/// @file dpf/keyword2.hpp
/// @brief `dpf::keyword2`, a ranked pattern language meant to replace `dpf::keyword`
/// @details A pattern is an anchored expression: literals, classes, `.`,
///          concatenation, alternation, `?`, and `{n}` / `{n,m}`. There is no
///          unbounded `*` or `+`. Each value in the language has one rank in
///          `0 .. |L|-1`, and that rank is the DPF input.
///
///          Significant characters keep their own spelling. A pad field is
///          opted into explicitly:
///
///              pad('0')[0-9]{0,4}
///              pad('\0')[a-z]{0,3}
///
///          The quoted character is digit 0. The other characters of the class,
///          in the order written, take digits 1, 2, …. Leading pads do not
///          change the rank, and the domain size is still `radix^max`.
///          `dpf::keyword` is unchanged: its implicit `alphabet[0]` pad stays.
///
///          Rank order is structural. Concatenation is mixed-radix with the
///          left piece in the high place, so a fixed-width spelling sorts in
///          lexicographic byte order. A pad field sorts by its integer value
///          (left-pad order: in `pad('\0')[a-z]{0,3}`, `b` is before `aa`).
///          A variable repetition `{n,m}` is shortlex: shorter sequences occupy
///          the lower ranks. Alternatives occupy contiguous blocks in source
///          order, and must be unambiguous.
///
///          The pattern rejects itself when a pad field or a variable
///          repetition is not delimited, when two spellings share a value by
///          accident, when the token automaton would exceed 64 states, when a
///          spelling is longer than 64, or when `|L|` does not fit in 256 bits.
/// @copyright Copyright (c) 2019-2026 Ryan Henry and [others](@ref authors)
/// @license Released under a GNU General Public v2.0 (GPLv2) license;
///          see [LICENSE.md](@ref license) for details.

#ifndef LIBDPF_INCLUDE_DPF_KEYWORD2_HPP__
#define LIBDPF_INCLUDE_DPF_KEYWORD2_HPP__

#include <cstddef>
#include <cstdint>
#include <istream>
#include <limits>
#include <ostream>
#include <stdexcept>
#include <string>
#include <string_view>
#include <type_traits>

#include "hedley/hedley.h"

#include "dpf/modint.hpp"
#include "dpf/utils.hpp"

namespace dpf
{

/// @brief Why `dpf::keyword2` refused a pattern.
enum class keyword2_error : std::uint8_t
{
    ok = 0,
    syntax,
    delim,
    overlap,
    states,
    length,
    width
};

namespace detail
{

inline constexpr std::uint16_t kw2_nodes = 64;
inline constexpr std::uint16_t kw2_kids = 192;
inline constexpr std::uint16_t kw2_len_cap = 64;
inline constexpr std::uint16_t kw2_dfa_cap = 64;
inline constexpr std::uint16_t kw2_nfa_cap = 160;
inline constexpr std::uint16_t kw2_none = 0xffff;

struct u256
{
    std::uint64_t w[4]{};

    constexpr bool zero() const
    {
        return w[0] == 0 && w[1] == 0 && w[2] == 0 && w[3] == 0;
    }

    constexpr bool one() const
    {
        return w[0] == 1 && w[1] == 0 && w[2] == 0 && w[3] == 0;
    }
};

struct card
{
    u256 v{};
    bool all = false;
    bool bad = false;

    constexpr bool zero() const { return !all && !bad && v.zero(); }
    constexpr bool one() const { return !all && !bad && v.one(); }
};

constexpr card card_u64(std::uint64_t x)
{
    card c;
    c.v.w[0] = x;
    return c;
}

constexpr card card_one() { return card_u64(1); }

constexpr int cmp_u(u256 a, u256 b)
{
    for (int i = 3; i >= 0; --i)
    {
        if (a.w[i] < b.w[i]) return -1;
        if (a.w[i] > b.w[i]) return 1;
    }
    return 0;
}

constexpr u256 sub_u(u256 a, u256 b)
{
    u256 r;
    std::uint64_t borrow = 0;
    for (int i = 0; i < 4; ++i)
    {
        unsigned __int128 aa = a.w[i];
        unsigned __int128 bb = static_cast<unsigned __int128>(b.w[i]) + borrow;
        if (aa >= bb)
        {
            r.w[i] = static_cast<std::uint64_t>(aa - bb);
            borrow = 0;
        }
        else
        {
            r.w[i] = static_cast<std::uint64_t>(
                (aa + (static_cast<unsigned __int128>(1) << 64)) - bb);
            borrow = 1;
        }
    }
    return r;
}

constexpr u256 dec_u(u256 a) { return sub_u(a, card_one().v); }

constexpr card add_card(card a, card b)
{
    if (a.bad || b.bad) { card r; r.bad = true; return r; }
    if (a.zero()) return b;
    if (b.zero()) return a;
    if (a.all || b.all) { card r; r.bad = true; return r; }
    card r;
    std::uint64_t carry = 0;
    for (int i = 0; i < 4; ++i)
    {
        unsigned __int128 s = static_cast<unsigned __int128>(a.v.w[i])
            + b.v.w[i] + carry;
        r.v.w[i] = static_cast<std::uint64_t>(s);
        carry = static_cast<std::uint64_t>(s >> 64);
    }
    if (carry)
    {
        if (r.v.zero()) r.all = true;
        else r.bad = true;
    }
    return r;
}

constexpr card mul_card(card a, card b)
{
    if (a.bad || b.bad) { card r; r.bad = true; return r; }
    if (a.zero() || b.zero()) return {};
    if (a.one()) return b;
    if (b.one()) return a;
    if (a.all || b.all) { card r; r.bad = true; return r; }
    std::uint64_t out[8]{};
    for (int i = 0; i < 4; ++i)
    {
        unsigned __int128 carry = 0;
        for (int j = 0; j < 4; ++j)
        {
            unsigned __int128 cur = out[i + j]
                + static_cast<unsigned __int128>(a.v.w[i]) * b.v.w[j] + carry;
            out[i + j] = static_cast<std::uint64_t>(cur);
            carry = cur >> 64;
        }
        out[i + 4] = static_cast<std::uint64_t>(carry);
    }
    card r;
    bool hi = out[4] | out[5] | out[6] | out[7];
    if (hi)
    {
        bool exact = out[4] == 1 && out[5] == 0 && out[6] == 0 && out[7] == 0
            && out[0] == 0 && out[1] == 0 && out[2] == 0 && out[3] == 0;
        if (exact) r.all = true;
        else r.bad = true;
        return r;
    }
    for (int i = 0; i < 4; ++i) r.v.w[i] = out[i];
    return r;
}

constexpr u256 mul_add_u(u256 rank, card place, u256 extra)
{
    if (place.one()) return add_card(card{rank, false, false}, card{extra, false, false}).v;
    if (place.zero()) return extra;
    if (rank.zero()) return extra;
    card prod = mul_card(card{rank, false, false}, place);
    return add_card(prod, card{extra, false, false}).v;
}

constexpr void divmod_u(u256 n, u256 d, u256 & q, u256 & r)
{
    q = {};
    std::uint64_t rw[5]{};
    for (int bit = 255; bit >= 0; --bit)
    {
        std::uint64_t c = 0;
        for (int i = 0; i < 5; ++i)
        {
            std::uint64_t nc = rw[i] >> 63;
            rw[i] = (rw[i] << 1) | c;
            c = nc;
        }
        if ((n.w[bit / 64] >> (bit % 64)) & 1u) rw[0] |= 1u;
        bool ge = rw[4] != 0;
        if (!ge)
        {
            ge = true;
            for (int i = 3; i >= 0; --i)
            {
                if (rw[i] > d.w[i]) break;
                if (rw[i] < d.w[i]) { ge = false; break; }
            }
        }
        if (!ge) continue;
        std::uint64_t borrow = 0;
        for (int i = 0; i < 4; ++i)
        {
            unsigned __int128 aa = rw[i];
            unsigned __int128 bb = static_cast<unsigned __int128>(d.w[i]) + borrow;
            if (aa >= bb)
            {
                rw[i] = static_cast<std::uint64_t>(aa - bb);
                borrow = 0;
            }
            else
            {
                rw[i] = static_cast<std::uint64_t>(
                    (aa + (static_cast<unsigned __int128>(1) << 64)) - bb);
                borrow = 1;
            }
        }
        rw[4] -= borrow;
        q.w[bit / 64] |= std::uint64_t{1} << (bit % 64);
    }
    r = {};
    for (int i = 0; i < 4; ++i) r.w[i] = rw[i];
}

constexpr void divmod_card(u256 n, card d, u256 & q, u256 & r)
{
    if (d.all) { q = {}; r = n; return; }
    divmod_u(n, d.v, q, r);
}

constexpr int cmp_card_u(u256 n, card d)
{
    if (d.all) return -1;
    if (d.bad) return 1;
    return cmp_u(n, d.v);
}

constexpr int bit_length_u(u256 a)
{
    for (int i = 3; i >= 0; --i)
    {
        if (a.w[i] == 0) continue;
        int b = 63;
        while (((a.w[i] >> b) & 1u) == 0) --b;
        return i * 64 + b + 1;
    }
    return 0;
}

constexpr int popcount64(std::uint64_t x)
{
    int n = 0;
    while (x)
    {
        n += static_cast<int>(x & 1u);
        x >>= 1;
    }
    return n;
}

constexpr int popcount_bits(const std::uint64_t b[4])
{
    return popcount64(b[0]) + popcount64(b[1]) + popcount64(b[2]) + popcount64(b[3]);
}

constexpr bool bit_test(const std::uint64_t b[4], unsigned ch)
{
    return (b[ch / 64] >> (ch % 64)) & 1u;
}

constexpr void bit_set(std::uint64_t b[4], unsigned ch)
{
    b[ch / 64] |= std::uint64_t{1} << (ch % 64);
}

constexpr void bit_or(std::uint64_t d[4], const std::uint64_t s[4])
{
    for (int i = 0; i < 4; ++i) d[i] |= s[i];
}

constexpr void bit_fill(std::uint64_t b[4])
{
    for (int i = 0; i < 4; ++i) b[i] = ~std::uint64_t{0};
}

constexpr bool bit_overlap(const std::uint64_t a[4], const std::uint64_t b[4])
{
    return (a[0] & b[0]) || (a[1] & b[1]) || (a[2] & b[2]) || (a[3] & b[3]);
}

constexpr int rank_below(const std::uint64_t b[4], unsigned ch)
{
    int r = 0;
    unsigned wi = ch / 64;
    unsigned bi = ch % 64;
    for (unsigned i = 0; i < wi; ++i) r += popcount64(b[i]);
    if (bi)
    {
        std::uint64_t mask = ~std::uint64_t{0} >> (64 - bi);
        r += popcount64(b[wi] & mask);
    }
    return r;
}

constexpr unsigned char bit_at_index(const std::uint64_t b[4], int index)
{
    for (unsigned ch = 0; ch < 256; ++ch)
        if (bit_test(b, ch) && index-- == 0) return static_cast<unsigned char>(ch);
    return 0;
}

enum class node_kind : std::uint8_t { empty, lit, cls, dot, pad, cat, alt, rep };

struct node
{
    node_kind k = node_kind::empty;
    std::uint16_t a = 0;
    std::uint16_t n = 0;
    std::uint16_t minv = 0;
    std::uint16_t maxv = 0;
    std::uint8_t ch = 0;
    std::uint16_t radix = 0;
    std::uint64_t bits[4]{};
    std::uint8_t digs[256]{};
    card lang{};
    bool nullable = false;
    std::uint16_t min_len = 0;
    std::uint16_t max_len = 0;
    std::uint64_t first[4]{};
};

struct ast
{
    node nodes[kw2_nodes]{};
    std::uint16_t kids[kw2_kids]{};
    std::uint16_t nnodes = 0;
    std::uint16_t nkids = 0;
    std::uint16_t root = 0;
};

struct program
{
    ast tree{};
    card lang{};
    std::uint16_t bits = 1;
    keyword2_error error = keyword2_error::ok;
    std::uint16_t err_pos = 0;
};

constexpr void fail(program & p, keyword2_error e, std::uint16_t pos)
{
    if (p.error == keyword2_error::ok)
    {
        p.error = e;
        p.err_pos = pos;
    }
}

struct parser
{
    program * p;
    const char * s;
    std::uint16_t i = 0;
    std::uint16_t n = 0;

    constexpr bool alive() const { return p->error == keyword2_error::ok; }
    constexpr char peek() const { return i < n ? s[i] : '\0'; }
    constexpr bool eat(char c)
    {
        if (peek() != c) return false;
        ++i;
        return true;
    }

    constexpr int hexval(char c) const
    {
        if (c >= '0' && c <= '9') return c - '0';
        if (c >= 'a' && c <= 'f') return c - 'a' + 10;
        if (c >= 'A' && c <= 'F') return c - 'A' + 10;
        return -1;
    }

    constexpr bool parse_escape(unsigned char & out)
    {
        if (!eat('\\')) return false;
        char c = peek();
        if (c == '\0') { fail(*p, keyword2_error::syntax, i); return false; }
        ++i;
        switch (c)
        {
        case '0': out = 0; return true;
        case 'n': out = '\n'; return true;
        case 't': out = '\t'; return true;
        case 'r': out = '\r'; return true;
        case '\\': out = '\\'; return true;
        case '\'': out = '\''; return true;
        case '"': out = '"'; return true;
        case '-': out = '-'; return true;
        case ']': out = ']'; return true;
        case '[': out = '['; return true;
        case '(': out = '('; return true;
        case ')': out = ')'; return true;
        case '{': out = '{'; return true;
        case '}': out = '}'; return true;
        case '|': out = '|'; return true;
        case '.': out = '.'; return true;
        case '?': out = '?'; return true;
        case 'x':
        {
            int h = hexval(peek());
            if (h < 0) { fail(*p, keyword2_error::syntax, i); return false; }
            ++i;
            int l = hexval(peek());
            if (l < 0) { fail(*p, keyword2_error::syntax, i); return false; }
            ++i;
            out = static_cast<unsigned char>((h << 4) | l);
            return true;
        }
        default:
            fail(*p, keyword2_error::syntax, i);
            return false;
        }
    }

    constexpr bool parse_quoted(unsigned char & out)
    {
        if (!eat('\'')) { fail(*p, keyword2_error::syntax, i); return false; }
        if (peek() == '\\')
        {
            if (!parse_escape(out)) return false;
        }
        else
        {
            if (peek() == '\0' || peek() == '\'')
            {
                fail(*p, keyword2_error::syntax, i);
                return false;
            }
            out = static_cast<unsigned char>(peek());
            ++i;
        }
        if (!eat('\'')) { fail(*p, keyword2_error::syntax, i); return false; }
        return true;
    }

    constexpr std::uint16_t parse_num()
    {
        if (peek() < '0' || peek() > '9')
        {
            fail(*p, keyword2_error::syntax, i);
            return 0;
        }
        unsigned v = 0;
        while (peek() >= '0' && peek() <= '9')
        {
            v = v * 10u + static_cast<unsigned>(peek() - '0');
            ++i;
            if (v > kw2_len_cap)
            {
                fail(*p, keyword2_error::length, i);
                return 0;
            }
        }
        return static_cast<std::uint16_t>(v);
    }

    constexpr bool parse_quant(std::uint16_t & lo, std::uint16_t & hi)
    {
        if (eat('?')) { lo = 0; hi = 1; return true; }
        if (peek() == '*' || peek() == '+')
        {
            fail(*p, keyword2_error::syntax, i);
            return false;
        }
        if (!eat('{')) return false;
        lo = parse_num();
        if (!alive()) return false;
        if (eat(','))
        {
            if (peek() == '}')
            {
                fail(*p, keyword2_error::syntax, i);
                return false;
            }
            hi = parse_num();
        }
        else hi = lo;
        if (!eat('}')) { fail(*p, keyword2_error::syntax, i); return false; }
        if (lo > hi) { fail(*p, keyword2_error::syntax, i); return false; }
        return true;
    }

    constexpr std::uint16_t add_node()
    {
        if (p->tree.nnodes >= kw2_nodes)
        {
            fail(*p, keyword2_error::states, i);
            return 0;
        }
        return p->tree.nnodes++;
    }

    constexpr std::uint16_t add_kid(std::uint16_t id)
    {
        if (p->tree.nkids >= kw2_kids)
        {
            fail(*p, keyword2_error::states, i);
            return 0;
        }
        std::uint16_t slot = p->tree.nkids++;
        p->tree.kids[slot] = id;
        return slot;
    }

    constexpr void add_class_char(node & nd, unsigned char ch, bool ordered)
    {
        if (!bit_test(nd.bits, ch))
        {
            bit_set(nd.bits, ch);
            if (ordered && ch != nd.ch && nd.radix < 256)
                nd.digs[nd.radix++] = ch;
        }
    }

    constexpr bool parse_class_body(node & nd, bool ordered)
    {
        if (!eat('[')) { fail(*p, keyword2_error::syntax, i); return false; }
        bool neg = eat('^');
        if (neg && ordered)
        {
            fail(*p, keyword2_error::syntax, i);
            return false;
        }
        if (peek() == ']') { fail(*p, keyword2_error::syntax, i); return false; }
        while (alive() && peek() != ']' && peek() != '\0')
        {
            unsigned char lo = 0;
            if (peek() == '\\') { if (!parse_escape(lo)) return false; }
            else { lo = static_cast<unsigned char>(peek()); ++i; }
            if (peek() == '-' && i + 1 < n && s[i + 1] != ']')
            {
                ++i;
                unsigned char hi = 0;
                if (peek() == '\\') { if (!parse_escape(hi)) return false; }
                else { hi = static_cast<unsigned char>(peek()); ++i; }
                if (hi < lo) { fail(*p, keyword2_error::syntax, i); return false; }
                for (unsigned c = lo; c <= hi && alive(); ++c)
                    add_class_char(nd, static_cast<unsigned char>(c), ordered);
            }
            else add_class_char(nd, lo, ordered);
        }
        if (!eat(']')) { fail(*p, keyword2_error::syntax, i); return false; }
        if (neg)
        {
            for (int w = 0; w < 4; ++w) nd.bits[w] = ~nd.bits[w];
        }
        if (popcount_bits(nd.bits) == 0)
        {
            fail(*p, keyword2_error::syntax, i);
            return false;
        }
        return alive();
    }

    constexpr std::uint16_t wrap_rep(std::uint16_t unit, std::uint16_t lo, std::uint16_t hi)
    {
        std::uint16_t id = add_node();
        if (!alive()) return 0;
        node & nd = p->tree.nodes[id];
        nd.k = node_kind::rep;
        nd.minv = lo;
        nd.maxv = hi;
        nd.a = p->tree.nkids;
        nd.n = 1;
        add_kid(unit);
        return id;
    }

    constexpr std::uint16_t parse_pad()
    {
        i = static_cast<std::uint16_t>(i + 4);
        std::uint16_t id = add_node();
        if (!alive()) return 0;
        node & nd = p->tree.nodes[id];
        nd.k = node_kind::pad;
        unsigned char padc = 0;
        if (!parse_quoted(padc)) return 0;
        if (!eat(')')) { fail(*p, keyword2_error::syntax, i); return 0; }
        nd.ch = padc;
        nd.digs[0] = padc;
        nd.radix = 1;
        if (!parse_class_body(nd, true)) return 0;
        std::uint16_t lo = 0, hi = 0;
        if (!parse_quant(lo, hi) || p->error != keyword2_error::ok)
        {
            if (p->error == keyword2_error::ok) fail(*p, keyword2_error::syntax, i);
            return 0;
        }
        nd.minv = lo;
        nd.maxv = hi;
        bit_set(nd.bits, padc);
        return id;
    }

    constexpr bool is_meta(char c) const
    {
        return c == '.' || c == '|' || c == '(' || c == ')' || c == '[' || c == ']'
            || c == '{' || c == '}' || c == '?' || c == '\\' || c == '*' || c == '+';
    }

    constexpr std::uint16_t parse_atom()
    {
        if (!alive()) return 0;
        if (eat('('))
        {
            std::uint16_t inner = parse_alt();
            if (!eat(')')) { fail(*p, keyword2_error::syntax, i); return 0; }
            return inner;
        }
        if (eat('.'))
        {
            std::uint16_t id = add_node();
            if (!alive()) return 0;
            p->tree.nodes[id].k = node_kind::dot;
            return id;
        }
        if (peek() == '[')
        {
            std::uint16_t id = add_node();
            if (!alive()) return 0;
            p->tree.nodes[id].k = node_kind::cls;
            if (!parse_class_body(p->tree.nodes[id], false)) return 0;
            return id;
        }
        unsigned char ch = 0;
        if (peek() == '\\')
        {
            if (!parse_escape(ch)) return 0;
        }
        else if (peek() == '\0' || is_meta(peek()))
        {
            fail(*p, keyword2_error::syntax, i);
            return 0;
        }
        else
        {
            ch = static_cast<unsigned char>(peek());
            ++i;
        }
        std::uint16_t id = add_node();
        if (!alive()) return 0;
        p->tree.nodes[id].k = node_kind::lit;
        p->tree.nodes[id].ch = ch;
        return id;
    }

    constexpr bool starts_pad() const
    {
        return i + 3 < n && s[i] == 'p' && s[i + 1] == 'a' && s[i + 2] == 'd' && s[i + 3] == '(';
    }

    constexpr bool piece_starts() const
    {
        if (i >= n) return false;
        char c = s[i];
        if (c == '|' || c == ')') return false;
        return true;
    }

    constexpr std::uint16_t parse_piece()
    {
        if (!alive()) return 0;
        if (starts_pad()) return parse_pad();
        std::uint16_t id = parse_atom();
        if (!alive()) return 0;
        std::uint16_t lo = 0, hi = 0;
        std::uint16_t before = i;
        if (parse_quant(lo, hi))
        {
            if (!alive()) return 0;
            if (p->tree.nodes[id].k == node_kind::pad)
            {
                fail(*p, keyword2_error::syntax, before);
                return 0;
            }
            return wrap_rep(id, lo, hi);
        }
        return id;
    }

    constexpr std::uint16_t parse_concat()
    {
        if (!alive()) return 0;
        if (!piece_starts())
        {
            std::uint16_t id = add_node();
            if (!alive()) return 0;
            p->tree.nodes[id].k = node_kind::empty;
            return id;
        }
        std::uint16_t local[kw2_nodes]{};
        std::uint16_t ln = 0;
        local[ln++] = parse_piece();
        if (!alive()) return 0;
        if (!piece_starts()) return local[0];
        while (alive() && piece_starts() && ln < kw2_nodes)
            local[ln++] = parse_piece();
        std::uint16_t id = add_node();
        if (!alive()) return 0;
        node & nd = p->tree.nodes[id];
        nd.k = node_kind::cat;
        nd.a = p->tree.nkids;
        nd.n = ln;
        for (std::uint16_t i = 0; i < ln; ++i) add_kid(local[i]);
        return id;
    }

    constexpr std::uint16_t parse_alt()
    {
        if (!alive()) return 0;
        std::uint16_t local[kw2_nodes]{};
        std::uint16_t ln = 0;
        local[ln++] = parse_concat();
        if (!alive() || peek() != '|') return local[0];
        while (alive() && eat('|') && ln < kw2_nodes)
            local[ln++] = parse_concat();
        std::uint16_t id = add_node();
        if (!alive()) return 0;
        node & nd = p->tree.nodes[id];
        nd.k = node_kind::alt;
        nd.a = p->tree.nkids;
        nd.n = ln;
        for (std::uint16_t i = 0; i < ln; ++i) add_kid(local[i]);
        return id;
    }
};

constexpr card pow_small(std::uint16_t radix, std::uint16_t exp)
{
    card r = card_one();
    card f = card_u64(radix);
    for (std::uint16_t i = 0; i < exp; ++i) r = mul_card(r, f);
    return r;
}

constexpr card rep_card(card s, std::uint16_t lo, std::uint16_t hi)
{
    card sum{};
    card p = card_one();
    for (std::uint16_t k = 0; k <= hi; ++k)
    {
        if (k >= lo) sum = add_card(sum, p);
        if (k != hi) p = mul_card(p, s);
        if (sum.bad || p.bad) return sum.bad ? sum : p;
    }
    return sum;
}

constexpr void saturate_len(std::uint16_t & dst, std::uint32_t v)
{
    dst = v > kw2_len_cap ? static_cast<std::uint16_t>(kw2_len_cap + 1)
                          : static_cast<std::uint16_t>(v);
}

constexpr void annotate(program & p, std::uint16_t id)
{
    if (p.error != keyword2_error::ok) return;
    node & nd = p.tree.nodes[id];
    switch (nd.k)
    {
    case node_kind::empty:
        nd.lang = card_one();
        nd.nullable = true;
        nd.min_len = 0;
        nd.max_len = 0;
        break;
    case node_kind::lit:
        nd.lang = card_one();
        bit_set(nd.first, nd.ch);
        nd.min_len = 1;
        nd.max_len = 1;
        break;
    case node_kind::cls:
        nd.lang = card_u64(static_cast<std::uint64_t>(popcount_bits(nd.bits)));
        bit_or(nd.first, nd.bits);
        nd.min_len = 1;
        nd.max_len = 1;
        break;
    case node_kind::dot:
        nd.lang = card_u64(256);
        bit_fill(nd.first);
        bit_fill(nd.bits);
        nd.min_len = 1;
        nd.max_len = 1;
        break;
    case node_kind::pad:
        nd.lang = pow_small(nd.radix == 0 ? 1 : nd.radix, nd.maxv);
        bit_or(nd.first, nd.bits);
        nd.nullable = nd.minv == 0;
        saturate_len(nd.min_len, nd.minv);
        saturate_len(nd.max_len, nd.maxv);
        break;
    case node_kind::cat:
    {
        nd.lang = card_one();
        std::uint32_t mn = 0, mx = 0;
        for (std::uint16_t c = 0; c < nd.n; ++c)
        {
            std::uint16_t cid = p.tree.kids[nd.a + c];
            annotate(p, cid);
            if (p.error != keyword2_error::ok) return;
            const node & ch = p.tree.nodes[cid];
            nd.lang = mul_card(nd.lang, ch.lang);
            mn += ch.min_len;
            mx += ch.max_len;
        }
        for (int w = 0; w < 4; ++w) nd.first[w] = 0;
        for (std::uint16_t c = 0; c < nd.n; ++c)
        {
            const node & ch = p.tree.nodes[p.tree.kids[nd.a + c]];
            bit_or(nd.first, ch.first);
            if (!ch.nullable) break;
        }
        nd.nullable = true;
        for (std::uint16_t c = 0; c < nd.n; ++c)
            if (!p.tree.nodes[p.tree.kids[nd.a + c]].nullable) nd.nullable = false;
        saturate_len(nd.min_len, mn);
        saturate_len(nd.max_len, mx);
        break;
    }
    case node_kind::alt:
    {
        nd.lang = {};
        nd.nullable = false;
        std::uint16_t mn = kw2_len_cap + 1, mx = 0;
        for (std::uint16_t c = 0; c < nd.n; ++c)
        {
            std::uint16_t cid = p.tree.kids[nd.a + c];
            annotate(p, cid);
            if (p.error != keyword2_error::ok) return;
            const node & ch = p.tree.nodes[cid];
            nd.lang = add_card(nd.lang, ch.lang);
            bit_or(nd.first, ch.first);
            if (ch.nullable) nd.nullable = true;
            if (ch.min_len < mn) mn = ch.min_len;
            if (ch.max_len > mx) mx = ch.max_len;
        }
        nd.min_len = mn > kw2_len_cap ? static_cast<std::uint16_t>(kw2_len_cap + 1) : mn;
        nd.max_len = mx;
        break;
    }
    case node_kind::rep:
    {
        std::uint16_t uid = p.tree.kids[nd.a];
        annotate(p, uid);
        if (p.error != keyword2_error::ok) return;
        const node & u = p.tree.nodes[uid];
        if (u.nullable) { fail(p, keyword2_error::delim, 0); return; }
        nd.lang = rep_card(u.lang, nd.minv, nd.maxv);
        bit_or(nd.first, u.first);
        nd.nullable = nd.minv == 0;
        saturate_len(nd.min_len, static_cast<std::uint32_t>(nd.minv) * u.min_len);
        saturate_len(nd.max_len, static_cast<std::uint32_t>(nd.maxv) * u.max_len);
        break;
    }
    }
    if (nd.lang.bad) fail(p, keyword2_error::width, 0);
}

constexpr void check_delim(program & p, std::uint16_t id, const std::uint64_t follow[4])
{
    if (p.error != keyword2_error::ok) return;
    node & nd = p.tree.nodes[id];
    switch (nd.k)
    {
    case node_kind::pad:
        if (bit_overlap(nd.bits, follow)) fail(p, keyword2_error::delim, 0);
        break;
    case node_kind::rep:
    {
        std::uint16_t uid = p.tree.kids[nd.a];
        std::uint64_t inner[4]{};
        bit_or(inner, follow);
        if (nd.maxv > 1) bit_or(inner, p.tree.nodes[uid].first);
        if (nd.minv != nd.maxv && bit_overlap(p.tree.nodes[uid].first, follow))
            fail(p, keyword2_error::delim, 0);
        check_delim(p, uid, inner);
        break;
    }
    case node_kind::cat:
    {
        std::uint64_t fol[4]{};
        bit_or(fol, follow);
        for (int c = static_cast<int>(nd.n) - 1; c >= 0; --c)
        {
            std::uint16_t cid = p.tree.kids[nd.a + static_cast<std::uint16_t>(c)];
            check_delim(p, cid, fol);
            const node & ch = p.tree.nodes[cid];
            if (ch.nullable) bit_or(fol, ch.first);
            else
            {
                for (int w = 0; w < 4; ++w) fol[w] = 0;
                bit_or(fol, ch.first);
            }
        }
        break;
    }
    case node_kind::alt:
        for (std::uint16_t c = 0; c < nd.n; ++c)
            check_delim(p, p.tree.kids[nd.a + c], follow);
        break;
    default:
        break;
    }
}

struct nfa
{
    struct st
    {
        std::uint16_t eps0 = kw2_none;
        std::uint16_t eps1 = kw2_none;
        std::uint16_t dest = kw2_none;
        std::uint64_t bits[4]{};
        bool accept = false;
    };
    st st[kw2_nfa_cap]{};
    std::uint16_t n = 0;
    std::uint16_t start = 0;
};

struct frag { std::uint16_t in = 0, out = 0; };

constexpr std::uint16_t nfa_new(nfa & n, bool & bad)
{
    if (n.n >= kw2_nfa_cap) { bad = true; return 0; }
    std::uint16_t id = n.n++;
    n.st[id].eps0 = kw2_none;
    n.st[id].eps1 = kw2_none;
    n.st[id].dest = kw2_none;
    n.st[id].accept = false;
    for (int w = 0; w < 4; ++w) n.st[id].bits[w] = 0;
    return id;
}

constexpr void nfa_link(nfa & n, bool & bad, std::uint16_t from, std::uint16_t to)
{
    if (bad) return;
    auto & s = n.st[from];
    if (s.eps0 == kw2_none) { s.eps0 = to; return; }
    if (s.eps1 == kw2_none) { s.eps1 = to; return; }
    std::uint16_t r = nfa_new(n, bad);
    if (bad) return;
    n.st[r].eps0 = s.eps0;
    n.st[r].eps1 = s.eps1;
    s.eps0 = r;
    s.eps1 = to;
}

constexpr frag nfa_byte_chain(nfa & n, bool & bad, const std::uint64_t bits[4],
    std::uint16_t lo, std::uint16_t hi)
{
    frag f;
    f.in = nfa_new(n, bad);
    if (bad) return f;
    if (hi == 0)
    {
        f.out = f.in;
        return f;
    }
    f.out = nfa_new(n, bad);
    if (bad) return f;
    if (lo == 0) nfa_link(n, bad, f.in, f.out);
    std::uint16_t prev = f.in;
    for (std::uint16_t i = 0; i < hi && !bad; ++i)
    {
        std::uint16_t nxt = (i + 1 == hi) ? f.out : nfa_new(n, bad);
        if (bad) return f;
        n.st[prev].dest = nxt;
        for (int w = 0; w < 4; ++w) n.st[prev].bits[w] = bits[w];
        if (i + 1 >= lo && nxt != f.out) nfa_link(n, bad, nxt, f.out);
        prev = nxt;
    }
    return f;
}

constexpr frag nfa_build(nfa & n, bool & bad, const program & p, std::uint16_t id);

constexpr frag nfa_build(nfa & n, bool & bad, const program & p, std::uint16_t id)
{
    const node & nd = p.tree.nodes[id];
    if (nd.k == node_kind::empty)
    {
        frag f;
        f.in = f.out = nfa_new(n, bad);
        return f;
    }
    if (nd.k == node_kind::lit || nd.k == node_kind::cls || nd.k == node_kind::dot)
    {
        std::uint64_t bits[4]{};
        if (nd.k == node_kind::lit) bit_set(bits, nd.ch);
        else if (nd.k == node_kind::dot) bit_fill(bits);
        else for (int w = 0; w < 4; ++w) bits[w] = nd.bits[w];
        return nfa_byte_chain(n, bad, bits, 1, 1);
    }
    if (nd.k == node_kind::pad)
        return nfa_byte_chain(n, bad, nd.bits, nd.minv, nd.maxv);
    if (nd.k == node_kind::rep)
    {
        std::uint16_t uid = p.tree.kids[nd.a];
        const node & u = p.tree.nodes[uid];
        if (u.k == node_kind::lit || u.k == node_kind::cls || u.k == node_kind::dot)
        {
            std::uint64_t bits[4]{};
            if (u.k == node_kind::lit) bit_set(bits, u.ch);
            else if (u.k == node_kind::dot) bit_fill(bits);
            else for (int w = 0; w < 4; ++w) bits[w] = u.bits[w];
            return nfa_byte_chain(n, bad, bits, nd.minv, nd.maxv);
        }
        frag f;
        f.in = nfa_new(n, bad);
        f.out = nfa_new(n, bad);
        if (nd.maxv == 0)
        {
            nfa_link(n, bad, f.in, f.out);
            return f;
        }
        std::uint16_t prev = f.in;
        for (std::uint16_t i = 0; i < nd.maxv && !bad; ++i)
        {
            if (i >= nd.minv) nfa_link(n, bad, prev, f.out);
            frag c = nfa_build(n, bad, p, uid);
            nfa_link(n, bad, prev, c.in);
            prev = c.out;
        }
        nfa_link(n, bad, prev, f.out);
        return f;
    }
    if (nd.k == node_kind::cat)
    {
        frag cur = nfa_build(n, bad, p, p.tree.kids[nd.a]);
        for (std::uint16_t c = 1; c < nd.n && !bad; ++c)
        {
            frag nxt = nfa_build(n, bad, p, p.tree.kids[nd.a + c]);
            nfa_link(n, bad, cur.out, nxt.in);
            cur.out = nxt.out;
        }
        return cur;
    }
    frag f;
    f.in = nfa_new(n, bad);
    f.out = nfa_new(n, bad);
    for (std::uint16_t c = 0; c < nd.n && !bad; ++c)
    {
        frag b = nfa_build(n, bad, p, p.tree.kids[nd.a + c]);
        nfa_link(n, bad, f.in, b.in);
        nfa_link(n, bad, b.out, f.out);
    }
    return f;
}

constexpr bool nfa_intersect(const nfa & n, std::uint16_t a0, std::uint16_t b0)
{
    if (n.n == 0 || a0 == kw2_none || b0 == kw2_none) return false;
    constexpr std::uint16_t cap = kw2_nfa_cap;
    unsigned char seen[(cap * cap + 7) / 8]{};
    auto mark = [&](std::uint16_t a, std::uint16_t b) {
        std::uint32_t bit = static_cast<std::uint32_t>(a) * cap + b;
        seen[bit / 8] = static_cast<unsigned char>(seen[bit / 8] | (1u << (bit % 8)));
    };
    auto test = [&](std::uint16_t a, std::uint16_t b) {
        std::uint32_t bit = static_cast<std::uint32_t>(a) * cap + b;
        return (seen[bit / 8] >> (bit % 8)) & 1u;
    };
    std::uint16_t qa[cap * cap]{};
    std::uint16_t qb[cap * cap]{};
    int qh = 0, qt = 0;
    // Explicit stack for epsilon product, then byte steps via a queue of concrete states.
    std::uint16_t sa[cap * 4]{}, sb[cap * 4]{};
    int sp = 0;
    auto consider = [&](std::uint16_t a, std::uint16_t b) {
        if (a >= n.n || b >= n.n || test(a, b) || sp >= cap * 4) return;
        sa[sp] = a;
        sb[sp] = b;
        ++sp;
    };
    consider(a0, b0);
    // We collect byte-ready pairs in qa after closing eps.
    while (sp)
    {
        --sp;
        std::uint16_t a = sa[sp], b = sb[sp];
        if (test(a, b)) continue;
        mark(a, b);
        if (qt >= cap * cap) return true;
        qa[qt] = a;
        qb[qt] = b;
        ++qt;
        if (n.st[a].eps0 != kw2_none) consider(n.st[a].eps0, b);
        if (n.st[a].eps1 != kw2_none) consider(n.st[a].eps1, b);
        if (n.st[b].eps0 != kw2_none) consider(a, n.st[b].eps0);
        if (n.st[b].eps1 != kw2_none) consider(a, n.st[b].eps1);
    }
    while (qh < qt)
    {
        std::uint16_t a = qa[qh], b = qb[qh];
        ++qh;
        if (n.st[a].accept && n.st[b].accept) return true;
        if (n.st[a].dest == kw2_none || n.st[b].dest == kw2_none) continue;
        if (!bit_overlap(n.st[a].bits, n.st[b].bits)) continue;
        // Step both, then epsilon-close into the queue by resetting the stack search
        // only for the new pair. Reuse consider on a fresh seen? The pair (dest,dest)
        // may already be seen. Push dests through a nested eps walk that respects seen.
        std::uint16_t da = n.st[a].dest, db = n.st[b].dest;
        sp = 0;
        consider(da, db);
        while (sp)
        {
            --sp;
            std::uint16_t x = sa[sp], y = sb[sp];
            if (test(x, y)) continue;
            mark(x, y);
            if (qt >= cap * cap) return true;
            qa[qt] = x;
            qb[qt] = y;
            ++qt;
            if (n.st[x].eps0 != kw2_none) consider(n.st[x].eps0, y);
            if (n.st[x].eps1 != kw2_none) consider(n.st[x].eps1, y);
            if (n.st[y].eps0 != kw2_none) consider(x, n.st[y].eps0);
            if (n.st[y].eps1 != kw2_none) consider(x, n.st[y].eps1);
        }
    }
    return false;
}

struct subset
{
    std::uint64_t w[3]{};

    constexpr bool operator==(subset o) const
    {
        return w[0] == o.w[0] && w[1] == o.w[1] && w[2] == o.w[2];
    }
};

constexpr bool sub_test(subset s, unsigned i) { return (s.w[i / 64] >> (i % 64)) & 1u; }
constexpr void sub_set(subset & s, unsigned i) { s.w[i / 64] |= std::uint64_t{1} << (i % 64); }

constexpr int eps_accept_ways(const nfa & n, const std::uint16_t * seeds, int nseeds)
{
    int ways[kw2_nfa_cap]{};
    unsigned char color[kw2_nfa_cap]{};
    std::uint16_t order[kw2_nfa_cap]{};
    int on = 0;
    std::uint16_t stack[kw2_nfa_cap]{};
    int sp = 0;
    for (int i = 0; i < nseeds; ++i)
    {
        if (color[seeds[i]] == 0) { stack[sp++] = seeds[i]; color[seeds[i]] = 1; }
        ways[seeds[i]] += 1;
    }
    // color 1 = in stack, 2 = done. The stack above only seeds discovery.
    for (int i = 0; i < kw2_nfa_cap; ++i) color[i] = 0;
    sp = 0;
    for (int i = 0; i < nseeds; ++i) stack[sp++] = seeds[i];
    while (sp)
    {
        std::uint16_t s = stack[sp - 1];
        if (color[s] == 0)
        {
            color[s] = 1;
            auto push = [&](std::uint16_t t) {
                if (t == kw2_none) return;
                if (color[t] == 1) return;
                if (color[t] == 0) stack[sp++] = t;
            };
            push(n.st[s].eps0);
            push(n.st[s].eps1);
            continue;
        }
        if (color[s] == 1)
        {
            color[s] = 2;
            order[on++] = s;
            --sp;
        }
        else --sp;
    }
    // `ways` currently counts seeds. Rebuild from zero and propagate in topo.
    int seed_ways[kw2_nfa_cap]{};
    for (int i = 0; i < nseeds; ++i) seed_ways[seeds[i]] += 1;
    for (int i = 0; i < kw2_nfa_cap; ++i) ways[i] = seed_ways[i];
    for (int i = on - 1; i >= 0; --i)
    {
        std::uint16_t s = order[i];
        auto add = [&](std::uint16_t t) {
            if (t == kw2_none) return;
            ways[t] += ways[s];
        };
        add(n.st[s].eps0);
        add(n.st[s].eps1);
    }
    int acc = 0;
    for (std::uint16_t s = 0; s < n.n; ++s)
        if (n.st[s].accept) acc += ways[s];
    return acc;
}

constexpr void check_ambiguous(program & p)
{
    if (p.error != keyword2_error::ok) return;
    nfa n{};
    bool bad = false;
    frag root = nfa_build(n, bad, p, p.tree.root);
    if (bad) { fail(p, keyword2_error::states, 0); return; }
    n.st[root.out].accept = true;
    n.start = root.in;

    subset states[kw2_dfa_cap]{};
    int ns = 0;
    auto intern = [&](subset s) -> int {
        for (int i = 0; i < ns; ++i)
            if (states[i] == s) return i;
        if (ns >= kw2_dfa_cap) return -1;
        states[ns] = s;
        return ns++;
    };

    auto close_seeds = [&](const std::uint16_t * seeds, int nseeds, subset & dst) {
        std::uint16_t stack[kw2_nfa_cap]{};
        int sp = 0;
        for (int i = 0; i < nseeds; ++i) stack[sp++] = seeds[i];
        while (sp)
        {
            std::uint16_t s = stack[--sp];
            if (s >= n.n || sub_test(dst, s)) continue;
            sub_set(dst, s);
            if (n.st[s].eps0 != kw2_none) stack[sp++] = n.st[s].eps0;
            if (n.st[s].eps1 != kw2_none) stack[sp++] = n.st[s].eps1;
        }
    };

    std::uint16_t seed0[1] = {n.start};
    subset start{};
    close_seeds(seed0, 1, start);
    if (eps_accept_ways(n, seed0, 1) > 1) { fail(p, keyword2_error::overlap, 0); return; }
    if (intern(start) < 0) { fail(p, keyword2_error::states, 0); return; }

    for (int si = 0; si < ns; ++si)
    {
        for (unsigned b = 0; b < 256; ++b)
        {
            std::uint16_t hits[32]{};
            int nh = 0;
            for (std::uint16_t s = 0; s < n.n; ++s)
            {
                if (!sub_test(states[si], s)) continue;
                if (n.st[s].dest == kw2_none || !bit_test(n.st[s].bits, b)) continue;
                if (nh < 32) hits[nh++] = s;
            }
            if (nh == 0) continue;
            if (nh >= 2)
            {
                for (int i = 0; i < nh; ++i)
                    for (int j = i + 1; j < nh; ++j)
                        if (nfa_intersect(n, n.st[hits[i]].dest, n.st[hits[j]].dest))
                        {
                            fail(p, keyword2_error::overlap, 0);
                            return;
                        }
            }
            std::uint16_t dests[32]{};
            for (int i = 0; i < nh; ++i) dests[i] = n.st[hits[i]].dest;
            if (eps_accept_ways(n, dests, nh) > 1)
            {
                fail(p, keyword2_error::overlap, 0);
                return;
            }
            subset nxt{};
            close_seeds(dests, nh, nxt);
            if (intern(nxt) < 0) { fail(p, keyword2_error::states, 0); return; }
        }
    }
}

constexpr card block_before(card s, std::uint16_t lo, int k)
{
    card sum{};
    card p = card_one();
    for (int j = 0; j < k; ++j)
    {
        if (j >= static_cast<int>(lo)) sum = add_card(sum, p);
        p = mul_card(p, s);
    }
    return sum;
}

struct hit
{
    bool ok = false;
    std::size_t pos = 0;
    u256 rank{};
};

constexpr int pad_digit(const node & nd, unsigned char ch)
{
    for (std::uint16_t d = 0; d < nd.radix; ++d)
        if (nd.digs[d] == ch) return static_cast<int>(d);
    return -1;
}

struct seq_tail
{
    const std::uint16_t * ids = nullptr;
    std::uint16_t i = 0;
    std::uint16_t n = 0;
    u256 rank{};
};

struct ctx
{
    const program * prog = nullptr;
    const char * s = nullptr;
    std::size_t len = 0;
    seq_tail wrap[24]{};
    int sp = 0;
    int depth = 0;
};

constexpr hit run_seq(ctx & c, const std::uint16_t * ids, std::uint16_t nids,
    std::uint16_t at, std::size_t pos, u256 rank);

constexpr hit finish_seq(ctx & c, std::size_t pos, u256 rank)
{
    if (c.sp > 0)
    {
        seq_tail w = c.wrap[--c.sp];
        return run_seq(c, w.ids, w.n, w.i, pos, add_card(card{w.rank, false, false}, card{rank, false, false}).v);
    }
    hit h;
    h.ok = pos == c.len;
    h.pos = pos;
    h.rank = rank;
    return h;
}

constexpr hit run_id(ctx & c, std::uint16_t id, std::size_t pos, u256 rank_before,
    const std::uint16_t * rest, std::uint16_t ri, std::uint16_t rn)
{
    if (++c.depth > 256) { --c.depth; return {}; }
    const node & nd = c.prog->tree.nodes[id];
    hit result{};
    switch (nd.k)
    {
    case node_kind::empty:
        result = run_seq(c, rest, rn, ri, pos, mul_add_u(rank_before, nd.lang, u256{}));
        break;
    case node_kind::lit:
        if (pos < c.len && static_cast<unsigned char>(c.s[pos]) == nd.ch)
            result = run_seq(c, rest, rn, ri, pos + 1, mul_add_u(rank_before, nd.lang, u256{}));
        break;
    case node_kind::cls:
    case node_kind::dot:
        if (pos < c.len && bit_test(nd.bits, static_cast<unsigned char>(c.s[pos])))
        {
            u256 piece{};
            unsigned char ch = static_cast<unsigned char>(c.s[pos]);
            piece.w[0] = nd.k == node_kind::dot
                ? ch : static_cast<std::uint64_t>(rank_below(nd.bits, ch));
            result = run_seq(c, rest, rn, ri, pos + 1, mul_add_u(rank_before, nd.lang, piece));
        }
        break;
    case node_kind::pad:
    {
        std::size_t end = pos;
        while (end < c.len && end - pos < nd.maxv
            && bit_test(nd.bits, static_cast<unsigned char>(c.s[end])))
            ++end;
        if (end - pos < nd.minv) break;
        u256 val{};
        bool good = true;
        for (std::size_t k = pos; k < end; ++k)
        {
            int d = pad_digit(nd, static_cast<unsigned char>(c.s[k]));
            if (d < 0) { good = false; break; }
            val = add_card(mul_card(card{val, false, false}, card_u64(nd.radix)),
                card_u64(static_cast<std::uint64_t>(d))).v;
        }
        if (good)
            result = run_seq(c, rest, rn, ri, end, mul_add_u(rank_before, nd.lang, val));
        break;
    }
    case node_kind::cat:
    {
        std::uint16_t buf[kw2_kids]{};
        std::uint16_t m = 0;
        for (std::uint16_t i = 0; i < nd.n && m < kw2_kids; ++i)
            buf[m++] = c.prog->tree.kids[nd.a + i];
        for (std::uint16_t j = ri; j < rn && m < kw2_kids; ++j)
            buf[m++] = rest[j];
        result = run_seq(c, buf, m, 0, pos, rank_before);
        break;
    }
    case node_kind::alt:
    {
        card offset{};
        for (std::uint16_t b = 0; b < nd.n; ++b)
        {
            std::uint16_t cid = c.prog->tree.kids[nd.a + b];
            if (c.sp >= 24) break;
            int mark = c.sp;
            c.wrap[c.sp++] = seq_tail{rest, ri, rn, mul_add_u(rank_before, nd.lang, offset.v)};
            hit h = run_id(c, cid, pos, u256{}, nullptr, 0, 0);
            if (c.sp > mark) --c.sp;
            if (h.ok) { result = h; break; }
            offset = add_card(offset, c.prog->tree.nodes[cid].lang);
        }
        break;
    }
    case node_kind::rep:
    {
        std::uint16_t unit = c.prog->tree.kids[nd.a];
        for (int k = static_cast<int>(nd.maxv); k >= static_cast<int>(nd.minv); --k)
        {
            std::uint16_t copies[kw2_len_cap]{};
            for (int i = 0; i < k; ++i) copies[i] = unit;
            card block = block_before(c.prog->tree.nodes[unit].lang, nd.minv, k);
            if (c.sp >= 24) break;
            int mark = c.sp;
            u256 base = mul_add_u(rank_before, nd.lang, block.v);
            c.wrap[c.sp++] = seq_tail{rest, ri, rn, base};
            hit h = run_seq(c, copies, static_cast<std::uint16_t>(k), 0, pos, u256{});
            if (c.sp > mark) --c.sp;
            if (h.ok) { result = h; break; }
        }
        break;
    }
    }
    --c.depth;
    return result;
}

constexpr hit run_seq(ctx & c, const std::uint16_t * ids, std::uint16_t nids,
    std::uint16_t at, std::size_t pos, u256 rank)
{
    if (at == nids) return finish_seq(c, pos, rank);
    return run_id(c, ids[at], pos, rank, ids, static_cast<std::uint16_t>(at + 1), nids);
}

constexpr hit match_full(const program & p, const char * s, std::size_t n)
{
    std::uint16_t root = p.tree.root;
    ctx c;
    c.prog = &p;
    c.s = s;
    c.len = n;
    return run_id(c, root, 0, u256{}, nullptr, 0, 0);
}

HEDLEY_NON_NULL(4)
constexpr int unrank_node(const program & p, std::uint16_t id, u256 rank, char * out, int n);

constexpr int unrank_node(const program & p, std::uint16_t id, u256 rank, char * out, int n)
{
    const node & nd = p.tree.nodes[id];
    switch (nd.k)
    {
    case node_kind::empty:
        return n;
    case node_kind::lit:
        out[n++] = static_cast<char>(nd.ch);
        return n;
    case node_kind::cls:
    case node_kind::dot:
        out[n++] = static_cast<char>(nd.k == node_kind::dot
            ? static_cast<unsigned char>(rank.w[0])
            : bit_at_index(nd.bits, static_cast<int>(rank.w[0])));
        return n;
    case node_kind::pad:
    {
        unsigned char digits[kw2_len_cap]{};
        u256 cur = rank;
        for (int i = static_cast<int>(nd.maxv) - 1; i >= 0; --i)
        {
            u256 q, r;
            divmod_u(cur, card_u64(nd.radix).v, q, r);
            digits[i] = static_cast<unsigned char>(r.w[0]);
            cur = q;
        }
        int start = 0;
        while (start < static_cast<int>(nd.maxv) - static_cast<int>(nd.minv)
            && digits[start] == 0) ++start;
        for (int i = start; i < static_cast<int>(nd.maxv); ++i)
            out[n++] = static_cast<char>(nd.digs[digits[i]]);
        return n;
    }
    case node_kind::cat:
    {
        card suf = card_one();
        card place[kw2_nodes]{};
        for (int c = static_cast<int>(nd.n) - 1; c >= 0; --c)
        {
            place[c] = suf;
            suf = mul_card(suf, p.tree.nodes[p.tree.kids[nd.a + static_cast<std::uint16_t>(c)]].lang);
        }
        u256 rem = rank;
        for (std::uint16_t c = 0; c < nd.n; ++c)
        {
            u256 q, r;
            divmod_card(rem, place[c], q, r);
            n = unrank_node(p, p.tree.kids[nd.a + c], q, out, n);
            rem = r;
        }
        return n;
    }
    case node_kind::alt:
    {
        u256 rem = rank;
        for (std::uint16_t c = 0; c < nd.n; ++c)
        {
            const node & ch = p.tree.nodes[p.tree.kids[nd.a + c]];
            if (cmp_card_u(rem, ch.lang) < 0)
                return unrank_node(p, p.tree.kids[nd.a + c], rem, out, n);
            rem = sub_u(rem, ch.lang.v);
        }
        return n;
    }
    case node_kind::rep:
    {
        std::uint16_t unit = p.tree.kids[nd.a];
        card S = p.tree.nodes[unit].lang;
        u256 rem = rank;
        card pow = card_one();
        for (std::uint16_t j = 0; j < nd.minv; ++j) pow = mul_card(pow, S);
        int k = static_cast<int>(nd.minv);
        for (; k <= static_cast<int>(nd.maxv); ++k)
        {
            if (cmp_card_u(rem, pow) < 0) break;
            rem = sub_u(rem, pow.v);
            if (k == static_cast<int>(nd.maxv)) break;
            pow = mul_card(pow, S);
        }
        u256 rs[kw2_len_cap]{};
        for (int i = k - 1; i >= 0; --i)
        {
            u256 q, r;
            divmod_card(rem, S, q, r);
            rs[i] = r;
            rem = q;
        }
        for (int i = 0; i < k; ++i)
            n = unrank_node(p, unit, rs[i], out, n);
        return n;
    }
    }
    return n;
}

HEDLEY_NON_NULL(3)
constexpr int unrank_root(const program & p, u256 rank, char * out)
{
    if (!p.lang.all && cmp_card_u(rank, p.lang) >= 0) return -1;
    return unrank_node(p, p.tree.root, rank, out, 0);
}

HEDLEY_NON_NULL(1)
constexpr program compile_pattern(const char * pattern)
{
    program p{};
    parser ps{&p, pattern, 0, 0};
    while (pattern[ps.n] != '\0' && ps.n < 1023) ++ps.n;
    if (pattern[ps.n] != '\0')
    {
        fail(p, keyword2_error::syntax, ps.n);
        return p;
    }
    p.tree.root = ps.parse_alt();
    if (p.error == keyword2_error::ok && ps.i != ps.n)
        fail(p, keyword2_error::syntax, ps.i);
    if (p.error != keyword2_error::ok) return p;
    annotate(p, p.tree.root);
    if (p.error != keyword2_error::ok) return p;
    if (p.tree.nodes[p.tree.root].max_len > kw2_len_cap)
    {
        fail(p, keyword2_error::length, 0);
        return p;
    }
    p.lang = p.tree.nodes[p.tree.root].lang;
    if (p.lang.bad || p.lang.zero())
    {
        fail(p, keyword2_error::width, 0);
        return p;
    }
    if (p.lang.all) p.bits = 256;
    else if (p.lang.one()) p.bits = 1;
    else p.bits = static_cast<std::uint16_t>(bit_length_u(dec_u(p.lang.v)));
    if (p.bits < 1) p.bits = 1;
    if (p.bits > 256) { fail(p, keyword2_error::width, 0); return p; }
    std::uint64_t none[4]{};
    check_delim(p, p.tree.root, none);
    if (p.error != keyword2_error::ok) return p;
    check_ambiguous(p);
    return p;
}

template <const char * Pattern>
struct keyword2_info
{
    static constexpr program compiled = compile_pattern(Pattern);
    static constexpr std::size_t bits = compiled.bits < 1 ? 1 : compiled.bits;
};

template <std::size_t Bits>
constexpr auto pack_rank(u256 r)
{
    using integral = utils::nonvoid_integral_type_from_bitlength_t<Bits>;
    if constexpr (Bits <= 64) return static_cast<integral>(r.w[0]);
    else if constexpr (Bits <= 128)
        return static_cast<integral>(
            (static_cast<unsigned __int128>(r.w[1]) << 64) | r.w[0]);
    else
        return uint256_t{uint128_t{r.w[3], r.w[2]}, uint128_t{r.w[1], r.w[0]}};
}

template <std::size_t Bits, typename Integral>
constexpr u256 unpack_rank(Integral v)
{
    u256 r;
    if constexpr (Bits <= 64) r.w[0] = static_cast<std::uint64_t>(v);
    else if constexpr (Bits <= 128)
    {
        auto x = static_cast<unsigned __int128>(v);
        r.w[0] = static_cast<std::uint64_t>(x);
        r.w[1] = static_cast<std::uint64_t>(x >> 64);
    }
    else
    {
        uint128_t lo = static_cast<uint128_t>(v);
        uint256_t hi = v >> 128;
        uint128_t ho = static_cast<uint128_t>(hi);
        r.w[0] = static_cast<std::uint64_t>(lo);
        r.w[1] = static_cast<std::uint64_t>(static_cast<uint128_t>(lo >> 64));
        r.w[2] = static_cast<std::uint64_t>(ho);
        r.w[3] = static_cast<std::uint64_t>(static_cast<uint128_t>(ho >> 64));
    }
    return r;
}

}  // namespace detail

/// @brief Ranked keyword whose language is the pattern `Pattern`.
/// @note A domain. It stores a `modint` rank. It is not a leaf type.
/// @tparam Pattern null-terminated pattern with static storage.
/// @see dpf::keyword
/// @see dpf::modint
///         `pad('0')[0-9]{0,4}` is a decimal of at most 4 digits.
///         `[0-9a-f]{8}` is exactly 8 significant hex digits.
template <const char * Pattern>
class keyword2
  : public modint<detail::keyword2_info<Pattern>::bits>
{
    using info = detail::keyword2_info<Pattern>;
    static constexpr detail::program const & prog = info::compiled;

    static_assert(prog.error != keyword2_error::syntax,
        "keyword2: syntax error in pattern");
    static_assert(prog.error != keyword2_error::delim,
        "keyword2: pad field or variable repetition is not delimited");
    static_assert(prog.error != keyword2_error::overlap,
        "keyword2: pattern is ambiguous");
    static_assert(prog.error != keyword2_error::states,
        "keyword2: pattern exceeds the 64-state cap");
    static_assert(prog.error != keyword2_error::length,
        "keyword2: pattern accepts a string longer than 64");
    static_assert(prog.error != keyword2_error::width,
        "keyword2: language does not fit in 256 bits");
    static_assert(prog.error == keyword2_error::ok, "keyword2: invalid pattern");

  public:
    using parent = modint<info::bits>;
    using integral_type = typename parent::integral_type;

    static constexpr std::size_t bits = info::bits;

    constexpr keyword2() noexcept = default;

    constexpr keyword2(const keyword2 &) noexcept = default;
    constexpr keyword2(keyword2 &&) noexcept = default;

    constexpr keyword2(std::string_view str)
      : parent(encode_(str)) { }

    HEDLEY_NON_NULL(1)
    constexpr keyword2(const char * str)
      : keyword2(std::string_view(str)) { }

    constexpr keyword2 & operator=(std::string_view str)
    {
        parent::operator=(encode_(str));
        return *this;
    }

    constexpr keyword2 & operator=(const keyword2 &) noexcept = default;
    constexpr keyword2 & operator=(keyword2 &&) noexcept = default;

    ~keyword2() noexcept = default;

    /// @brief Rank, including values outside the language that fill the bit width.
    /// @param rank the `rank`
    /// @return Rank, including values outside the language that fill the bit width
    static constexpr keyword2 from_rank(integral_type rank) noexcept
    {
        return keyword2{rank};
    }

    constexpr integral_type rank() const noexcept
    {
        return parent::reduced_value();
    }

    /// @brief Bitwise complement of the rank, in the `2^bits` domain.
    /// @return Bitwise complement of the rank, in the `2^bits` domain
    constexpr keyword2 operator~() const noexcept
    {
        return keyword2{parent::operator~()};
    }

    operator std::string() const
    {
        char buf[detail::kw2_len_cap];
        int n = detail::unrank_root(prog,
            detail::unpack_rank<bits>(parent::reduced_value()), buf);
        if (n < 0) throw std::domain_error("keyword2: rank is outside the language");
        return std::string(buf, buf + n);
    }

  private:
    constexpr explicit keyword2(integral_type rank) noexcept
      : parent(rank) { }

    constexpr keyword2(parent val) noexcept
      : parent(val) { }

    static constexpr integral_type encode_(std::string_view str)
    {
        detail::hit h = detail::match_full(prog, str.data(), str.size());
        utils::constexpr_maybe_throw<std::domain_error>(!h.ok,
            "keyword2: string is not in the pattern language");
        return detail::pack_rank<bits>(h.rank);
    }

    friend std::ostream & operator<<(std::ostream & os, const keyword2 & k)
    {
        return os << static_cast<std::string>(k);
    }

    friend std::istream & operator>>(std::istream & is, keyword2 & k)
    {
        std::string tmp;
        if (!(is >> tmp)) return is;
        try { k = keyword2(std::string_view(tmp)); }
        catch (const std::exception &) { is.setstate(std::ios::failbit); }
        return is;
    }

    friend struct utils::countl_zero_symmetric_difference<keyword2>;
    friend struct utils::msb_of<keyword2>;
    friend struct utils::mod_pow_2<keyword2>;
    friend struct utils::make_from_integral_value<keyword2>;
};

/// @brief Compile diagnostic for a pattern that should not become a type.
/// @tparam Pattern null-terminated pattern with static storage
/// @return Compile diagnostic for a pattern that should not become a type
template <const char * Pattern>
constexpr keyword2_error keyword2_status() noexcept
{
    return detail::keyword2_info<Pattern>::compiled.error;
}

template <const char * Pattern>
std::string to_string(const keyword2<Pattern> & str)
{
    return static_cast<std::string>(str);
}

namespace utils
{

template <const char * Pattern>
struct bitlength_of<dpf::keyword2<Pattern>>
  : std::integral_constant<std::size_t, dpf::keyword2<Pattern>::bits> { };

template <const char * Pattern>
struct msb_of<dpf::keyword2<Pattern>>
{
    using T = dpf::keyword2<Pattern>;
    using U = typename T::integral_type;
    static constexpr T value = T::from_rank(U{1} << bitlength_of_v<T> - 1ul);
};

template <const char * Pattern>
struct countl_zero_symmetric_difference<dpf::keyword2<Pattern>>
  : countl_zero_symmetric_difference<typename dpf::keyword2<Pattern>::parent> { };

template <const char * Pattern>
struct mod_pow_2<dpf::keyword2<Pattern>>
  : mod_pow_2<typename dpf::keyword2<Pattern>::parent> { };

template <const char * Pattern>
struct make_from_integral_value<dpf::keyword2<Pattern>>
{
    using T = dpf::keyword2<Pattern>;
    using integral_type = integral_type_from_bitlength_t<bitlength_of_v<T>>;
    constexpr T operator()(integral_type val) const noexcept
    {
        return T::from_rank(val);
    }
};

}  // namespace utils

}  // namespace dpf

namespace std
{

template <const char * Pattern>
class numeric_limits<dpf::keyword2<Pattern>>
{
  public:
    using keyword_type = dpf::keyword2<Pattern>;
    static constexpr bool is_specialized = true;
    static constexpr bool is_signed = false;
    static constexpr bool is_integer = true;
    static constexpr bool is_exact = true;
    static constexpr bool has_infinity = false;
    static constexpr bool has_quiet_NaN = false;
    static constexpr bool has_signaling_NaN = false;
    static constexpr std::float_denorm_style has_denorm = std::denorm_absent;
    static constexpr bool has_denorm_loss = false;
    static constexpr std::float_round_style round_style = std::round_toward_zero;
    static constexpr bool is_iec559 = false;
    static constexpr bool is_bounded = true;
    static constexpr bool is_modulo = true;
    static constexpr int digits = keyword_type::bits;
    static constexpr int digits10 = static_cast<int>(
        (static_cast<unsigned long long>(keyword_type::bits) * 30103ull) / 100000ull);
    static constexpr int max_digits10 = 0;
    static constexpr int radix = 2;
    static constexpr int min_exponent = 0;
    static constexpr int max_exponent = 0;
    static constexpr int min_exponent10 = 0;
    static constexpr int max_exponent10 = 0;
    static constexpr bool traps
        = std::numeric_limits<typename keyword_type::integral_type>::traps;
    static constexpr bool tinyness_before = false;

    static constexpr keyword_type min() noexcept { return keyword_type::from_rank(0); }
    static constexpr keyword_type lowest() noexcept { return min(); }
    static constexpr keyword_type max() noexcept
    {
        constexpr auto & prog = dpf::detail::keyword2_info<Pattern>::compiled;
        if (prog.lang.all)
            return keyword_type::from_rank(~typename keyword_type::integral_type{0});
        return keyword_type::from_rank(
            dpf::detail::pack_rank<keyword_type::bits>(dpf::detail::dec_u(prog.lang.v)));
    }
    static constexpr keyword_type epsilon() noexcept { return keyword_type::from_rank(0); }
    static constexpr keyword_type round_error() noexcept { return keyword_type::from_rank(0); }
    static constexpr keyword_type infinity() noexcept { return keyword_type::from_rank(0); }
    static constexpr keyword_type quiet_NaN() noexcept { return keyword_type::from_rank(0); }
    static constexpr keyword_type signaling_NaN() noexcept { return keyword_type::from_rank(0); }
    static constexpr keyword_type denorm_min() noexcept { return keyword_type::from_rank(0); }
};

template <const char * Pattern>
class numeric_limits<dpf::keyword2<Pattern> const>
  : public numeric_limits<dpf::keyword2<Pattern>> { };

template <const char * Pattern>
class numeric_limits<dpf::keyword2<Pattern> volatile>
  : public numeric_limits<dpf::keyword2<Pattern>> { };

template <const char * Pattern>
class numeric_limits<dpf::keyword2<Pattern> const volatile>
  : public numeric_limits<dpf::keyword2<Pattern>> { };

}  // namespace std

#endif  // LIBDPF_INCLUDE_DPF_KEYWORD2_HPP__