edit_distance_unbanded.hpp

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// -----------------------------------------------------------------------------------------------------
// Copyright (c) 2006-2021, Knut Reinert & Freie Universität Berlin
// Copyright (c) 2016-2021, Knut Reinert & MPI für molekulare Genetik
// This file may be used, modified and/or redistributed under the terms of the 3-clause BSD-License
// shipped with this file and also available at: https://github.com/seqan/seqan3/blob/master/LICENSE.md
// -----------------------------------------------------------------------------------------------------
 
#pragma once
 
#include <algorithm>
#include <algorithm>
#include <bitset>
#include <seqan3/std/ranges>
#include <utility>
 
#include <seqan3/alignment/matrix/detail/advanceable_alignment_coordinate.hpp>
#include <seqan3/alignment/matrix/detail/edit_distance_score_matrix_full.hpp>
#include <seqan3/alignment/matrix/detail/edit_distance_trace_matrix_full.hpp>
#include <seqan3/alignment/matrix/detail/matrix_concept.hpp>
#include <seqan3/alignment/pairwise/alignment_result.hpp>
#include <seqan3/alignment/pairwise/edit_distance_fwd.hpp>
#include <seqan3/core/configuration/configuration.hpp>
 
namespace seqan3::detail
{
template <typename derived_t, typename edit_traits>
class edit_distance_unbanded_max_errors_policy :
    edit_traits
{
protected:
    static_assert(edit_traits::use_max_errors, "This policy assumes that edit_traits::use_max_errors is true.");
 
    friend derived_t;
 
    edit_distance_unbanded_max_errors_policy() noexcept = default;  
    edit_distance_unbanded_max_errors_policy(edit_distance_unbanded_max_errors_policy const &) noexcept
        = default; 
    edit_distance_unbanded_max_errors_policy(edit_distance_unbanded_max_errors_policy &&) noexcept
        = default; 
    edit_distance_unbanded_max_errors_policy & operator=(edit_distance_unbanded_max_errors_policy const &) noexcept
        = default; 
    edit_distance_unbanded_max_errors_policy & operator=(edit_distance_unbanded_max_errors_policy &&) noexcept
        = default; 
    ~edit_distance_unbanded_max_errors_policy() noexcept = default; 
 
 
    using typename edit_traits::word_type;
    using typename edit_traits::score_type;
 
    score_type max_errors{255};
    size_t last_block{0u};
    word_type last_score_mask{};
 
    void max_errors_init(size_t block_count) noexcept
    {
        derived_t * self = static_cast<derived_t *>(this);
 
        max_errors = -get<align_cfg::min_score>(self->config).score;
 
        assert(max_errors >= score_type{0});
 
        if (std::ranges::empty(self->query)) // [[unlikely]]
        {
            last_block = 0u;
            self->score_mask = 0u;
            last_score_mask = self->score_mask;
            return;
        }
 
        last_block = block_count - 1u;
        last_score_mask = self->score_mask;
 
        // local_max_errors either stores the maximal number of _score (me.max_errors) or the needle size minus one. It
        // is used for the mask computation and setting the initial score (the minus one is there because of the Ukkonen
        // trick).
        size_t const local_max_errors = std::min<size_t>(max_errors, std::ranges::size(self->query) - 1u);
        self->score_mask = word_type{1u} << (local_max_errors % self->word_size);
        last_block = std::min(local_max_errors / self->word_size, last_block);
        self->_score = local_max_errors + 1u;
    }
 
    bool is_last_active_cell_within_last_row() const noexcept
    {
        derived_t const * self = static_cast<derived_t const *>(this);
        return (self->score_mask == this->last_score_mask) && (this->last_block == self->vp.size() - 1u);
    }
 
    bool prev_last_active_cell() noexcept
    {
        derived_t * self = static_cast<derived_t *>(this);
        self->score_mask >>= 1u;
        if (self->score_mask != 0u)
            return true;
 
        if constexpr (edit_traits::is_global)
        {
            if (last_block == 0u) // [[unlikely]]
                return false;
        }
 
        last_block--;
 
        self->score_mask = word_type{1u} << (edit_traits::word_size - 1u);
        return true;
    }
 
    void next_last_active_cell() noexcept
    {
        derived_t * self = static_cast<derived_t *>(this);
        self->score_mask <<= 1u;
        if (self->score_mask)
            return;
 
        self->score_mask = 1u;
        last_block++;
    }
 
    bool update_last_active_cell() noexcept
    {
        derived_t * self = static_cast<derived_t *>(this);
        // update the last active cell
        while (!(self->_score <= max_errors))
        {
            self->advance_score(self->vn[last_block], self->vp[last_block], self->score_mask);
            if (!prev_last_active_cell())
            {
                // prev_last_active_cell = false can only happen for global alignments
                assert(edit_traits::is_global);
                // we abort here if we don't need to compute a matrix, because the continued
                // computation can't produce an alignment.
                return !edit_traits::compute_matrix;
            }
        }
 
        if (is_last_active_cell_within_last_row())
        {
            assert(self->_score <= max_errors);
 
            if constexpr(edit_traits::is_semi_global)
                self->update_best_score();
 
            return self->on_hit();
        }
        else
        {
            next_last_active_cell();
            self->advance_score(self->vp[last_block], self->vn[last_block], self->score_mask);
        }
 
        return false;
    }
 
    static size_t max_rows(word_type const score_mask, unsigned const last_block,
                           score_type const score, score_type const max_errors) noexcept
    {
        using score_matrix_type = typename edit_traits::score_matrix_type;
        return score_matrix_type::max_rows(score_mask,
                                           last_block,
                                           score,
                                           max_errors);
    }
};
 
template <typename derived_t, typename edit_traits>
class edit_distance_unbanded_global_policy :
    edit_traits
{
protected:
    static_assert(edit_traits::is_global || edit_traits::is_semi_global,
                  "This policy assumes that edit_traits::is_global or edit_traits::is_semi_global is true.");
 
    friend derived_t;
 
    edit_distance_unbanded_global_policy() noexcept = default;  
    edit_distance_unbanded_global_policy(edit_distance_unbanded_global_policy const &) noexcept
        = default; 
    edit_distance_unbanded_global_policy(edit_distance_unbanded_global_policy &&) noexcept
        = default; 
    edit_distance_unbanded_global_policy & operator=(edit_distance_unbanded_global_policy const &) noexcept
        = default; 
    edit_distance_unbanded_global_policy & operator=(edit_distance_unbanded_global_policy &&) noexcept
        = default; 
    ~edit_distance_unbanded_global_policy() noexcept = default; 
 
 
    using typename edit_traits::score_type;
 
    score_type _best_score{};
 
    void score_init() noexcept
    {
        derived_t const * self = static_cast<derived_t const *>(this);
        _best_score = self->_score;
    }
 
    bool is_valid() const noexcept
    {
        [[maybe_unused]] derived_t const * self = static_cast<derived_t const *>(this);
        // This condition uses the observation that after each computation of a column, _score has either the initial
        // value of the first row (i.e. the entire column consist of INF's), has the value _score = max_errors + 1
        // (there exists a cell within the column that has value <= max_errors, but is not on the last row) or _score <=
        // max_errors (the score of the last active cell is <= max_errors)
        if constexpr(edit_traits::use_max_errors)
            return _best_score <= self->max_errors;
 
        // When not using max_errors there is always a valid alignment, because the last row will always be updated and
        // with it the score.
        return true;
    }
 
    seqan3::detail::advanceable_alignment_coordinate<> invalid_coordinate() const noexcept
    {
        derived_t const * self = static_cast<derived_t const *>(this);
        return {column_index_type{std::ranges::size(self->database)}, row_index_type{std::ranges::size(self->query)}};
    }
 
    void update_best_score() noexcept
    {
        derived_t const * self = static_cast<derived_t const *>(this);
        _best_score = self->_score;
    }
 
    size_t end_positions_first() const noexcept
    {
        derived_t const * self = static_cast<derived_t const *>(this);
        return std::ranges::size(self->database);
    }
 
public:
    std::optional<score_type> score() const noexcept
    {
        derived_t const * self = static_cast<derived_t const *>(this);
        static_assert(edit_traits::compute_score, "score() can only be computed if you specify the result type within "
                                                  "your alignment config.");
        if (!self->is_valid())
            return std::nullopt;
 
        return -_best_score;
    }
 
    seqan3::detail::advanceable_alignment_coordinate<> end_positions() const noexcept
    {
        derived_t const * self = static_cast<derived_t const *>(this);
        static_assert(edit_traits::compute_end_positions, "end_positions() can only be computed if you specify the "
                                                          "result type within your alignment config.");
        if (!self->is_valid())
            return self->invalid_coordinate();
 
        column_index_type const first{self->end_positions_first()};
        row_index_type const second{std::ranges::size(self->query)};
        return {first, second};
    }
};
 
template <typename derived_t, typename edit_traits>
class edit_distance_unbanded_semi_global_policy :
    public edit_distance_unbanded_global_policy<derived_t, edit_traits>
{
protected:
    static_assert(edit_traits::is_semi_global, "This policy assumes that edit_traits::is_semi_global is true.");
 
    friend derived_t;
 
    edit_distance_unbanded_semi_global_policy() noexcept = default;  
    edit_distance_unbanded_semi_global_policy(edit_distance_unbanded_semi_global_policy const &) noexcept
        = default; 
    edit_distance_unbanded_semi_global_policy(edit_distance_unbanded_semi_global_policy &&) noexcept
        = default; 
    edit_distance_unbanded_semi_global_policy & operator=(edit_distance_unbanded_semi_global_policy const &) noexcept
        = default; 
    edit_distance_unbanded_semi_global_policy & operator=(edit_distance_unbanded_semi_global_policy &&) noexcept
        = default; 
    ~edit_distance_unbanded_semi_global_policy() noexcept = default; 
 
 
    using base_t = edit_distance_unbanded_global_policy<derived_t, edit_traits>;
    using database_iterator = typename edit_traits::database_iterator;
    using base_t::_best_score;
 
    database_iterator _best_score_col{};
 
    void score_init() noexcept
    {
        derived_t const * self = static_cast<derived_t const *>(this);
        base_t::score_init();
        _best_score_col = self->database_it_end;
    }
 
    void update_best_score() noexcept
    {
        derived_t const * self = static_cast<derived_t const *>(this);
        // we have to make sure that update_best_score is only called after a score update within the last row.
        if constexpr(edit_traits::use_max_errors)
        {
            assert(std::ranges::empty(self->query) || self->is_last_active_cell_within_last_row());
        }
 
        _best_score_col = (self->_score <= _best_score) ? self->database_it : _best_score_col;
        _best_score     = (self->_score <= _best_score) ? self->_score : _best_score;
    }
 
    size_t end_positions_first() const noexcept
    {
        derived_t const * self = static_cast<derived_t const *>(this);
        // offset == 0u is a special case if database sequence is empty, because in this case the best column is zero.
        size_t offset = std::ranges::empty(self->database) ? 0u : 1u;
        return std::ranges::distance(std::ranges::begin(self->database), _best_score_col) + offset;
    }
};
 
template <typename derived_t, typename edit_traits>
class edit_distance_unbanded_score_matrix_policy :
    edit_traits
{
protected:
    static_assert(edit_traits::compute_score_matrix,
                  "This policy assumes that edit_traits::compute_score_matrix is true.");
 
    friend derived_t;
 
    edit_distance_unbanded_score_matrix_policy() noexcept = default;  
    edit_distance_unbanded_score_matrix_policy(edit_distance_unbanded_score_matrix_policy const &) noexcept
        = default; 
    edit_distance_unbanded_score_matrix_policy(edit_distance_unbanded_score_matrix_policy &&) noexcept
        = default; 
    edit_distance_unbanded_score_matrix_policy & operator=(edit_distance_unbanded_score_matrix_policy const &) noexcept
        = default; 
    edit_distance_unbanded_score_matrix_policy & operator=(edit_distance_unbanded_score_matrix_policy &&) noexcept
        = default; 
    ~edit_distance_unbanded_score_matrix_policy() noexcept = default; 
 
 
    using typename edit_traits::score_matrix_type;
 
    score_matrix_type _score_matrix{};
 
    void score_matrix_init()
    {
        derived_t const * self = static_cast<derived_t const *>(this);
 
        _score_matrix = score_matrix_type{std::ranges::size(self->query) + 1u};
        _score_matrix.reserve(std::ranges::size(self->database) + 1u);
    }
 
public:
    score_matrix_type const & score_matrix() const noexcept
    {
        static_assert(edit_traits::compute_score_matrix, "score_matrix() can only be computed if you specify the "
                                                         "result type within your alignment config.");
        return _score_matrix;
    }
};
 
template <typename derived_t, typename edit_traits>
class edit_distance_unbanded_trace_matrix_policy :
    edit_traits
{
protected:
    static_assert(edit_traits::compute_trace_matrix,
                  "This policy assumes that edit_traits::compute_trace_matrix is true.");
 
    friend derived_t;
 
    edit_distance_unbanded_trace_matrix_policy() noexcept = default;  
    edit_distance_unbanded_trace_matrix_policy(edit_distance_unbanded_trace_matrix_policy const &) noexcept
        = default; 
    edit_distance_unbanded_trace_matrix_policy(edit_distance_unbanded_trace_matrix_policy &&) noexcept
        = default; 
    edit_distance_unbanded_trace_matrix_policy & operator=(edit_distance_unbanded_trace_matrix_policy const &) noexcept
        = default; 
    edit_distance_unbanded_trace_matrix_policy & operator=(edit_distance_unbanded_trace_matrix_policy &&) noexcept
        = default; 
    ~edit_distance_unbanded_trace_matrix_policy() noexcept = default; 
 
 
    using typename edit_traits::word_type;
    using typename edit_traits::trace_matrix_type;
    using typename edit_traits::alignment_result_type;
 
    std::vector<word_type> hp{};
    std::vector<word_type> db{};
 
    trace_matrix_type _trace_matrix{};
 
    void trace_matrix_init(size_t block_count)
    {
        derived_t const * self = static_cast<derived_t const *>(this);
 
        _trace_matrix = trace_matrix_type{std::ranges::size(self->query) + 1u};
        _trace_matrix.reserve(std::ranges::size(self->database) + 1u);
 
        hp.resize(block_count, 0u);
        db.resize(block_count, 0u);
    }
 
public:
    trace_matrix_type const & trace_matrix() const noexcept
    {
        static_assert(edit_traits::compute_trace_matrix, "trace_matrix() can only be computed if you specify the "
                                                         "result type within your alignment config.");
        return _trace_matrix;
    }
 
    seqan3::detail::advanceable_alignment_coordinate<> begin_positions() const noexcept
    {
        derived_t const * self = static_cast<derived_t const *>(this);
        static_assert(edit_traits::compute_begin_positions, "begin_positions() can only be computed if you specify the "
                                                            "result type within your alignment config.");
        if (!self->is_valid())
            return self->invalid_coordinate();
 
        auto [first, second] = self->end_positions();
        detail::matrix_coordinate const end_positions{detail::row_index_type{second}, detail::column_index_type{first}};
        auto trace_path = self->trace_matrix().trace_path(end_positions);
        auto trace_path_it = std::ranges::begin(trace_path);
        std::ranges::advance(trace_path_it, std::ranges::end(trace_path));
        detail::matrix_coordinate const begin_positions = trace_path_it.coordinate();
        return {detail::column_index_type{begin_positions.col}, detail::row_index_type{begin_positions.row}};
    }
 
    auto alignment() const noexcept
    {
        using alignment_t = std::remove_cvref_t<decltype(std::declval<alignment_result_type &>().alignment())>;
 
        derived_t const * self = static_cast<derived_t const *>(this);
        static_assert(edit_traits::compute_sequence_alignment, "alignment() can only be computed if you specify the "
                                                               "result type within your alignment config.");
 
        if (!self->is_valid())
            return alignment_t{};
 
        auto [first, second] = self->end_positions();
        detail::matrix_coordinate const end_positions{detail::row_index_type{second}, detail::column_index_type{first}};
        aligned_sequence_builder builder{self->database, self->query};
        auto trace_path = self->trace_matrix().trace_path(end_positions);
        return builder(trace_path).alignment;
    }
};
 
template <typename value_t>
class proxy_reference
{
public:
    proxy_reference() noexcept = default;                                    
    proxy_reference(proxy_reference const &) noexcept = default;             
    proxy_reference(proxy_reference &&) noexcept = default;                  
    proxy_reference & operator=(proxy_reference const &) noexcept = default; 
    proxy_reference & operator=(proxy_reference &&) noexcept = default;      
    ~proxy_reference() = default;                                            
 
    proxy_reference(value_t & t) noexcept
        : ptr(std::addressof(t))
    {}
 
    proxy_reference(value_t &&) = delete; 
 
    template <typename other_value_t>
        requires std::convertible_to<other_value_t, value_t>
    proxy_reference & operator=(other_value_t && u) noexcept
    {
        get() = std::forward<other_value_t>(u);
        return *this;
    }
 
    value_t & get() const noexcept
    {
        assert(ptr != nullptr);
        return *ptr;
    }
 
    operator value_t & () const noexcept
    {
        return get();
    }
 
private:
    value_t * ptr{nullptr};
};
 
template <std::ranges::viewable_range database_t,
          std::ranges::viewable_range query_t,
          typename align_config_t,
          typename edit_traits>
class edit_distance_unbanded :
// Hide this section in doxygen, because it messes up the inheritance.
    public edit_distance_base<
        edit_traits::use_max_errors,
        edit_distance_unbanded_max_errors_policy,
        edit_traits,
        edit_distance_unbanded<database_t, query_t, align_config_t, edit_traits>>,
    public edit_distance_base<
        edit_traits::is_global,
        edit_distance_unbanded_global_policy,
        edit_traits,
        edit_distance_unbanded<database_t, query_t, align_config_t, edit_traits>>,
    public edit_distance_base<
        edit_traits::is_semi_global,
        edit_distance_unbanded_semi_global_policy,
        edit_traits,
        edit_distance_unbanded<database_t, query_t, align_config_t, edit_traits>>,
    public edit_distance_base<
        edit_traits::compute_score_matrix,
        edit_distance_unbanded_score_matrix_policy,
        edit_traits,
        edit_distance_unbanded<database_t, query_t, align_config_t, edit_traits>>,
    public edit_distance_base<
        edit_traits::compute_trace_matrix,
        edit_distance_unbanded_trace_matrix_policy,
        edit_traits,
        edit_distance_unbanded<database_t, query_t, align_config_t, edit_traits>>
{
public:
    using typename edit_traits::word_type;
    using typename edit_traits::score_type;
    using typename edit_traits::database_type;
    using typename edit_traits::query_type;
    using typename edit_traits::align_config_type;
    using edit_traits::word_size;
 
private:
    template <typename other_derived_t, typename other_edit_traits>
    friend class edit_distance_unbanded_max_errors_policy;
    template <typename other_derived_t, typename other_edit_traits>
    friend class edit_distance_unbanded_global_policy;
    template <typename other_derived_t, typename other_edit_traits>
    friend class edit_distance_unbanded_semi_global_policy;
    template <typename other_derived_t, typename other_edit_traits>
    friend class edit_distance_unbanded_score_matrix_policy;
    template <typename other_derived_t, typename other_edit_traits>
    friend class edit_distance_unbanded_trace_matrix_policy;
 
    using typename edit_traits::database_iterator;
    using typename edit_traits::query_alphabet_type;
    using typename edit_traits::alignment_result_type;
    using edit_traits::use_max_errors;
    using edit_traits::is_semi_global;
    using edit_traits::is_global;
    using edit_traits::compute_score;
    using edit_traits::compute_end_positions;
    using edit_traits::compute_begin_positions;
    using edit_traits::compute_sequence_alignment;
    using edit_traits::compute_score_matrix;
    using edit_traits::compute_trace_matrix;
    using edit_traits::compute_matrix;
    using typename edit_traits::score_matrix_type;
    using typename edit_traits::trace_matrix_type;
 
    database_t database;
    query_t query;
    align_config_t config;
 
    static constexpr word_type hp0 = is_global ? 1u : 0u;
    static constexpr word_type hn0 = 0u;
    static constexpr word_type vp0 = ~word_type{0u};
    static constexpr word_type vn0 = 0u;
 
    score_type _score{};
    word_type score_mask{0u};
    std::vector<word_type> vp{};
    std::vector<word_type> vn{};
    std::vector<word_type> bit_masks{};
 
    database_iterator database_it{};
    database_iterator database_it_end{};
 
    struct compute_state_trace_matrix
    {
        proxy_reference<word_type> db{};
    };
 
    struct compute_state : enable_state_t<edit_traits::compute_trace_matrix, compute_state_trace_matrix>
    {
        using hp_type = std::conditional_t<edit_traits::compute_trace_matrix, proxy_reference<word_type>, word_type>;
 
        word_type b{};
        word_type d0{};
        hp_type hp{};
        word_type hn{};
        proxy_reference<word_type> vp{};
        proxy_reference<word_type> vn{};
        word_type carry_d0{};
        word_type carry_hp{hp0};
        word_type carry_hn{};
    };
 
    void add_state()
    {
        if constexpr(!use_max_errors && compute_score_matrix)
            this->_score_matrix.add_column(vp, vn);
 
        if constexpr(!use_max_errors && compute_trace_matrix)
            this->_trace_matrix.add_column(this->hp, this->db, vp);
 
        if constexpr(use_max_errors && compute_matrix)
        {
            size_t max_rows = this->max_rows(score_mask, this->last_block, _score, this->max_errors);
            if constexpr(compute_score_matrix)
                this->_score_matrix.add_column(vp, vn, max_rows);
 
            if constexpr(compute_trace_matrix)
                this->_trace_matrix.add_column(this->hp, this->db, vp, max_rows);
        }
    }
 
public:
     edit_distance_unbanded() = delete;                                            
     edit_distance_unbanded(edit_distance_unbanded const &) = default;             
     edit_distance_unbanded(edit_distance_unbanded &&) = default;                  
     edit_distance_unbanded & operator=(edit_distance_unbanded const &) = default; 
     edit_distance_unbanded & operator=(edit_distance_unbanded &&) = default;      
     ~edit_distance_unbanded() = default;                                          
 
    edit_distance_unbanded(database_t _database,
                           query_t _query,
                           align_config_t _config,
                           edit_traits const & SEQAN3_DOXYGEN_ONLY(_traits)) :
        database{std::forward<database_t>(_database)},
        query{std::forward<query_t>(_query)},
        config{std::forward<align_config_t>(_config)},
        _score{static_cast<score_type>(std::ranges::size(query))},
        database_it{ranges::begin(database)},
        database_it_end{ranges::end(database)}
    {
        static constexpr size_t alphabet_size_ = alphabet_size<query_alphabet_type>;
 
        size_t const block_count = (std::ranges::size(query) - 1u + word_size) / word_size;
        score_mask = word_type{1u} << ((std::ranges::size(query) - 1u + word_size) % word_size);
 
        this->score_init();
        if constexpr(use_max_errors)
            this->max_errors_init(block_count);
 
        if constexpr(compute_score_matrix)
            this->score_matrix_init();
 
        if constexpr(compute_trace_matrix)
            this->trace_matrix_init(block_count);
 
        vp.resize(block_count, vp0);
        vn.resize(block_count, vn0);
        bit_masks.resize((alphabet_size_ + 1u) * block_count, 0u);
 
        // encoding the letters as bit-vectors
        for (size_t j = 0u; j < std::ranges::size(query); j++)
        {
            size_t const i = block_count * seqan3::to_rank(query[j]) + j / word_size;
            bit_masks[i] |= word_type{1u} << (j % word_size);
        }
 
        add_state();
    }
 
private:
    template <bool with_carry>
    static void compute_step(compute_state & state) noexcept
    {
        word_type x, t;
        assert(state.carry_d0 <= 1u);
        assert(state.carry_hp <= 1u);
        assert(state.carry_hn <= 1u);
 
        x = state.b | state.vn;
        t = state.vp + (x & state.vp) + state.carry_d0;
 
        state.d0 = (t ^ state.vp) | x;
        state.hn = state.vp & state.d0;
        state.hp = state.vn | ~(state.vp | state.d0);
 
        if constexpr(with_carry)
            state.carry_d0 = (state.carry_d0 != 0u) ? t <= state.vp : t < state.vp;
 
        x = (state.hp << 1u) | state.carry_hp;
        state.vn = x & state.d0;
        state.vp = (state.hn << 1u) | ~(x | state.d0) | state.carry_hn;
 
        if constexpr(with_carry)
        {
            state.carry_hp = state.hp >> (word_size - 1u);
            state.carry_hn = state.hn >> (word_size - 1u);
        }
    }
 
    template <bool with_carry>
    void compute_kernel(compute_state & state, size_t const block_offset, size_t const current_block) noexcept
    {
        state.vp = proxy_reference<word_type>{this->vp[current_block]};
        state.vn = proxy_reference<word_type>{this->vn[current_block]};
        if constexpr(compute_trace_matrix)
        {
            state.hp = proxy_reference<word_type>{this->hp[current_block]};
            state.db = proxy_reference<word_type>{this->db[current_block]};
        }
        state.b = bit_masks[block_offset + current_block];
 
        compute_step<with_carry>(state);
        if constexpr(compute_trace_matrix)
            state.db = ~(state.b ^ state.d0);
    }
 
    void advance_score(word_type P, word_type N, word_type mask) noexcept
    {
        if ((P & mask) != word_type{0u})
            _score++;
        else if ((N & mask) != word_type{0u})
            _score--;
    }
 
    bool on_hit() noexcept
    {
        // TODO: call external on_hit functor
        return false;
    }
 
    inline bool small_patterns();
 
    inline bool large_patterns();
 
    inline void compute_empty_query_sequence()
    {
        assert(std::ranges::empty(query));
 
        bool abort_computation = false;
 
        for (; database_it != database_it_end; ++database_it)
        {
            if constexpr(is_global)
                ++_score;
            else // is_semi_global
                this->update_best_score();
 
            // call on_hit
            if constexpr(use_max_errors)
                abort_computation = on_hit();
 
            this->add_state();
            if (abort_computation)
                break;
        }
    }
 
    void compute()
    {
        // limit search width for prefix search (if no matrix needs to be computed)
        if constexpr(use_max_errors && is_global && !compute_matrix)
        {
            // Note: For global alignments we know that the database can only be max_length long to have a score less
            // than or equal max_errors in the last cell.
            //
            // The following matrix shows a minimal value for each entry (because a diagonal must be +0 or +1, each
            // diagonal is at least the value of the initial value in the first row)
            // 0 1 2 3 4 5 6...
            // 1 0 1 2 3 4 5...
            // ...
            // m ... 3 2 1 0 1 2 3 4 5
            // Thus, after |query| + max_errors entries the score will always be higher than max_errors.
            size_t const max_length = std::ranges::size(query) + this->max_errors + 1u;
            size_t const haystack_length = std::min(std::ranges::size(database), max_length);
            database_it_end -= std::ranges::size(database) - haystack_length;
        }
 
        // distinguish between the version for needles not longer than
        // one machine word and the version for longer needles
        // A special cases is if the second sequence is empty (vp.size() == 0u).
        if (vp.size() == 0u) // [[unlikely]]
            compute_empty_query_sequence();
        else if (vp.size() == 1u)
            small_patterns();
        else
            large_patterns();
 
        if constexpr(is_global)
            this->update_best_score();
    }
 
public:
    template <typename callback_t>
    void operator()([[maybe_unused]] size_t const idx, callback_t && callback)
    {
        using traits_type = alignment_configuration_traits<align_config_t>;
        using result_value_type = typename alignment_result_value_type_accessor<alignment_result_type>::type;
 
        compute();
 
        // First cache the begin and end positions if enabled by the edit distance traits.
        // Note, that they might be activated even if the user did not configure them, but in order to
        // compute for example the alignment both information are required and enabled internally.
        auto cached_end_positions = this->invalid_coordinate();
        auto cached_begin_positions = this->invalid_coordinate();
 
        if constexpr (compute_end_positions)
            cached_end_positions = this->end_positions();
 
        if constexpr (compute_begin_positions && !compute_sequence_alignment)
        {
            static_assert(compute_end_positions, "End positions required to compute the begin positions.");
            cached_begin_positions = this->begin_positions();
        }
 
        // Fill the result value type. Note we need to ask what was enabled on the user side in order to store
        // the correct information in the alignment result type. This information is stored in the alignment
        // configuration traits and not in the edit distance traits.
        result_value_type res_vt{};
 
        if constexpr (traits_type::output_sequence1_id)
            res_vt.sequence1_id = idx;
 
        if constexpr (traits_type::output_sequence2_id)
            res_vt.sequence2_id = idx;
 
        if constexpr (traits_type::compute_score)
            res_vt.score = this->score().value_or(matrix_inf<score_type>);
 
        if constexpr (traits_type::compute_sequence_alignment)
        {
            if (this->is_valid())
            {
                auto [first, second] = cached_end_positions;
                detail::matrix_coordinate const end_positions{detail::row_index_type{second},
                                                              detail::column_index_type{first}};
 
                aligned_sequence_builder builder{this->database, this->query};
                auto trace_res = builder(this->trace_matrix().trace_path(end_positions));
                res_vt.alignment = std::move(trace_res.alignment);
                cached_begin_positions.first = trace_res.first_sequence_slice_positions.first;
                cached_begin_positions.second = trace_res.second_sequence_slice_positions.first;
            }
        }
 
        if constexpr (traits_type::compute_end_positions)
            res_vt.end_positions = std::move(cached_end_positions);
 
        if constexpr (traits_type::compute_begin_positions)
            res_vt.begin_positions = std::move(cached_begin_positions);
 
        callback(alignment_result_type{std::move(res_vt)});
    }
};
 
template <std::ranges::viewable_range database_t,
          std::ranges::viewable_range query_t,
          typename align_config_t,
          typename traits_t>
bool edit_distance_unbanded<database_t, query_t, align_config_t, traits_t>::small_patterns()
{
    bool abort_computation = false;
 
    // computing the blocks
    while (database_it != database_it_end)
    {
        compute_state state{};
        size_t const block_offset = seqan3::to_rank((query_alphabet_type) *database_it);
 
        compute_kernel<false>(state, block_offset, 0u);
        advance_score(state.hp, state.hn, score_mask);
 
        // semi-global without max_errors guarantees that the score stays within the last row
        if constexpr(is_semi_global && !use_max_errors)
            this->update_best_score();
 
        // updating the last active cell
        if constexpr(use_max_errors)
            abort_computation = this->update_last_active_cell();
 
        add_state();
        ++database_it;
        if (abort_computation)
            return true;
    }
 
    return false;
}
 
template <std::ranges::viewable_range database_t,
          std::ranges::viewable_range query_t,
          typename align_config_t,
          typename traits_t>
bool edit_distance_unbanded<database_t, query_t, align_config_t, traits_t>::large_patterns()
{
    bool abort_computation = false;
 
    while (database_it != database_it_end)
    {
        compute_state state{};
        size_t const block_offset = vp.size() * seqan3::to_rank((query_alphabet_type) *database_it);
 
        size_t block_count = vp.size();
        if constexpr(use_max_errors)
            block_count = this->last_block + 1;
 
        // compute each block in the current column; carries between blocks will be propagated.
        for (size_t current_block = 0u; current_block < block_count; current_block++)
            compute_kernel<true>(state, block_offset, current_block);
 
        advance_score(state.hp, state.hn, score_mask);
 
        // semi-global without max_errors guarantees that the score stays within the last row
        if constexpr(is_semi_global && !use_max_errors)
            this->update_best_score();
 
        if constexpr(use_max_errors)
        {
            // if the last active cell reached the end within the current block we have to compute the next block.
            bool additional_block = score_mask >> (word_size - 1u);
            bool reached_last_block = this->last_block + 1u == vp.size();
            // If there is no next block we skip the computation.
            if (reached_last_block)
                additional_block = false;
 
            if (additional_block)
            {
                size_t const current_block = this->last_block + 1u;
                // this might not be necessary, but carry_d0 = 1u might have an influence on the result of vn and vp.
                vp[current_block] = vp0;
                vn[current_block] = vn0;
                compute_kernel<false>(state, block_offset, current_block);
            }
 
            // updating the last active cell
            abort_computation = this->update_last_active_cell();
        }
 
        add_state();
        ++database_it;
 
        if (abort_computation)
            return true;
    }
 
    return false;
}
 
template <typename database_t, typename query_t, typename config_t, typename traits_t>
edit_distance_unbanded(database_t && database, query_t && query, config_t config, traits_t)
    -> edit_distance_unbanded<database_t, query_t, config_t, traits_t>;
 
} // namespace seqan3::detail