cxxrtl: fix sshr sign-extension.

[yosys.git] / backends / cxxrtl / cxxrtl.h

/*
 *  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 <sstream>

#include <backends/cxxrtl/cxxrtl_capi.h>

// 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.
#ifndef __has_attribute
#       define __has_attribute(x) 0
#endif
#if __has_attribute(always_inline)
#define CXXRTL_ALWAYS_INLINE inline __attribute__((__always_inline__))
#else
#define CXXRTL_ALWAYS_INLINE inline
#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;

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

        // 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 (carry != 0)
                        result.data[result.chunks - 1] = 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);
        }

        // 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;
        }

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

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

        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;
                        carry = (result.data[n] <  data[n]) ||
                                (result.data[n] == data[n] && carry);
                }
                result.data[result.chunks - 1] &= result.msb_mask;
                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
        }
};

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

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

        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;

        // 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;

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

// 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 {
        enum : uint32_t {
                VALUE  = CXXRTL_VALUE,
                WIRE   = CXXRTL_WIRE,
                MEMORY = CXXRTL_MEMORY,
                ALIAS  = CXXRTL_ALIAS,
        };

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

        template<size_t Bits>
        debug_item(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;
                width   = Bits;
                lsb_at  = lsb_offset;
                depth   = 1;
                zero_at = 0;
                curr    = item.data;
                next    = item.data;
        }

        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;
                width   = Bits;
                lsb_at  = lsb_offset;
                depth   = 1;
                zero_at = 0;
                curr    = const_cast<chunk_t*>(item.data);
                next    = nullptr;
        }

        template<size_t Bits>
        debug_item(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    = WIRE;
                width   = Bits;
                lsb_at  = lsb_offset;
                depth   = 1;
                zero_at = 0;
                curr    = item.curr.data;
                next    = item.next.data;
        }

        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;
                width   = Width;
                lsb_at  = 0;
                depth   = item.data.size();
                zero_at = zero_offset;
                curr    = item.data.empty() ? nullptr : item.data[0].data;
                next    = 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;
                width   = Bits;
                lsb_at  = lsb_offset;
                depth   = 1;
                zero_at = 0;
                curr    = const_cast<chunk_t*>(item.data);
                next    = 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;
                width   = Bits;
                lsb_at  = lsb_offset;
                depth   = 1;
                zero_at = 0;
                curr    = const_cast<chunk_t*>(item.curr.data);
                next    = nullptr;
        }
};
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);
        }
};

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

        module(const module &) = delete;
        module &operator=(const module &) = delete;

        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 structure used to communicate with the implementation of the C interface.
typedef struct _cxxrtl_toplevel {
        std::unique_ptr<cxxrtl::module> module;
} *cxxrtl_toplevel;

// 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>().template 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>().template 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>().template 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>().template 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.template 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.template 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.template 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.template 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) {
        value<BitsY> product;
        value<BitsY> multiplicand = a.template zcast<BitsY>();
        const value<BitsB> &multiplier = b;
        uint32_t multiplicand_shift = 0;
        for (size_t step = 0; step < BitsB; step++) {
                if (multiplier.bit(step)) {
                        multiplicand = multiplicand.shl(value<32> { multiplicand_shift });
                        product = product.add(multiplicand);
                        multiplicand_shift = 0;
                }
                multiplicand_shift++;
        }
        return product;
}

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) {
        value<BitsB + 1> ub = b.template sext<BitsB + 1>();
        if (ub.is_neg()) ub = ub.neg();
        value<BitsY> y = mul_uu<BitsY>(a.template scast<BitsY>(), ub);
        return b.is_neg() ? y.neg() : y;
}

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