perm16_impl.hpp

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//****************************************************************************//
//     Copyright (C) 2016-2024 Florent Hivert <Florent.Hivert@lisn.fr>,       //
//                                                                            //
//  This file is part of HP-Combi <https://github.com/libsemigroups/HPCombi>  //
//                                                                            //
//  HP-Combi is free software: you can redistribute it and/or modify it       //
//  under the terms of the GNU General Public License as published by the     //
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//  (at your option) any later version.                                       //
//                                                                            //
//  HP-Combi is distributed in the hope that it will be useful, but WITHOUT   //
//  ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or     //
//  FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License      //
//  for  more details.                                                        //
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//  You should have received a copy of the GNU General Public License along   //
//  with HP-Combi. If not, see <https://www.gnu.org/licenses/>.               //
//****************************************************************************//
 
// NOLINT(build/header_guard)

 
namespace HPCombi {
inline PTransf16::PTransf16(std::initializer_list<uint8_t> il)
    : Vect16(Epu8.id()) {
    HPCOMBI_ASSERT(il.size() <= 16);
    std::copy(il.begin(), il.end(), HPCombi::as_array(v).begin());
}
 
inline PTransf16::PTransf16(std::vector<uint8_t> dom, std::vector<uint8_t> rng,
                            size_t /*unused */)
    : Vect16(Epu8(0xFF)) {
    HPCOMBI_ASSERT(dom.size() == rng.size());
    HPCOMBI_ASSERT(dom.size() <= 16);
    for (size_t i = 0; i < dom.size(); ++i) {
        HPCOMBI_ASSERT(dom[i] < 16);
        v[dom[i]] = rng[i];
    }
}
 
inline epu8 PTransf16::domain_mask(bool complement) const {
    return complement ? v == Epu8(0xFF) : v != Epu8(0xFF);
}
inline uint32_t PTransf16::domain_bitset(bool complement) const {
    return simde_mm_movemask_epi8(domain_mask(complement));
}
inline PTransf16 PTransf16::right_one() const {
    return domain_mask(true) | Epu8.id();
}
 
#ifdef SIMDE_X86_SSE4_2_NATIVE
inline epu8 PTransf16::image_mask_cmpestrm(bool complement) const {
    return complement ? _mm_cmpestrm(v, 16, one().v, 16, FIND_IN_VECT)
                      : _mm_cmpestrm(v, 16, one().v, 16, FIND_IN_VECT_COMPL);
}
#endif
inline epu8 PTransf16::image_mask_ref(bool complement) const {
    epu8 res{};
    for (auto x : *this)
        if (x != 0xFF)
            res[x] = 0xFF;
    return complement ? static_cast<epu8>(!res) : res;
}
 
inline uint32_t PTransf16::image_bitset(bool complement) const {
    return simde_mm_movemask_epi8(image_mask(complement));
}
inline PTransf16 PTransf16::left_one() const {
    return image_mask(true) | Epu8.id();
}
inline uint32_t PTransf16::rank_ref() const {
    decltype(Epu8)::array tmp{};
    static_assert(decltype(Epu8)::size == 16, "Wrong size of EPU8 array");
    for (auto x : *this)
        if (x != 0xFF)
            tmp[x] = 1;
    return std::accumulate(tmp.begin(), tmp.end(), uint8_t(0));
}
 
inline uint32_t PTransf16::rank_cmpestrm() const {
    return __builtin_popcountl(image_bitset());
}
 
inline uint32_t PTransf16::rank() const {
#ifdef SIMDE_X86_SSE4_2_NATIVE
    return rank_cmpestrm();
#else
    return rank_ref();
#endif
}
 
inline epu8 PTransf16::fix_points_mask(bool complement) const {
    return complement ? v != one().v : v == one().v;
}
inline uint32_t PTransf16::fix_points_bitset(bool complement) const {
    return simde_mm_movemask_epi8(fix_points_mask(complement));
}
 
inline uint8_t PTransf16::smallest_fix_point() const {
    return __builtin_ffs(fix_points_bitset(false)) - 1;
}

inline uint8_t PTransf16::smallest_moved_point() const {
    return __builtin_ffs(fix_points_bitset(true)) - 1;
}

inline uint8_t PTransf16::largest_fix_point() const {
    uint32_t res = fix_points_bitset(false);
    return res == 0 ? 0xFF : 31 - __builtin_clz(res);
}

inline uint8_t PTransf16::largest_moved_point() const {
    uint32_t res = fix_points_bitset(true);
    return res == 0 ? 0xFF : 31 - __builtin_clz(res);
}

inline uint8_t PTransf16::nb_fix_points() const {
    return __builtin_popcountl(fix_points_bitset());
}
 
inline static constexpr uint8_t hilo_exchng_fun(uint8_t i) {
    return i < 8 ? i + 8 : i - 8;
}
static constexpr epu8 hilo_exchng = Epu8(hilo_exchng_fun);
inline static constexpr uint8_t hilo_mask_fun(uint8_t i) {
    return i < 8 ? 0x0 : 0xFF;
}
static constexpr epu8 hilo_mask = Epu8(hilo_mask_fun);
 
inline Transf16::Transf16(uint64_t compressed) {
    epu8 res = simde_mm_set_epi64x(compressed, compressed);
    v = simde_mm_blendv_epi8(res & Epu8(0x0F), res >> 4, hilo_mask);
}
 
inline Transf16::operator uint64_t() const {
    epu8 res =
        static_cast<epu8>(simde_mm_slli_epi32(static_cast<simde__m128i>(v), 4));
    res = HPCombi::permuted(res, hilo_exchng) + v;
    return simde_mm_extract_epi64(res, 0);
}
 
inline PPerm16 PPerm16::inverse_ref() const {
    epu8 res = Epu8(0xFF);
    for (size_t i = 0; i < 16; ++i)
        if (v[i] < 16)
            res[v[i]] = i;
    return res;
}
 
#ifdef SIMDE_X86_SSE4_2_NATIVE
inline PPerm16 PPerm16::inverse_find() const {
    epu8 mask = _mm_cmpestrm(v, 16, one(), 16, FIND_IN_VECT);
    return permutation_of(v, one()) | mask;
}
#endif
 
inline Perm16 Perm16::random(uint64_t n) {
    static std::random_device rd;
    static std::mt19937 g(rd());
 
    Perm16 res = one();
    auto ar = res.as_array();
 
    std::shuffle(ar.begin(), ar.begin() + n, g);
    return res;
}
 
// From Ruskey : Combinatorial Generation page 138
inline Perm16 Perm16::unrankSJT(int n, int r) {
    int j;
    std::array<int, 16> dir;
    epu8 res{};
    for (j = 0; j < n; ++j)
        res[j] = 0xFF;
    for (j = n - 1; j >= 0; --j) {
        int k, rem, c;
        rem = r % (j + 1);
        r = r / (j + 1);
        if ((r & 1) != 0) {
            k = -1;
            dir[j] = +1;
        } else {
            k = n;
            dir[j] = -1;
        }
        c = -1;
        do {
            k = k + dir[j];
            if (res[k] == 0xFF)
                ++c;
        } while (c < rem);
        res[k] = j;
    }
    return res;
}
 
inline Perm16 Perm16::elementary_transposition(uint64_t i) {
    HPCOMBI_ASSERT(i < 16);
    epu8 res = one();
    res[i] = i + 1;
    res[i + 1] = i;
    return res;
}
 
inline Perm16 Perm16::inverse_ref() const {
    epu8 res;
    for (size_t i = 0; i < 16; ++i)
        res[v[i]] = i;
    return res;
}
 
inline Perm16 Perm16::inverse_arr() const {
    epu8 res;
    auto &arres = HPCombi::as_array(res);
    auto self = as_array();
    for (size_t i = 0; i < 16; ++i)
        arres[self[i]] = i;
    return res;
}
 
inline Perm16 Perm16::inverse_sort() const {
    // G++-7 compile this shift by 3 additions.
    // epu8 res = (v << 4) + one().v;
    // I call directly the shift intrinsic
    epu8 res = static_cast<epu8>(
                   simde_mm_slli_epi32(static_cast<simde__m128i>(v), 4)) +
               one().v;
    res = sorted(res) & Epu8(0x0F);
    return res;
}
 
// We declare PERM16 as a correct Monoid
namespace power_helper {
 
// TODO required?
using Perm16 = Perm16;
 
template <> struct Monoid<Perm16> {
    static const Perm16 one() { return Perm16::one(); }
    static Perm16 prod(Perm16 a, Perm16 b) { return a * b; }
};
 
}  // namespace power_helper
 
inline Perm16 Perm16::inverse_cycl() const {
    Perm16 res = one();
    Perm16 newpow = pow<8>(*this);
    for (int i = 9; i <= 16; i++) {
        Perm16 oldpow = newpow;
        newpow = oldpow * *this;
        res.v = simde_mm_blendv_epi8(res, oldpow, newpow.v == one().v);
    }
    return res;
}
 
static constexpr uint32_t lcm_range(uint8_t n) {
    uint32_t res = 1;
    for (uint8_t i = 1; i <= n; ++i)
        res = std::lcm(res, i);
    return res;
}
 
inline Perm16 Perm16::inverse_pow() const {
    return pow<lcm_range(16) - 1>(*this);
}
 
inline epu8 Perm16::lehmer_ref() const {
    epu8 res{};
    for (size_t i = 0; i < 16; i++)
        for (size_t j = i + 1; j < 16; j++)
            if (v[i] > v[j])
                res[i]++;
    return res;
}
 
inline epu8 Perm16::lehmer_arr() const {
    decltype(Epu8)::array res{};
    decltype(Epu8)::array ar = as_array();
    for (size_t i = 0; i < 16; i++)
        for (size_t j = i + 1; j < 16; j++)
            if (ar[i] > ar[j])
                res[i]++;
    return Epu8(res);
}
 
inline epu8 Perm16::lehmer() const {
    epu8 vsh = v, res = -one().v;
    for (int i = 1; i < 16; i++) {
        vsh = shifted_left(vsh);
        res -= (v >= vsh);
    }
    return res;
}
 
inline uint8_t Perm16::length_ref() const {
    uint8_t res = 0;
    for (size_t i = 0; i < 16; i++)
        for (size_t j = i + 1; j < 16; j++)
            if (v[i] > v[j])
                res++;
    return res;
}
 
inline uint8_t Perm16::length_arr() const {
    uint8_t res = 0;
    decltype(Epu8)::array ar = as_array();
    for (size_t i = 0; i < 16; i++)
        for (size_t j = i + 1; j < 16; j++)
            if (ar[i] > ar[j])
                res++;
    return res;
}
 
inline uint8_t Perm16::length() const { return horiz_sum(lehmer()); }
 
inline uint8_t Perm16::nb_descents_ref() const {
    uint8_t res = 0;
    for (size_t i = 0; i < 16 - 1; i++)
        if (v[i] > v[i + 1])
            res++;
    return res;
}
inline uint8_t Perm16::nb_descents() const {
    return __builtin_popcountl(simde_mm_movemask_epi8(v < shifted_right(v)));
}
 
inline uint8_t Perm16::nb_cycles_ref() const {
    std::array<bool, 16> b{};
    uint8_t c = 0;
    for (size_t i = 0; i < 16; i++) {
        if (!b[i]) {
            for (size_t j = i; !b[j]; j = v[j])
                b[j] = true;
            c++;
        }
    }
    return c;
}
 
inline epu8 Perm16::cycles_partition() const {
    epu8 x0, x1 = one();
    Perm16 p = *this;
    x0 = simde_mm_min_epi8(x1, HPCombi::permuted(x1, p));
    p = p * p;
    x1 = simde_mm_min_epi8(x0, HPCombi::permuted(x0, p));
    p = p * p;
    x0 = simde_mm_min_epi8(x1, HPCombi::permuted(x1, p));
    p = p * p;
    x1 = simde_mm_min_epi8(x0, HPCombi::permuted(x0, p));
    return x1;
}
 
inline uint8_t Perm16::nb_cycles_unroll() const {
    epu8 res = (Epu8.id() == cycles_partition());
    return __builtin_popcountl(simde_mm_movemask_epi8(res));
}
 
inline bool Perm16::left_weak_leq_ref(Perm16 other) const {
    for (size_t i = 0; i < 16; i++) {
        for (size_t j = i + 1; j < 16; j++) {
            if ((v[i] > v[j]) && (other[i] < other[j]))
                return false;
        }
    }
    return true;
}
 
inline bool Perm16::left_weak_leq(Perm16 other) const {
    epu8 srot = v, orot = other;
    for (size_t i = 0; i < 15; i++) {
        srot = shifted_right(srot);
        orot = shifted_right(orot);
        uint64_t sinv = simde_mm_movemask_epi8(v < srot);
        uint64_t oinv = simde_mm_movemask_epi8(other.v < orot);
        if ((sinv & oinv) != sinv)
            return false;
    }
    return true;
}
 
inline bool Perm16::left_weak_leq_length(Perm16 other) const {
    Perm16 prod = *this * other.inverse();
    return other.length() == length() + prod.length();
}
 
}  // namespace HPCombi