	auto old_fill  = os.fill('0');
	os << val.bits << '\'' << std::hex;
	for (size_t n = val.chunks - 1; n != (size_t)-1; n--) {
		if (n == val.chunks - 1 && Bits % value<Bits>::chunk::bits != 0)
			os.width((Bits % value<Bits>::chunk::bits + 3) / 4);
		else
			os.width((value<Bits>::chunk::bits + 3) / 4);
		os << val.data[n];
	}
	os.fill(old_fill);
	os.width(old_width);
	os.flags(old_flags);
	return os;
}

template<size_t Bits>
struct wire {
	static constexpr size_t bits = Bits;

	value<Bits> curr;
	value<Bits> next;

	wire() = default;
	explicit constexpr wire(const value<Bits> &init) : curr(init), next(init) {}
	template<typename... Init>
	explicit constexpr wire(Init ...init) : curr{init...}, next{init...} {}

	// Copying and copy-assigning values is natural. If, however, a value is replaced with a wire,
	// e.g. because a module is built with a different optimization level, then existing code could
	// unintentionally copy a wire instead, which would create a subtle but serious bug. To make sure
	// this doesn't happen, prohibit copying and copy-assigning wires.
	wire(const wire<Bits> &) = delete;
	wire<Bits> &operator=(const wire<Bits> &) = delete;

	wire(wire<Bits> &&) = default;
	wire<Bits> &operator=(wire<Bits> &&) = default;

	template<class IntegerT>
	CXXRTL_ALWAYS_INLINE
	IntegerT get() const {
		return curr.template get<IntegerT>();
	}

	template<class IntegerT>
	CXXRTL_ALWAYS_INLINE
	void set(IntegerT other) {
		next.template set<IntegerT>(other);
	}

	bool commit() {
		if (curr != next) {
			curr = next;
			return true;
		}
		return false;
	}
};

template<size_t Bits>
std::ostream &operator<<(std::ostream &os, const wire<Bits> &val) {
	os << val.curr;
	return os;
}

template<size_t Width>
struct memory {
	std::vector<value<Width>> data;

	size_t depth() const {
		return data.size();
	}

	memory() = delete;
	explicit memory(size_t depth) : data(depth) {}

	memory(const memory<Width> &) = delete;
	memory<Width> &operator=(const memory<Width> &) = delete;

	memory(memory<Width> &&) = default;
	memory<Width> &operator=(memory<Width> &&) = default;

	// The only way to get the compiler to put the initializer in .rodata and do not copy it on stack is to stuff it
	// into a plain array. You'd think an std::initializer_list would work here, but it doesn't, because you can't
	// construct an initializer_list in a constexpr (or something) and so if you try to do that the whole thing is
	// first copied on the stack (probably overflowing it) and then again into `data`.
	template<size_t Size>
	struct init {
		size_t offset;
		value<Width> data[Size];
	};

	template<size_t... InitSize>
	explicit memory(size_t depth, const init<InitSize> &...init) : data(depth) {
		data.resize(depth);
		// This utterly reprehensible construct is the most reasonable way to apply a function to every element
		// of a parameter pack, if the elements all have different types and so cannot be cast to an initializer list.
		auto _ = {std::move(std::begin(init.data), std::end(init.data), data.begin() + init.offset)...};
		(void)_;
	}

	// An operator for direct memory reads. May be used at any time during the simulation.
	const value<Width> &operator [](size_t index) const {
		assert(index < data.size());
		return data[index];
	}

	// An operator for direct memory writes. May only be used before the simulation is started. If used
	// after the simulation is started, the design may malfunction.
	value<Width> &operator [](size_t index) {
		assert(index < data.size());
		return data[index];
	}

	// A simple way to make a writable memory would be to use an array of wires instead of an array of values.
	// However, there are two significant downsides to this approach: first, it has large overhead (2× space
	// overhead, and O(depth) time overhead during commit); second, it does not simplify handling write port
	// priorities. Although in principle write ports could be ordered or conditionally enabled in generated
	// code based on their priorities and selected addresses, the feedback arc set problem is computationally
	// expensive, and the heuristic based algorithms are not easily modified to guarantee (rather than prefer)
	// a particular write port evaluation order.
	//
	// The approach used here instead is to queue writes into a buffer during the eval phase, then perform
	// the writes during the commit phase in the priority order. This approach has low overhead, with both space
	// and time proportional to the amount of write ports. Because virtually every memory in a practical design
	// has at most two write ports, linear search is used on every write, being the fastest and simplest approach.
	struct write {
		size_t index;
		value<Width> val;
		value<Width> mask;
		int priority;
	};
	std::vector<write> write_queue;

	void update(size_t index, const value<Width> &val, const value<Width> &mask, int priority = 0) {
		assert(index < data.size());
		// Queue up the write while keeping the queue sorted by priority.
		write_queue.insert(
			std::upper_bound(write_queue.begin(), write_queue.end(), priority,
				[](const int a, const write& b) { return a < b.priority; }),
			write { index, val, mask, priority });
	}

	bool commit() {
		bool changed = false;
		for (const write &entry : write_queue) {
			value<Width> elem = data[entry.index];
			elem = elem.update(entry.val, entry.mask);
			changed |= (data[entry.index] != elem);
			data[entry.index] = elem;
		}
		write_queue.clear();
		return changed;
	}
};

struct metadata {
	const enum {
		MISSING = 0,
		UINT   	= 1,
		SINT   	= 2,
		STRING 	= 3,
		DOUBLE 	= 4,
	} value_type;

	// In debug mode, using the wrong .as_*() function will assert.
	// In release mode, using the wrong .as_*() function will safely return a default value.
	const unsigned    uint_value = 0;
	const signed      sint_value = 0;
	const std::string string_value = "";
	const double      double_value = 0.0;

	metadata() : value_type(MISSING) {}
	metadata(unsigned value) : value_type(UINT), uint_value(value) {}
	metadata(signed value) : value_type(SINT), sint_value(value) {}
	metadata(const std::string &value) : value_type(STRING), string_value(value) {}
	metadata(const char *value) : value_type(STRING), string_value(value) {}
	metadata(double value) : value_type(DOUBLE), double_value(value) {}

	metadata(const metadata &) = default;
	metadata &operator=(const metadata &) = delete;

	unsigned as_uint() const {
		assert(value_type == UINT);
		return uint_value;
	}

	signed as_sint() const {
		assert(value_type == SINT);
		return sint_value;
	}

	const std::string &as_string() const {
		assert(value_type == STRING);
		return string_value;
	}

	double as_double() const {
		assert(value_type == DOUBLE);
		return double_value;
	}
};

typedef std::map<std::string, metadata> metadata_map;

// Tag class to disambiguate values/wires and their aliases.
struct debug_alias {};

// Tag declaration to disambiguate values and debug outlines.
using debug_outline = ::_cxxrtl_outline;

// This structure is intended for consumption via foreign function interfaces, like Python's ctypes.
// Because of this it uses a C-style layout that is easy to parse rather than more idiomatic C++.
//
// To avoid violating strict aliasing rules, this structure has to be a subclass of the one used
// in the C API, or it would not be possible to cast between the pointers to these.
struct debug_item : ::cxxrtl_object {
	// Object types.
	enum : uint32_t {
		VALUE   = CXXRTL_VALUE,
		WIRE    = CXXRTL_WIRE,
		MEMORY  = CXXRTL_MEMORY,
		ALIAS   = CXXRTL_ALIAS,
		OUTLINE = CXXRTL_OUTLINE,
	};

	// Object flags.
	enum : uint32_t {
		INPUT  = CXXRTL_INPUT,
		OUTPUT = CXXRTL_OUTPUT,
		INOUT  = CXXRTL_INOUT,
		DRIVEN_SYNC = CXXRTL_DRIVEN_SYNC,
		DRIVEN_COMB = CXXRTL_DRIVEN_COMB,
		UNDRIVEN    = CXXRTL_UNDRIVEN,
	};

	debug_item(const ::cxxrtl_object &object) : cxxrtl_object(object) {}

	template<size_t Bits>
	debug_item(value<Bits> &item, size_t lsb_offset = 0, uint32_t flags_ = 0) {
		static_assert(sizeof(item) == value<Bits>::chunks * sizeof(chunk_t),
		              "value<Bits> is not compatible with C layout");
		type    = VALUE;
		flags   = flags_;
		width   = Bits;
		lsb_at  = lsb_offset;
		depth   = 1;
		zero_at = 0;
		curr    = item.data;
		next    = item.data;
		outline = nullptr;
	}

	template<size_t Bits>
	debug_item(const value<Bits> &item, size_t lsb_offset = 0) {
		static_assert(sizeof(item) == value<Bits>::chunks * sizeof(chunk_t),
		              "value<Bits> is not compatible with C layout");
		type    = VALUE;
		flags   = DRIVEN_COMB;
		width   = Bits;
		lsb_at  = lsb_offset;
		depth   = 1;
		zero_at = 0;
		curr    = const_cast<chunk_t*>(item.data);
		next    = nullptr;
		outline = nullptr;
	}

	template<size_t Bits>
	debug_item(wire<Bits> &item, size_t lsb_offset = 0, uint32_t flags_ = 0) {
		static_assert(sizeof(item.curr) == value<Bits>::chunks * sizeof(chunk_t) &&
		              sizeof(item.next) == value<Bits>::chunks * sizeof(chunk_t),
		              "wire<Bits> is not compatible with C layout");
		type    = WIRE;
		flags   = flags_;
		width   = Bits;
		lsb_at  = lsb_offset;
		depth   = 1;
		zero_at = 0;
		curr    = item.curr.data;
		next    = item.next.data;
		outline = nullptr;
	}

	template<size_t Width>
	debug_item(memory<Width> &item, size_t zero_offset = 0) {
		static_assert(sizeof(item.data[0]) == value<Width>::chunks * sizeof(chunk_t),
		              "memory<Width> is not compatible with C layout");
		type    = MEMORY;
		flags   = 0;
		width   = Width;
		lsb_at  = 0;
		depth   = item.data.size();
		zero_at = zero_offset;
		curr    = item.data.empty() ? nullptr : item.data[0].data;
		next    = nullptr;
		outline = nullptr;
	}

	template<size_t Bits>
	debug_item(debug_alias, const value<Bits> &item, size_t lsb_offset = 0) {
		static_assert(sizeof(item) == value<Bits>::chunks * sizeof(chunk_t),
		              "value<Bits> is not compatible with C layout");
		type    = ALIAS;
		flags   = DRIVEN_COMB;
		width   = Bits;
		lsb_at  = lsb_offset;
		depth   = 1;
		zero_at = 0;
		curr    = const_cast<chunk_t*>(item.data);
		next    = nullptr;
		outline = nullptr;
	}

	template<size_t Bits>
	debug_item(debug_alias, const wire<Bits> &item, size_t lsb_offset = 0) {
		static_assert(sizeof(item.curr) == value<Bits>::chunks * sizeof(chunk_t) &&
		              sizeof(item.next) == value<Bits>::chunks * sizeof(chunk_t),
		              "wire<Bits> is not compatible with C layout");
		type    = ALIAS;
		flags   = DRIVEN_COMB;
		width   = Bits;
		lsb_at  = lsb_offset;
		depth   = 1;
		zero_at = 0;
		curr    = const_cast<chunk_t*>(item.curr.data);
		next    = nullptr;
		outline = nullptr;
	}

	template<size_t Bits>
	debug_item(debug_outline &group, const value<Bits> &item, size_t lsb_offset = 0) {
		static_assert(sizeof(item) == value<Bits>::chunks * sizeof(chunk_t),
		              "value<Bits> is not compatible with C layout");
		type    = OUTLINE;
		flags   = DRIVEN_COMB;
		width   = Bits;
		lsb_at  = lsb_offset;
		depth   = 1;
		zero_at = 0;
		curr    = const_cast<chunk_t*>(item.data);
		next    = nullptr;
		outline = &group;
	}
};
static_assert(std::is_standard_layout<debug_item>::value, "debug_item is not compatible with C layout");

struct debug_items {
	std::map<std::string, std::vector<debug_item>> table;

	void add(const std::string &name, debug_item &&item) {
		std::vector<debug_item> &parts = table[name];
		parts.emplace_back(item);
		std::sort(parts.begin(), parts.end(),
			[](const debug_item &a, const debug_item &b) {
				return a.lsb_at < b.lsb_at;
			});
	}

	size_t count(const std::string &name) const {
		if (table.count(name) == 0)
			return 0;
		return table.at(name).size();
	}

	const std::vector<debug_item> &parts_at(const std::string &name) const {
		return table.at(name);
	}

	const debug_item &at(const std::string &name) const {
		const std::vector<debug_item> &parts = table.at(name);
		assert(parts.size() == 1);
		return parts.at(0);
	}

	const debug_item &operator [](const std::string &name) const {
		return at(name);
	}
};

// Tag class to disambiguate module move constructor and module constructor that takes black boxes
// out of another instance of the module.
struct adopt {};

struct module {
	module() {}
	virtual ~module() {}

	// Modules with black boxes cannot be copied. Although not all designs include black boxes,
	// delete the copy constructor and copy assignment operator to make sure that any downstream
	// code that manipulates modules doesn't accidentally depend on their availability.
	module(const module &) = delete;
	module &operator=(const module &) = delete;

	module(module &&) = default;
	module &operator=(module &&) = default;

	virtual void reset() = 0;

	virtual bool eval() = 0;
	virtual bool commit() = 0;

	size_t step() {
		size_t deltas = 0;
		bool converged = false;
		do {
			converged = eval();
			deltas++;
		} while (commit() && !converged);
		return deltas;
	}

	virtual void debug_info(debug_items &items, std::string path = "") {
		(void)items, (void)path;
	}
};

} // namespace cxxrtl

// Internal structures used to communicate with the implementation of the C interface.

typedef struct _cxxrtl_toplevel {
	std::unique_ptr<cxxrtl::module> module;
} *cxxrtl_toplevel;

typedef struct _cxxrtl_outline {
	std::function<void()> eval;
} *cxxrtl_outline;

// Definitions of internal Yosys cells. Other than the functions in this namespace, CXXRTL is fully generic
// and indepenent of Yosys implementation details.
//
// The `write_cxxrtl` pass translates internal cells (cells with names that start with `$`) to calls of these
// functions. All of Yosys arithmetic and logical cells perform sign or zero extension on their operands,
// whereas basic operations on arbitrary width values require operands to be of the same width. These functions
// bridge the gap by performing the necessary casts. They are named similar to `cell_A[B]`, where A and B are `u`
// if the corresponding operand is unsigned, and `s` if it is signed.
namespace cxxrtl_yosys {

using namespace cxxrtl;

// std::max isn't constexpr until C++14 for no particular reason (it's an oversight), so we define our own.
template<class T>
CXXRTL_ALWAYS_INLINE
constexpr T max(const T &a, const T &b) {
	return a > b ? a : b;
}

// Logic operations
template<size_t BitsY, size_t BitsA>
CXXRTL_ALWAYS_INLINE
value<BitsY> logic_not(const value<BitsA> &a) {
	return value<BitsY> { a ? 0u : 1u };
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> logic_and(const value<BitsA> &a, const value<BitsB> &b) {
	return value<BitsY> { (bool(a) && bool(b)) ? 1u : 0u };
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> logic_or(const value<BitsA> &a, const value<BitsB> &b) {
	return value<BitsY> { (bool(a) || bool(b)) ? 1u : 0u };
}

// Reduction operations
template<size_t BitsY, size_t BitsA>
CXXRTL_ALWAYS_INLINE
value<BitsY> reduce_and(const value<BitsA> &a) {
	return value<BitsY> { a.bit_not().is_zero() ? 1u : 0u };
}

template<size_t BitsY, size_t BitsA>
CXXRTL_ALWAYS_INLINE
value<BitsY> reduce_or(const value<BitsA> &a) {
	return value<BitsY> { a ? 1u : 0u };
}

template<size_t BitsY, size_t BitsA>
CXXRTL_ALWAYS_INLINE
value<BitsY> reduce_xor(const value<BitsA> &a) {
	return value<BitsY> { (a.ctpop() % 2) ? 1u : 0u };
}

template<size_t BitsY, size_t BitsA>
CXXRTL_ALWAYS_INLINE
value<BitsY> reduce_xnor(const value<BitsA> &a) {
	return value<BitsY> { (a.ctpop() % 2) ? 0u : 1u };
}

template<size_t BitsY, size_t BitsA>
CXXRTL_ALWAYS_INLINE
value<BitsY> reduce_bool(const value<BitsA> &a) {
	return value<BitsY> { a ? 1u : 0u };
}

// Bitwise operations
template<size_t BitsY, size_t BitsA>
CXXRTL_ALWAYS_INLINE
value<BitsY> not_u(const value<BitsA> &a) {
	return a.template zcast<BitsY>().bit_not();
}

template<size_t BitsY, size_t BitsA>
CXXRTL_ALWAYS_INLINE
value<BitsY> not_s(const value<BitsA> &a) {
	return a.template scast<BitsY>().bit_not();
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> and_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template zcast<BitsY>().bit_and(b.template zcast<BitsY>());
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> and_ss(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template scast<BitsY>().bit_and(b.template scast<BitsY>());
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> or_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template zcast<BitsY>().bit_or(b.template zcast<BitsY>());
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> or_ss(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template scast<BitsY>().bit_or(b.template scast<BitsY>());
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> xor_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template zcast<BitsY>().bit_xor(b.template zcast<BitsY>());
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> xor_ss(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template scast<BitsY>().bit_xor(b.template scast<BitsY>());
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> xnor_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template zcast<BitsY>().bit_xor(b.template zcast<BitsY>()).bit_not();
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> xnor_ss(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template scast<BitsY>().bit_xor(b.template scast<BitsY>()).bit_not();
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> shl_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template zcast<BitsY>().shl(b);
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> shl_su(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template scast<BitsY>().shl(b);
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> sshl_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template zcast<BitsY>().shl(b);
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> sshl_su(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template scast<BitsY>().shl(b);
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> shr_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return a.shr(b).template zcast<BitsY>();
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> shr_su(const value<BitsA> &a, const value<BitsB> &b) {
	return a.shr(b).template scast<BitsY>();
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> sshr_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return a.shr(b).template zcast<BitsY>();
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> sshr_su(const value<BitsA> &a, const value<BitsB> &b) {
	return a.sshr(b).template scast<BitsY>();
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> shift_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return shr_uu<BitsY>(a, b);
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> shift_su(const value<BitsA> &a, const value<BitsB> &b) {
	return shr_su<BitsY>(a, b);
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> shift_us(const value<BitsA> &a, const value<BitsB> &b) {
	return b.is_neg() ? shl_uu<BitsY>(a, b.template sext<BitsB + 1>().neg()) : shr_uu<BitsY>(a, b);
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> shift_ss(const value<BitsA> &a, const value<BitsB> &b) {
	return b.is_neg() ? shl_su<BitsY>(a, b.template sext<BitsB + 1>().neg()) : shr_su<BitsY>(a, b);
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> shiftx_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return shift_uu<BitsY>(a, b);
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> shiftx_su(const value<BitsA> &a, const value<BitsB> &b) {
	return shift_su<BitsY>(a, b);
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> shiftx_us(const value<BitsA> &a, const value<BitsB> &b) {
	return shift_us<BitsY>(a, b);
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> shiftx_ss(const value<BitsA> &a, const value<BitsB> &b) {
	return shift_ss<BitsY>(a, b);
}

// Comparison operations
template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> eq_uu(const value<BitsA> &a, const value<BitsB> &b) {
	constexpr size_t BitsExt = max(BitsA, BitsB);
	return value<BitsY>{ a.template zext<BitsExt>() == b.template zext<BitsExt>() ? 1u : 0u };
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> eq_ss(const value<BitsA> &a, const value<BitsB> &b) {
	constexpr size_t BitsExt = max(BitsA, BitsB);
	return value<BitsY>{ a.template sext<BitsExt>() == b.template sext<BitsExt>() ? 1u : 0u };
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> ne_uu(const value<BitsA> &a, const value<BitsB> &b) {
	constexpr size_t BitsExt = max(BitsA, BitsB);
	return value<BitsY>{ a.template zext<BitsExt>() != b.template zext<BitsExt>() ? 1u : 0u };
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> ne_ss(const value<BitsA> &a, const value<BitsB> &b) {
	constexpr size_t BitsExt = max(BitsA, BitsB);
	return value<BitsY>{ a.template sext<BitsExt>() != b.template sext<BitsExt>() ? 1u : 0u };
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> eqx_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return eq_uu<BitsY>(a, b);
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> eqx_ss(const value<BitsA> &a, const value<BitsB> &b) {
	return eq_ss<BitsY>(a, b);
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> nex_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return ne_uu<BitsY>(a, b);
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> nex_ss(const value<BitsA> &a, const value<BitsB> &b) {
	return ne_ss<BitsY>(a, b);
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> gt_uu(const value<BitsA> &a, const value<BitsB> &b) {
	constexpr size_t BitsExt = max(BitsA, BitsB);
	return value<BitsY> { b.template zext<BitsExt>().ucmp(a.template zext<BitsExt>()) ? 1u : 0u };
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> gt_ss(const value<BitsA> &a, const value<BitsB> &b) {
	constexpr size_t BitsExt = max(BitsA, BitsB);
	return value<BitsY> { b.template sext<BitsExt>().scmp(a.template sext<BitsExt>()) ? 1u : 0u };
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> ge_uu(const value<BitsA> &a, const value<BitsB> &b) {
	constexpr size_t BitsExt = max(BitsA, BitsB);
	return value<BitsY> { !a.template zext<BitsExt>().ucmp(b.template zext<BitsExt>()) ? 1u : 0u };
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> ge_ss(const value<BitsA> &a, const value<BitsB> &b) {
	constexpr size_t BitsExt = max(BitsA, BitsB);
	return value<BitsY> { !a.template sext<BitsExt>().scmp(b.template sext<BitsExt>()) ? 1u : 0u };
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> lt_uu(const value<BitsA> &a, const value<BitsB> &b) {
	constexpr size_t BitsExt = max(BitsA, BitsB);
	return value<BitsY> { a.template zext<BitsExt>().ucmp(b.template zext<BitsExt>()) ? 1u : 0u };
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> lt_ss(const value<BitsA> &a, const value<BitsB> &b) {
	constexpr size_t BitsExt = max(BitsA, BitsB);
	return value<BitsY> { a.template sext<BitsExt>().scmp(b.template sext<BitsExt>()) ? 1u : 0u };
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> le_uu(const value<BitsA> &a, const value<BitsB> &b) {
	constexpr size_t BitsExt = max(BitsA, BitsB);
	return value<BitsY> { !b.template zext<BitsExt>().ucmp(a.template zext<BitsExt>()) ? 1u : 0u };
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> le_ss(const value<BitsA> &a, const value<BitsB> &b) {
	constexpr size_t BitsExt = max(BitsA, BitsB);
	return value<BitsY> { !b.template sext<BitsExt>().scmp(a.template sext<BitsExt>()) ? 1u : 0u };
}

// Arithmetic operations
template<size_t BitsY, size_t BitsA>
CXXRTL_ALWAYS_INLINE
value<BitsY> pos_u(const value<BitsA> &a) {
	return a.template zcast<BitsY>();
}

template<size_t BitsY, size_t BitsA>
CXXRTL_ALWAYS_INLINE
value<BitsY> pos_s(const value<BitsA> &a) {
	return a.template scast<BitsY>();
}

template<size_t BitsY, size_t BitsA>
CXXRTL_ALWAYS_INLINE
value<BitsY> neg_u(const value<BitsA> &a) {
	return a.template zcast<BitsY>().neg();
}

template<size_t BitsY, size_t BitsA>
CXXRTL_ALWAYS_INLINE
value<BitsY> neg_s(const value<BitsA> &a) {
	return a.template scast<BitsY>().neg();
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> add_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template zcast<BitsY>().add(b.template zcast<BitsY>());
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> add_ss(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template scast<BitsY>().add(b.template scast<BitsY>());
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> sub_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template zcast<BitsY>().sub(b.template zcast<BitsY>());
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> sub_ss(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template scast<BitsY>().sub(b.template scast<BitsY>());
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> mul_uu(const value<BitsA> &a, const value<BitsB> &b) {
	constexpr size_t BitsM = BitsA >= BitsB ? BitsA : BitsB;
	return a.template zcast<BitsM>().template mul<BitsY>(b.template zcast<BitsM>());
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> mul_ss(const value<BitsA> &a, const value<BitsB> &b) {
	return a.template scast<BitsY>().template mul<BitsY>(b.template scast<BitsY>());
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
std::pair<value<BitsY>, value<BitsY>> divmod_uu(const value<BitsA> &a, const value<BitsB> &b) {
	constexpr size_t Bits = max(BitsY, max(BitsA, BitsB));
	value<Bits> quotient;
	value<Bits> dividend = a.template zext<Bits>();
	value<Bits> divisor = b.template zext<Bits>();
	if (dividend.ucmp(divisor))
		return {/*quotient=*/value<BitsY> { 0u }, /*remainder=*/dividend.template trunc<BitsY>()};
	uint32_t divisor_shift = dividend.ctlz() - divisor.ctlz();
	divisor = divisor.shl(value<32> { divisor_shift });
	for (size_t step = 0; step <= divisor_shift; step++) {
		quotient = quotient.shl(value<1> { 1u });
		if (!dividend.ucmp(divisor)) {
			dividend = dividend.sub(divisor);
			quotient.set_bit(0, true);
		}
		divisor = divisor.shr(value<1> { 1u });
	}
	return {quotient.template trunc<BitsY>(), /*remainder=*/dividend.template trunc<BitsY>()};
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
std::pair<value<BitsY>, value<BitsY>> divmod_ss(const value<BitsA> &a, const value<BitsB> &b) {
	value<BitsA + 1> ua = a.template sext<BitsA + 1>();
	value<BitsB + 1> ub = b.template sext<BitsB + 1>();
	if (ua.is_neg()) ua = ua.neg();
	if (ub.is_neg()) ub = ub.neg();
	value<BitsY> y, r;
	std::tie(y, r) = divmod_uu<BitsY>(ua, ub);
	if (a.is_neg() != b.is_neg()) y = y.neg();
	if (a.is_neg()) r = r.neg();
	return {y, r};
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> div_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return divmod_uu<BitsY>(a, b).first;
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> div_ss(const value<BitsA> &a, const value<BitsB> &b) {
	return divmod_ss<BitsY>(a, b).first;
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> mod_uu(const value<BitsA> &a, const value<BitsB> &b) {
	return divmod_uu<BitsY>(a, b).second;
}

template<size_t BitsY, size_t BitsA, size_t BitsB>
CXXRTL_ALWAYS_INLINE
value<BitsY> mod_ss(const value<BitsA> &a, const value<BitsB> &b) {
	return divmod_ss<BitsY>(a, b).second;
}

// Memory helper
struct memory_index {
	bool valid;
	size_t index;

	template<size_t BitsAddr>
	memory_index(const value<BitsAddr> &addr, size_t offset, size_t depth) {
		static_assert(value<BitsAddr>::chunks <= 1, "memory address is too wide");
		size_t offset_index = addr.data[0];

		valid = (offset_index >= offset && offset_index < offset + depth);
		index = offset_index - offset;
	}
};

} // namespace cxxrtl_yosys

#endif