libdpf/include/dpf/dcf.hpp

/// @file dpf/dcf.hpp
/// @brief Comparison-channel specs and GGM path-sum helpers for libdpf.
/// @details `lt`/`leq`/`gt`/`geq` (+ `_at`) take `(if_true, if_false=0)`.
///          Eval walks the same GGM tree as the DPF (per-level value CWs).
///          `eq` / `eq_at` are synonyms for ordinary point placements.
/// @note Following Boyle, Chandran, Gilboa, Gupta, Ishai, Kumar, and Rathee, EUROCRYPT 2021 (ePrint 2020/1392): a comparison is a DPF spine plus one value-correction word per level. `eq` is a point payload, not that DCF.
/// @copyright Copyright (c) 2019-2026 Ryan Henry and [others](@ref authors)
/// @license Released under a GNU General Public v2.0 (GPLv2) license.

#ifndef LIBDPF_INCLUDE_DPF_DCF_HPP__
#define LIBDPF_INCLUDE_DPF_DCF_HPP__

#include <cstddef>
#include <cstdint>
#include <type_traits>
#include <utility>
#include <limits>

#include "hedley/hedley.h"
#include "simde/simde/x86/avx2.h"

#include "dpf/utils.hpp"
#include "dpf/bit.hpp"
#include "dpf/xor_wrapper.hpp"
#include "dpf/twiddle.hpp"
#include "dpf/cmp_group.hpp"

namespace dpf
{

template <typename Beta>
struct ic_pack;

template <typename T>
struct is_ic_pack : std::false_type {};

template <typename Beta>
struct is_ic_pack<ic_pack<Beta>> : std::true_type {};

template <typename ...Ts>
inline constexpr bool no_ic_pack_v =
    (!is_ic_pack<std::decay_t<Ts>>::value && ...);

/// @brief Comparison kind for the optional DCF channel on a key.
/// @details `lt`/`leq`/`gt`/`geq` are the comparison predicates. The later kinds are
/// path paints: one constant on each sibling subtree of the secret point,
/// evaluated by the same value-correction walk.
enum class cmp_kind : uint8_t
{
    lt = 0,
    leq = 1,
    gt = 2,
    geq = 3,
    lcp = 4,                  // common-prefix length
    prefix = 5,               // matched prefix, in the lane's high bits
    mask = 6,                 // high-bit mask of that length
    one_hot = 7,              // 2^{length} (0 when the bit does not fit)
    break_bit = 8,            // secret bit at the first difference
    prefix_with_length = 9,   // (low-aligned prefix << length_bits) | length
    paint = 10                // caller-supplied unit plant
};

/// @brief True for the path-paint kinds. Comparisons stay `lt`/`leq`/`gt`/`geq`.
/// @param kind the comparison or paint kind
/// @return True for the path-paint kinds
HEDLEY_NO_THROW
inline constexpr bool is_paint_kind(cmp_kind kind) noexcept
{
    switch (kind)
    {
    case cmp_kind::lcp:
    case cmp_kind::prefix:
    case cmp_kind::mask:
    case cmp_kind::one_hot:
    case cmp_kind::break_bit:
    case cmp_kind::prefix_with_length:
    case cmp_kind::paint:
        return true;
    default:
        return false;
    }
}

/// @brief Unit plant for `path_paint`. `prefix` is the in-lane matched prefix.
using paint_callback = uint64_t (*)(std::size_t matched, uint64_t prefix,
    bool leaf, const void * ctx);

enum class cmp_trivial : uint8_t
{
    none = 0,
    always_true = 1,
    always_false = 2
};

namespace detail
{
namespace dcf_impl
{

template <typename Beta>
HEDLEY_NO_THROW
Beta default_false() noexcept
{
    if constexpr (std::is_same_v<Beta, dpf::bit>)
        return dpf::bit::zero;
    else
        return Beta{};
}

template <typename Beta>
HEDLEY_NO_THROW
uint64_t beta_delta_u64(const Beta & if_true, const Beta & if_false,
    uint64_t mask) noexcept
{
    if constexpr (std::is_same_v<Beta, dpf::bit>)
    {
        const uint64_t t = static_cast<bool>(if_true) ? 1ULL : 0ULL;
        const uint64_t f = static_cast<bool>(if_false) ? 1ULL : 0ULL;
        return (t ^ f) & mask;
    }
    else if constexpr (dpf::utils::is_xor_wrapper_v<Beta>)
    {
        return (static_cast<uint64_t>(if_true) ^ static_cast<uint64_t>(if_false))
            & mask;
    }
    else if constexpr (detail::has_integral_representation<Beta>::value)
    {
        using raw_type = typename Beta::integral_type;
        using unsigned_type = utils::make_unsigned_t<raw_type>;
        const auto t = static_cast<uint64_t>(
            static_cast<unsigned_type>(if_true.integral_representation()));
        const auto f = static_cast<uint64_t>(
            static_cast<unsigned_type>(if_false.integral_representation()));
        return (t - f) & mask;
    }
    else
    {
        return (static_cast<uint64_t>(if_true)
            - static_cast<uint64_t>(if_false)) & mask;
    }
}

template <typename Beta>
HEDLEY_NO_THROW
uint64_t beta_to_u64_simple(const Beta & beta, uint64_t mask) noexcept
{
    if constexpr (std::is_same_v<Beta, dpf::bit>)
        return (static_cast<bool>(beta) ? 1ULL : 0ULL) & mask;
    else if constexpr (detail::has_integral_representation<Beta>::value)
    {
        using raw_type = typename Beta::integral_type;
        using unsigned_type = utils::make_unsigned_t<raw_type>;
        return static_cast<uint64_t>(static_cast<unsigned_type>(
            beta.integral_representation())) & mask;
    }
    else
        return static_cast<uint64_t>(beta) & mask;
}

template <typename Beta>
HEDLEY_NO_THROW
Beta sub_beta(const Beta & a, const Beta & b) noexcept
{
    if constexpr (std::is_same_v<Beta, dpf::bit>)
        return dpf::bit{static_cast<bool>(a) ^ static_cast<bool>(b)};
    else if constexpr (dpf::utils::is_xor_wrapper_v<Beta>)
        return a ^ b;
    else
        return static_cast<Beta>(a - b);
}

template <typename Beta>
HEDLEY_NO_THROW
Beta u64_to_beta(uint64_t v) noexcept
{
    if constexpr (std::is_same_v<Beta, dpf::bit>)
        return dpf::bit{static_cast<bool>(v & 1u)};
    else if constexpr (detail::has_integral_representation<Beta>::value)
        return Beta::from_raw(static_cast<typename Beta::integral_type>(v));
    else
        return static_cast<Beta>(v);
}

HEDLEY_CONST
HEDLEY_NO_THROW
HEDLEY_ALWAYS_INLINE
constexpr uint64_t default_mask_for_bits(std::size_t out_bits) noexcept
{
    if (out_bits >= 64)
        return ~0ULL;
    if (out_bits == 0)
        return 0ULL;
    return (1ULL << out_bits) - 1ULL;
}

HEDLEY_CONST
HEDLEY_NO_THROW
HEDLEY_ALWAYS_INLINE
constexpr uint64_t neg_m(uint64_t x, uint64_t mask) noexcept
{
    return (0ULL - x) & mask;
}

HEDLEY_CONST
HEDLEY_NO_THROW
HEDLEY_ALWAYS_INLINE
constexpr uint64_t sgn_m(uint8_t t1, uint64_t x, uint64_t mask) noexcept
{
    return t1 ? neg_m(x, mask) : x;
}

/// @brief Convert a GGM node to a group element (low 64 bits, control bits cleared).
/// @param n the `n`
/// @param mask the bit mask
/// @return the returned `uint64_t`
HEDLEY_ALWAYS_INLINE
uint64_t convert_node(simde__m128i n, uint64_t mask) noexcept
{
    return static_cast<uint64_t>(
        simde_mm_cvtsi128_si64(dpf::unset_lo_2bits(n))) & mask;
}

/// @brief Draw the group-width blind `r` used to split the `cmp_addend` share.
/// @details `sample` yields one interior block; only `popcount(mask)` live bits are
/// kept, so the blind (and thus the addend share) never needs a full padded
/// `uint64_t` on the wire. Dealer and Doerner–Shelat gen call this with the
/// same block source so their keys stay byte-identical (matched tapes).
/// @tparam BlockSampler block sampler
/// @param mask the bit mask
/// @param sample the `sample`
/// @return the returned `uint64_t`
template <typename BlockSampler>
HEDLEY_ALWAYS_INLINE
HEDLEY_NO_THROW
uint64_t sample_addend_blind(uint64_t mask, BlockSampler && sample) noexcept
{
    return convert_node(dpf::unset_lo_2bits(sample()), mask);
}

/// @brief One level of value CW on GGM children. Updates running `Va`.
/// @details `ai` is the keep-path bit of the (effective) threshold.
/// @param c0L the `c0L`
/// @param c0R the `c0R`
/// @param c1L the `c1L`
/// @param c1R the `c1R`
/// @param t0 the `t0`
/// @param t1 the `t1`
/// @param ai the `ai`
/// @param Va the `Va`
/// @param beta the payload
/// @param mask the bit mask
/// @return One level of value CW on GGM children
HEDLEY_NO_THROW
inline uint64_t make_value_cw(simde__m128i c0L, simde__m128i c0R,
    simde__m128i c1L, simde__m128i c1R, uint8_t t0, uint8_t t1, int ai,
    uint64_t & Va, uint64_t beta, uint64_t mask) noexcept
{
    (void)t0;
    uint64_t v0K, v1K, v0Lo, v1Lo;
    if (ai == 0)
    {
        v0K = convert_node(c0L, mask);
        v1K = convert_node(c1L, mask);
        v0Lo = convert_node(c0R, mask);
        v1Lo = convert_node(c1R, mask);
    }
    else
    {
        v0K = convert_node(c0R, mask);
        v1K = convert_node(c1R, mask);
        v0Lo = convert_node(c0L, mask);
        v1Lo = convert_node(c1L, mask);
    }
    uint64_t vcw = sgn_m(t1,
        (v1Lo + neg_m(v0Lo, mask) + neg_m(Va, mask)) & mask, mask);
    // Lose-left (ai==1) is the x<α diverge: plant β there.
    if (ai == 1)
        vcw = (vcw + sgn_m(t1, beta, mask)) & mask;
    Va = (Va + neg_m(v1K, mask) + v0K + sgn_m(t1, vcw, mask)) & mask;
    return vcw;
}

/// @brief Same recurrence as `make_value_cw`, planting `plant` on the lose child
/// in both directions. `plant == 0` leaves the correction unchanged.
/// @param c0L the `c0L`
/// @param c0R the `c0R`
/// @param c1L the `c1L`
/// @param c1R the `c1R`
/// @param t0 the `t0`
/// @param t1 the `t1`
/// @param ai the `ai`
/// @param Va the `Va`
/// @param plant the unit plant
/// @param mask the bit mask
/// @return Same recurrence as `make_value_cw`, planting `plant` on the lose child in both
/// directions
HEDLEY_NO_THROW
inline uint64_t make_value_cw_planted(simde__m128i c0L, simde__m128i c0R,
    simde__m128i c1L, simde__m128i c1R, uint8_t t0, uint8_t t1, int ai,
    uint64_t & Va, uint64_t plant, uint64_t mask) noexcept
{
    (void)t0;
    uint64_t v0K, v1K, v0Lo, v1Lo;
    if (ai == 0)
    {
        v0K = convert_node(c0L, mask);
        v1K = convert_node(c1L, mask);
        v0Lo = convert_node(c0R, mask);
        v1Lo = convert_node(c1R, mask);
    }
    else
    {
        v0K = convert_node(c0R, mask);
        v1K = convert_node(c1R, mask);
        v0Lo = convert_node(c0L, mask);
        v1Lo = convert_node(c1L, mask);
    }
    uint64_t vcw = sgn_m(t1,
        (v1Lo + neg_m(v0Lo, mask) + neg_m(Va, mask)) & mask, mask);
    vcw = (vcw + sgn_m(t1, plant, mask)) & mask;
    Va = (Va + neg_m(v1K, mask) + v0K + sgn_m(t1, vcw, mask)) & mask;
    return vcw;
}

HEDLEY_NO_THROW
inline unsigned __int128 paint_lane_mask(std::size_t nbits) noexcept
{
    using u128 = unsigned __int128;
    if (nbits == 0)
        return 0;
    if (nbits >= 128)
        return ~u128{0};
    return (u128{1} << nbits) - 1;
}

/// @brief High `d` bits of an `nbits`-wide lane, in that lane's own positions.
/// @param alpha the secret input point
/// @param nbits the width in bits
/// @param d the `d`
/// @return High `d` bits of an `nbits`-wide lane, in that lane's own positions
HEDLEY_NO_THROW
inline unsigned __int128 paint_high_bits(unsigned __int128 alpha,
    std::size_t nbits, std::size_t d) noexcept
{
    alpha &= paint_lane_mask(nbits);
    if (d == 0 || nbits == 0)
        return 0;
    if (d >= nbits)
        return alpha;
    const std::size_t drop = nbits - d;
    return (alpha >> drop) << drop;
}

HEDLEY_NO_THROW
inline unsigned __int128 paint_low_aligned(unsigned __int128 alpha,
    std::size_t nbits, std::size_t d) noexcept
{
    alpha &= paint_lane_mask(nbits);
    if (d == 0 || nbits == 0)
        return 0;
    if (d >= nbits)
        return alpha;
    return alpha >> (nbits - d);
}

/// @brief Unit (β = 1) lose-subtree or leaf plant. The caller scales by δ.
/// @details `matched` is the number of leading bits already shared with α. A lose
/// subtree at that depth reconstructs to this value; `leaf` is the full match.
/// @param kind the comparison or paint kind
/// @param matched the number of leading bits shared with the secret point
/// @param alpha the secret input point
/// @param nbits the width in bits
/// @param length_bits the bits used to store the prefix length
/// @param leaf the leaf value
/// @param fn the `fn`
/// @param ctx the `ctx`
/// @return Unit (β = 1) lose-subtree or leaf plant
inline uint64_t paint_unit(cmp_kind kind, std::size_t matched,
    unsigned __int128 alpha, std::size_t nbits, std::size_t length_bits,
    bool leaf, paint_callback fn, const void * ctx)
{
    if (nbits == 0)
        return 0;
    const std::size_t d = leaf ? nbits : matched;
    switch (kind)
    {
    case cmp_kind::lcp:
        return static_cast<uint64_t>(d);
    case cmp_kind::prefix:
        return static_cast<uint64_t>(paint_high_bits(alpha, nbits, d));
    case cmp_kind::mask:
        return static_cast<uint64_t>(
            paint_high_bits(paint_lane_mask(nbits), nbits, d));
    case cmp_kind::one_hot:
        return d >= 64 ? 0ULL : (1ULL << d);
    case cmp_kind::break_bit:
        if (leaf || matched >= nbits)
            return 0;
        return static_cast<uint64_t>(
            (alpha >> (nbits - 1 - matched)) & 1);
    case cmp_kind::prefix_with_length:
    {
        if (length_bits >= 128)
            return static_cast<uint64_t>(d);
        unsigned __int128 packed =
            paint_low_aligned(alpha, nbits, d) << length_bits;
        packed |= static_cast<unsigned __int128>(d);
        return static_cast<uint64_t>(packed);
    }
    case cmp_kind::paint:
        if (fn == nullptr)
            return 0;
        return fn(d, static_cast<uint64_t>(paint_high_bits(alpha, nbits, d)),
            leaf, ctx);
    default:
        return 0;
    }
}

HEDLEY_NO_THROW
inline uint64_t scale_plant(uint64_t unit, uint64_t scale, uint64_t mask) noexcept
{
    return (unit * scale) & mask;
}

/// @brief Final leaf value CW. `on_path` is the payload reconstructed when the query
/// stays on α's path through all levels (0 for strict lt/geq; β for leq/gt).
/// @param s0 the `s0`
/// @param s1 the `s1`
/// @param t1 the `t1`
/// @param Va the `Va`
/// @param mask the bit mask
/// @param on_path the value reconstructed on the secret path
/// @return Final leaf value CW
HEDLEY_NO_THROW
inline uint64_t make_final_cw(simde__m128i s0, simde__m128i s1, uint8_t t1,
    uint64_t Va, uint64_t mask, uint64_t on_path = 0) noexcept
{
    uint64_t c0 = convert_node(s0, mask);
    uint64_t c1 = convert_node(s1, mask);
    return sgn_m(t1,
        (c1 + neg_m(c0, mask) + neg_m(Va, mask) + on_path) & mask, mask);
}

}  // namespace dcf_impl

/// @brief Comparison metadata on an incremental key (value CWs live on the key).
/// @details Payload δ = if_true − if_false is dealer-known and baked into `value_cw` /
/// `cw_last` only — never stored clear on the key (traditional DPF hiding).
/// The second output value (`if_false`) is held as a per-party additive share
/// on the key (`cmp_addend`), not as a public constant.
struct cmp_meta
{
    int nbits = 0;                 // comparison prefix length
    uint64_t mask = 0;
    cmp_kind kind = cmp_kind::lt;
    cmp_trivial trivial = cmp_trivial::none;
    bool eval_as_ge = false;       // invert path-sum (geq / gt)
    bool include_eq = false;       // plant δ on the α-path leaf (leq / gt)
    bool active = false;
    bool incremental = false;      // final correction saved at every depth
    int block_width = 0;           // 0 = per-level path-sum
    int tail_bits = 0;             // residual q; 0 when the tree covers every bit

    HEDLEY_NO_THROW
    bool empty() const noexcept { return !active; }
};

/// @brief Backward-compatible alias while call sites migrate.
using cmp_channel = cmp_meta;

}  // namespace detail

// ---------------------------------------------------------------------------
// Comparison specs: lt/leq/gt/geq (+ _at)
// ---------------------------------------------------------------------------

template <cmp_kind Kind, typename Beta>
struct cmp_pack
{
    static constexpr bool is_cmp = true;
    static constexpr cmp_kind kind = Kind;
    static constexpr std::size_t prefix = 0;
    static constexpr std::size_t block_width = 0;
    using beta_type = Beta;
    Beta if_true;
    Beta if_false;

    explicit cmp_pack(Beta t, Beta f = detail::dcf_impl::default_false<Beta>())
      : if_true{std::move(t)}, if_false{std::move(f)} { }
};

template <std::size_t N, cmp_kind Kind, typename Beta>
struct cmp_at_pack
{
    static constexpr bool is_cmp = true;
    static constexpr cmp_kind kind = Kind;
    static constexpr std::size_t prefix = N;
    static constexpr std::size_t block_width = 0;
    using beta_type = Beta;
    Beta if_true;
    Beta if_false;

    explicit cmp_at_pack(Beta t, Beta f = detail::dcf_impl::default_false<Beta>())
      : if_true{std::move(t)}, if_false{std::move(f)} { }
};

/// \complexity O(1). Builds a spec object. The n-level walk is `make_dpf` or `ds_advance_level`, not this function.
template <typename Beta>
inline auto lt(Beta t, Beta f = detail::dcf_impl::default_false<std::decay_t<Beta>>())
{
    return cmp_pack<cmp_kind::lt, std::decay_t<Beta>>(std::move(t), std::move(f));
}
/// \complexity O(1). Builds a spec object. The n-level walk is `make_dpf` or `ds_advance_level`, not this function.
template <typename Beta>
inline auto leq(Beta t, Beta f = detail::dcf_impl::default_false<std::decay_t<Beta>>())
{
    return cmp_pack<cmp_kind::leq, std::decay_t<Beta>>(std::move(t), std::move(f));
}
/// \complexity O(1). Builds a spec object. The n-level walk is `make_dpf` or `ds_advance_level`, not this function.
template <typename Beta>
inline auto gt(Beta t, Beta f = detail::dcf_impl::default_false<std::decay_t<Beta>>())
{
    return cmp_pack<cmp_kind::gt, std::decay_t<Beta>>(std::move(t), std::move(f));
}
/// \complexity O(1). Builds a spec object. The n-level walk is `make_dpf` or `ds_advance_level`, not this function.
template <typename Beta>
inline auto geq(Beta t, Beta f = detail::dcf_impl::default_false<std::decay_t<Beta>>())
{
    return cmp_pack<cmp_kind::geq, std::decay_t<Beta>>(std::move(t), std::move(f));
}

/// \complexity O(1). Builds a spec object. The n-level walk is `make_dpf` or `ds_advance_level`, not this function.
template <std::size_t N, typename Beta>
inline auto lt_at(Beta t, Beta f = detail::dcf_impl::default_false<std::decay_t<Beta>>())
{
    return cmp_at_pack<N, cmp_kind::lt, std::decay_t<Beta>>(std::move(t), std::move(f));
}
/// \complexity O(1). Builds a spec object. The n-level walk is `make_dpf` or `ds_advance_level`, not this function.
template <std::size_t N, typename Beta>
inline auto leq_at(Beta t, Beta f = detail::dcf_impl::default_false<std::decay_t<Beta>>())
{
    return cmp_at_pack<N, cmp_kind::leq, std::decay_t<Beta>>(std::move(t), std::move(f));
}
/// \complexity O(1). Builds a spec object. The n-level walk is `make_dpf` or `ds_advance_level`, not this function.
template <std::size_t N, typename Beta>
inline auto gt_at(Beta t, Beta f = detail::dcf_impl::default_false<std::decay_t<Beta>>())
{
    return cmp_at_pack<N, cmp_kind::gt, std::decay_t<Beta>>(std::move(t), std::move(f));
}
/// \complexity O(1). Builds a spec object. The n-level walk is `make_dpf` or `ds_advance_level`, not this function.
template <std::size_t N, typename Beta>
inline auto geq_at(Beta t, Beta f = detail::dcf_impl::default_false<std::decay_t<Beta>>())
{
    return cmp_at_pack<N, cmp_kind::geq, std::decay_t<Beta>>(std::move(t), std::move(f));
}

// ---------------------------------------------------------------------------
// Path paints. Same channel and same (if_true, if_false) scale as a comparison:
// the reconstructed value is if_false + (if_true − if_false) · unit(x).
// `unit` is the common-prefix length, the matched prefix, a mask, and so on.
// ---------------------------------------------------------------------------

template <typename T, typename = void>
struct spec_is_incremental : std::false_type {};
template <typename T>
struct spec_is_incremental<T, std::void_t<decltype(T::incremental)>>
    : std::bool_constant<T::incremental> {};

template <typename T, typename = void>
struct spec_length_bits : std::integral_constant<std::size_t, 0> {};
template <typename T>
struct spec_length_bits<T, std::void_t<decltype(T::length_bits)>>
    : std::integral_constant<std::size_t, T::length_bits> {};

template <cmp_kind Kind, typename Beta, std::size_t LengthBits = 0>
struct paint_pack
{
    static constexpr bool is_cmp = true;
    static constexpr cmp_kind kind = Kind;
    static constexpr std::size_t prefix = 0;
    static constexpr std::size_t block_width = 0;
    static constexpr std::size_t length_bits = LengthBits;
    static constexpr bool incremental = false;
    using beta_type = Beta;
    Beta if_true;
    Beta if_false;

    explicit paint_pack(Beta t, Beta f = detail::dcf_impl::default_false<Beta>())
      : if_true{std::move(t)}, if_false{std::move(f)} { }
};

template <std::size_t N, cmp_kind Kind, typename Beta, std::size_t LengthBits = 0>
struct paint_at_pack
{
    static constexpr bool is_cmp = true;
    static constexpr cmp_kind kind = Kind;
    static constexpr std::size_t prefix = N;
    static constexpr std::size_t block_width = 0;
    static constexpr std::size_t length_bits = LengthBits;
    static constexpr bool incremental = false;
    using beta_type = Beta;
    Beta if_true;
    Beta if_false;

    explicit paint_at_pack(Beta t, Beta f = detail::dcf_impl::default_false<Beta>())
      : if_true{std::move(t)}, if_false{std::move(f)} { }
};

template <typename Beta = uint64_t>
inline auto lcp(Beta t = Beta{1},
    Beta f = detail::dcf_impl::default_false<Beta>())
{
    return paint_pack<cmp_kind::lcp, Beta>(std::move(t), std::move(f));
}
template <std::size_t N, typename Beta = uint64_t>
inline auto lcp_at(Beta t = Beta{1},
    Beta f = detail::dcf_impl::default_false<Beta>())
{
    return paint_at_pack<N, cmp_kind::lcp, Beta>(std::move(t), std::move(f));
}

template <typename Beta = uint64_t>
inline auto common_prefix(Beta t = Beta{1},
    Beta f = detail::dcf_impl::default_false<Beta>())
{
    return paint_pack<cmp_kind::prefix, Beta>(std::move(t), std::move(f));
}
template <std::size_t N, typename Beta = uint64_t>
inline auto common_prefix_at(Beta t = Beta{1},
    Beta f = detail::dcf_impl::default_false<Beta>())
{
    return paint_at_pack<N, cmp_kind::prefix, Beta>(std::move(t), std::move(f));
}

template <typename Beta = uint64_t>
inline auto prefix_mask(Beta t = Beta{1},
    Beta f = detail::dcf_impl::default_false<Beta>())
{
    return paint_pack<cmp_kind::mask, Beta>(std::move(t), std::move(f));
}
template <std::size_t N, typename Beta = uint64_t>
inline auto prefix_mask_at(Beta t = Beta{1},
    Beta f = detail::dcf_impl::default_false<Beta>())
{
    return paint_at_pack<N, cmp_kind::mask, Beta>(std::move(t), std::move(f));
}

template <typename Beta = uint64_t>
inline auto diverge_one_hot(Beta t = Beta{1},
    Beta f = detail::dcf_impl::default_false<Beta>())
{
    return paint_pack<cmp_kind::one_hot, Beta>(std::move(t), std::move(f));
}
template <std::size_t N, typename Beta = uint64_t>
inline auto diverge_one_hot_at(Beta t = Beta{1},
    Beta f = detail::dcf_impl::default_false<Beta>())
{
    return paint_at_pack<N, cmp_kind::one_hot, Beta>(std::move(t), std::move(f));
}

template <typename Beta = uint64_t>
inline auto break_bit(Beta t = Beta{1},
    Beta f = detail::dcf_impl::default_false<Beta>())
{
    return paint_pack<cmp_kind::break_bit, Beta>(std::move(t), std::move(f));
}
template <std::size_t N, typename Beta = uint64_t>
inline auto break_bit_at(Beta t = Beta{1},
    Beta f = detail::dcf_impl::default_false<Beta>())
{
    return paint_at_pack<N, cmp_kind::break_bit, Beta>(std::move(t), std::move(f));
}

/// @brief Low `LengthBits` hold the common-prefix length. Above them sits the
/// matched prefix packed into the low bits of the lane (`α >> (N − d)`).
/// @tparam LengthBits length bits
/// @tparam Beta payload type
/// @param t the `t`
/// @param f the `f`
/// @return Low `LengthBits` hold the common-prefix length
template <std::size_t LengthBits = 8, typename Beta = uint64_t>
inline auto prefix_with_length(Beta t = Beta{1},
    Beta f = detail::dcf_impl::default_false<Beta>())
{
    return paint_pack<cmp_kind::prefix_with_length, Beta, LengthBits>(
        std::move(t), std::move(f));
}
template <std::size_t N, std::size_t LengthBits = 8, typename Beta = uint64_t>
inline auto prefix_with_length_at(Beta t = Beta{1},
    Beta f = detail::dcf_impl::default_false<Beta>())
{
    return paint_at_pack<N, cmp_kind::prefix_with_length, Beta, LengthBits>(
        std::move(t), std::move(f));
}

/// @brief Arbitrary unit plant. `fn(matched, in_lane_prefix, leaf)` returns the β = 1
/// value of that sibling subtree (`leaf` is the full match, `matched == N`).
/// @details The result is scaled by `if_true − if_false` like the canned recipes.
/// @tparam Beta payload type
/// @tparam Fn fn
template <typename Beta, typename Fn>
struct paint_fn_pack
{
    static constexpr bool is_cmp = true;
    static constexpr cmp_kind kind = cmp_kind::paint;
    static constexpr std::size_t prefix = 0;
    static constexpr std::size_t block_width = 0;
    static constexpr std::size_t length_bits = 0;
    static constexpr bool incremental = false;
    using beta_type = Beta;
    Beta if_true;
    Beta if_false;
    Fn fn;

    paint_fn_pack(Beta t, Beta f, Fn g)
      : if_true{std::move(t)}, if_false{std::move(f)}, fn{std::move(g)} { }
};

template <std::size_t N, typename Beta, typename Fn>
struct paint_fn_at_pack
{
    static constexpr bool is_cmp = true;
    static constexpr cmp_kind kind = cmp_kind::paint;
    static constexpr std::size_t prefix = N;
    static constexpr std::size_t block_width = 0;
    static constexpr std::size_t length_bits = 0;
    static constexpr bool incremental = false;
    using beta_type = Beta;
    Beta if_true;
    Beta if_false;
    Fn fn;

    paint_fn_at_pack(Beta t, Beta f, Fn g)
      : if_true{std::move(t)}, if_false{std::move(f)}, fn{std::move(g)} { }
};

template <typename Fn, typename Beta>
inline auto path_paint(Fn fn, Beta t,
    Beta f = detail::dcf_impl::default_false<Beta>())
{
    return paint_fn_pack<std::decay_t<Beta>, std::decay_t<Fn>>(
        std::move(t), std::move(f), std::move(fn));
}
template <typename Fn>
inline auto path_paint(Fn fn)
{
    return path_paint(std::move(fn), uint64_t{1});
}
template <std::size_t N, typename Fn, typename Beta>
inline auto path_paint_at(Fn fn, Beta t,
    Beta f = detail::dcf_impl::default_false<Beta>())
{
    return paint_fn_at_pack<N, std::decay_t<Beta>, std::decay_t<Fn>>(
        std::move(t), std::move(f), std::move(fn));
}

/// @brief Incremental comparison: the same predicate, correct at every prefix length.
/// @details Evaluate the full point with `cmp`, and a prefix with `cmp_prefix<L>`.
/// @tparam Spec comparison or interval specification
template <typename Spec>
struct idcf_pack
{
    static constexpr bool is_cmp = true;
    static constexpr bool incremental = true;
    static constexpr cmp_kind kind = Spec::kind;
    static constexpr std::size_t prefix = Spec::prefix;
    static constexpr std::size_t block_width = Spec::block_width;
    static constexpr std::size_t length_bits = spec_length_bits<Spec>::value;
    using inner_spec = Spec;
    using beta_type = typename Spec::beta_type;
    beta_type if_true;
    beta_type if_false;

    explicit idcf_pack(Spec spec)
      : if_true{std::move(spec.if_true)}, if_false{std::move(spec.if_false)} { }
};

template <typename Spec>
inline auto idcf(Spec spec)
{
    static_assert(is_paint_kind(Spec::kind) == false,
        "idcf wraps lt/leq/gt/geq; path paints are already one full-domain value");
    static_assert(Spec::block_width == 0,
        "idcf uses the per-level path, not blocked checkpoints");
    return idcf_pack<Spec>{std::move(spec)};
}

// ---------------------------------------------------------------------------
// Equality specs: eq / eq_at
// ---------------------------------------------------------------------------

template <typename Beta>
struct eq_pack
{
    static constexpr bool is_eq = true;
    static constexpr std::size_t prefix = 0;
    using beta_type = Beta;
    Beta if_true;
    Beta if_false;

    explicit eq_pack(Beta t, Beta f = detail::dcf_impl::default_false<Beta>())
      : if_true{std::move(t)}, if_false{std::move(f)} { }
};

template <std::size_t N, typename Beta>
struct eq_at_pack
{
    static constexpr bool is_eq = true;
    static constexpr std::size_t prefix = N;
    using beta_type = Beta;
    Beta if_true;
    Beta if_false;

    explicit eq_at_pack(Beta t, Beta f = detail::dcf_impl::default_false<Beta>())
      : if_true{std::move(t)}, if_false{std::move(f)} { }
};

template <typename Beta>
inline auto eq(Beta t, Beta f = detail::dcf_impl::default_false<std::decay_t<Beta>>())
{
    return eq_pack<std::decay_t<Beta>>(std::move(t), std::move(f));
}
template <std::size_t N, typename Beta>
inline auto eq_at(Beta t, Beta f = detail::dcf_impl::default_false<std::decay_t<Beta>>())
{
    return eq_at_pack<N, std::decay_t<Beta>>(std::move(t), std::move(f));
}

template <typename T, typename = void>
struct pack_has_fn : std::false_type {};
template <typename T>
struct pack_has_fn<T, std::void_t<decltype(std::declval<T &>().fn)>>
    : std::true_type {};

template <std::size_t BlockWidth, typename Spec>
struct block_width_pack
{
    static_assert(BlockWidth >= 1, "block_width<B> needs B >= 1");
    static_assert(Spec::block_width == 0, "comparison is already block_width");
    static constexpr bool is_cmp = true;
    static constexpr std::size_t block_width = BlockWidth;
    static constexpr cmp_kind kind = Spec::kind;
    static constexpr std::size_t prefix = Spec::prefix;
    static constexpr bool incremental = spec_is_incremental<Spec>::value;
    static constexpr std::size_t length_bits = spec_length_bits<Spec>::value;
    using inner_spec = Spec;
    using beta_type = typename Spec::beta_type;
    beta_type if_true;
    beta_type if_false;

    explicit block_width_pack(Spec spec)
      : if_true{std::move(spec.if_true)}, if_false{std::move(spec.if_false)} { }
};

template <std::size_t BlockWidth>
struct block_width_fn
{
    template <typename Spec>
    constexpr auto operator()(Spec spec) const
    {
        return block_width_pack<BlockWidth, Spec>{std::move(spec)};
    }
};

template <std::size_t BlockWidth>
inline constexpr block_width_fn<BlockWidth> block_width{};

// ---------------------------------------------------------------------------
// Same comparison shape, wildcard payload. Wrappers (`idcf`, `block_width`,
// `*_at`, path paints) keep their outer type; only the leaf beta changes.
// ---------------------------------------------------------------------------

template <typename T> struct is_idcf_pack : std::false_type {};
template <typename Spec>
struct is_idcf_pack<idcf_pack<Spec>> : std::true_type {};
template <typename T>
inline constexpr bool is_idcf_pack_v = is_idcf_pack<std::decay_t<T>>::value;

template <typename T> struct is_block_width_pack : std::false_type {};
template <std::size_t B, typename Spec>
struct is_block_width_pack<block_width_pack<B, Spec>> : std::true_type {};
template <typename T>
inline constexpr bool is_block_width_pack_v =
    is_block_width_pack<std::decay_t<T>>::value;

namespace detail
{

template <typename Spec>
auto cmp_wildcard_shape();

template <cmp_kind K, typename B>
auto cmp_wildcard_shape(cmp_pack<K, B>)
{
    using W = wildcard_value<concrete_type_t<B>>;
    return cmp_pack<K, W>(W{}, W{});
}
template <std::size_t N, cmp_kind K, typename B>
auto cmp_wildcard_shape(cmp_at_pack<N, K, B>)
{
    using W = wildcard_value<concrete_type_t<B>>;
    return cmp_at_pack<N, K, W>(W{}, W{});
}
template <cmp_kind K, typename B, std::size_t L>
auto cmp_wildcard_shape(paint_pack<K, B, L>)
{
    using W = wildcard_value<concrete_type_t<B>>;
    return paint_pack<K, W, L>(W{}, W{});
}
template <std::size_t N, cmp_kind K, typename B, std::size_t L>
auto cmp_wildcard_shape(paint_at_pack<N, K, B, L>)
{
    using W = wildcard_value<concrete_type_t<B>>;
    return paint_at_pack<N, K, W, L>(W{}, W{});
}
template <typename B, typename Fn>
auto cmp_wildcard_shape(paint_fn_pack<B, Fn> spec)
{
    using W = wildcard_value<concrete_type_t<B>>;
    return paint_fn_pack<W, std::decay_t<Fn>>(W{}, W{}, std::move(spec.fn));
}
template <std::size_t N, typename B, typename Fn>
auto cmp_wildcard_shape(paint_fn_at_pack<N, B, Fn> spec)
{
    using W = wildcard_value<concrete_type_t<B>>;
    return paint_fn_at_pack<N, W, std::decay_t<Fn>>(W{}, W{}, std::move(spec.fn));
}

template <typename Spec>
auto cmp_wildcard_shape()
{
    if constexpr (is_idcf_pack_v<Spec>)
        return idcf(cmp_wildcard_shape<typename Spec::inner_spec>());
    else if constexpr (is_block_width_pack_v<Spec>)
        return block_width<Spec::block_width>(
            cmp_wildcard_shape<typename Spec::inner_spec>());
    else
    {
        using B = typename Spec::beta_type;
        return cmp_wildcard_shape(Spec{B{}, B{}});
    }
}

}  // namespace detail

/// @brief The same comparison or paint spec, with a wildcard payload.
/// @details `idcf`, `block_width`, and `*_at` stay wrapped. A spec that is
///          already wildcard is returned unchanged. `path_paint` keeps `fn`.
template <typename Spec>
auto cmp_spec_as_wildcard(Spec spec)
{
    using S = std::decay_t<Spec>;
    if constexpr (is_wildcard_v<typename S::beta_type>)
        return spec;
    else if constexpr (pack_has_fn<S>::value)
        return detail::cmp_wildcard_shape(std::move(spec));
    else
        return detail::cmp_wildcard_shape<S>();
}

template <typename T> struct is_cmp_spec : std::false_type {};
template <cmp_kind K, typename B> struct is_cmp_spec<cmp_pack<K, B>> : std::true_type {};
template <std::size_t N, cmp_kind K, typename B>
struct is_cmp_spec<cmp_at_pack<N, K, B>> : std::true_type {};
template <cmp_kind K, typename B, std::size_t L>
struct is_cmp_spec<paint_pack<K, B, L>> : std::true_type {};
template <std::size_t N, cmp_kind K, typename B, std::size_t L>
struct is_cmp_spec<paint_at_pack<N, K, B, L>> : std::true_type {};
template <typename B, typename Fn>
struct is_cmp_spec<paint_fn_pack<B, Fn>> : std::true_type {};
template <std::size_t N, typename B, typename Fn>
struct is_cmp_spec<paint_fn_at_pack<N, B, Fn>> : std::true_type {};
template <typename Spec>
struct is_cmp_spec<idcf_pack<Spec>> : std::true_type {};
template <std::size_t B, typename Spec>
struct is_cmp_spec<block_width_pack<B, Spec>> : std::true_type {};
template <typename T>
inline constexpr bool is_cmp_spec_v = is_cmp_spec<T>::value;

template <typename T> struct is_eq_spec : std::false_type {};
template <typename B> struct is_eq_spec<eq_pack<B>> : std::true_type {};
template <std::size_t N, typename B>
struct is_eq_spec<eq_at_pack<N, B>> : std::true_type {};
template <typename T>
inline constexpr bool is_eq_spec_v = is_eq_spec<T>::value;

template <typename T>
inline constexpr bool is_dcf_spec_v = is_cmp_spec_v<T>;

}  // namespace dpf

#endif  // LIBDPF_INCLUDE_DPF_DCF_HPP__