CP-Algorithms Library

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:heavy_check_mark: cp-algo/util/sort.hpp

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#ifndef CP_ALGO_UTIL_SORT_HPP
#define CP_ALGO_UTIL_SORT_HPP
#include "bit.hpp"
#include <algorithm>
#include <numeric>
#include <ranges>
#include <vector>
namespace cp_algo {
    template<size_t maxc>
    void count_sort(auto &a, auto &&proj = std::identity{}) {
        std::array<int, maxc> cnt = {};
        for(auto &x: a) {
            cnt[proj(x)]++;
        }
        std::partial_sum(begin(cnt), end(cnt), begin(cnt));
        auto res = a;
        for(auto const& it: a | std::views::reverse) {
            res[--cnt[proj(it)]] = it;
        }
        a = std::move(res);
    }

    void radix_sort(auto &a) {
        if(empty(a)) {
            return;
        }
        auto [mn, mx] = std::ranges::minmax(a);
        with_bit_floor<1>(size(a), [&]<size_t floor>() {
            constexpr int base = std::min<size_t>(floor, 1 << 16);
            for(int64_t i = 1; i <= mx - mn; i *= base) {
                count_sort<base>(a, [&](auto x) {
                    return (x - mn) / i % base;
                });
            }
        });
    }
}
#endif // CP_ALGO_UTIL_SORT_HPP

#line 1 "cp-algo/util/sort.hpp"


#line 1 "cp-algo/util/bit.hpp"


#line 1 "cp-algo/util/simd.hpp"


#include <experimental/simd>
#include <cstdint>
#include <cstddef>
#include <memory>
namespace cp_algo {
    template<typename T, size_t len>
    using simd [[gnu::vector_size(len * sizeof(T))]] = T;
    using i64x4 = simd<int64_t, 4>;
    using u64x4 = simd<uint64_t, 4>;
    using u32x8 = simd<uint32_t, 8>;
    using i32x4 = simd<int32_t, 4>;
    using u32x4 = simd<uint32_t, 4>;
    using i16x4 = simd<int16_t, 4>;
    using u8x32 = simd<uint8_t, 32>;
    using dx4 = simd<double, 4>;

    [[gnu::target("avx2")]] inline dx4 abs(dx4 a) {
    return a < 0 ? -a : a;
    }

    // https://stackoverflow.com/a/77376595
    // works for ints in (-2^51, 2^51)
    static constexpr dx4 magic = dx4() + (3ULL << 51);
    [[gnu::target("avx2")]] inline i64x4 lround(dx4 x) {
        return i64x4(x + magic) - i64x4(magic);
    }
    [[gnu::target("avx2")]] inline dx4 to_double(i64x4 x) {
        return dx4(x + i64x4(magic)) - magic;
    }

    [[gnu::target("avx2")]] inline dx4 round(dx4 a) {
        return dx4{
            std::nearbyint(a[0]),
            std::nearbyint(a[1]),
            std::nearbyint(a[2]),
            std::nearbyint(a[3])
        };
    }

    [[gnu::target("avx2")]] inline u64x4 low32(u64x4 x) {
        return x & uint32_t(-1);
    }
    [[gnu::target("avx2")]] inline auto swap_bytes(auto x) {
        return decltype(x)(__builtin_shufflevector(u32x8(x), u32x8(x), 1, 0, 3, 2, 5, 4, 7, 6));
    }
    [[gnu::target("avx2")]] inline u64x4 montgomery_reduce(u64x4 x, uint32_t mod, uint32_t imod) {
        auto x_ninv = u64x4(_mm256_mul_epu32(__m256i(x), __m256i() + imod));
        x += u64x4(_mm256_mul_epu32(__m256i(x_ninv), __m256i() + mod));
        return swap_bytes(x);
    }

    [[gnu::target("avx2")]] inline u64x4 montgomery_mul(u64x4 x, u64x4 y, uint32_t mod, uint32_t imod) {
        return montgomery_reduce(u64x4(_mm256_mul_epu32(__m256i(x), __m256i(y))), mod, imod);
    }
    [[gnu::target("avx2")]] inline u32x8 montgomery_mul(u32x8 x, u32x8 y, uint32_t mod, uint32_t imod) {
        return u32x8(montgomery_mul(u64x4(x), u64x4(y), mod, imod)) |
               u32x8(swap_bytes(montgomery_mul(u64x4(swap_bytes(x)), u64x4(swap_bytes(y)), mod, imod)));
    }
    [[gnu::target("avx2")]] inline dx4 rotate_right(dx4 x) {
        static constexpr u64x4 shuffler = {3, 0, 1, 2};
        return __builtin_shuffle(x, shuffler);
    }

    template<std::size_t Align = 32>
    [[gnu::target("avx2")]] inline bool is_aligned(const auto* p) noexcept {
        return (reinterpret_cast<std::uintptr_t>(p) % Align) == 0;
    }

    template<class Target>
    [[gnu::target("avx2")]] inline Target& vector_cast(auto &&p) {
        return *reinterpret_cast<Target*>(std::assume_aligned<alignof(Target)>(&p));
    }
}

#line 5 "cp-algo/util/bit.hpp"
#include <array>
#include <bit>
namespace cp_algo {
    template<typename Uint>
    constexpr size_t bit_width = sizeof(Uint) * 8;

    // n < 64
    uint64_t mask(size_t n) {
        return (1ULL << n) - 1;
    }
    size_t order_of_bit(auto x, size_t k) {
        return k ? std::popcount(x << (bit_width<decltype(x)> - k)) : 0;
    }
    [[gnu::target("bmi2")]] inline size_t kth_set_bit(uint64_t x, size_t k) {
        return std::countr_zero(_pdep_u64(1ULL << k, x));
    }
    template<int fl = 0>
    void with_bit_floor(size_t n, auto &&callback) {
        if constexpr (fl >= 63) {
            return;
        } else if (n >> (fl + 1)) {
            with_bit_floor<fl + 1>(n, callback);
        } else {
            callback.template operator()<1ULL << fl>();
        }
    }
    void with_bit_ceil(size_t n, auto &&callback) {
        with_bit_floor(n, [&]<size_t N>() {
            if(N == n) {
                callback.template operator()<N>();
            } else {
                callback.template operator()<N << 1>();
            }
        });
    }

    [[gnu::target("avx2")]] inline uint32_t read_bits(char const* p) {
        return _mm256_movemask_epi8(__m256i(vector_cast<u8x32 const>(p[0]) + (127 - '0')));
    }
    [[gnu::target("avx2")]] inline uint64_t read_bits64(char const* p) {
        return read_bits(p) | (uint64_t(read_bits(p + 32)) << 32);
    }

    [[gnu::target("avx2")]] inline void write_bits(char *p, uint32_t bits) {
        static constexpr u8x32 shuffler = {
            0, 0, 0, 0, 0, 0, 0, 0,
            1, 1, 1, 1, 1, 1, 1, 1,
            2, 2, 2, 2, 2, 2, 2, 2,
            3, 3, 3, 3, 3, 3, 3, 3
        };
        auto shuffled = u8x32(_mm256_shuffle_epi8(__m256i() + bits, __m256i(shuffler)));
        static constexpr u8x32 mask = {
            1, 2, 4, 8, 16, 32, 64, 128,
            1, 2, 4, 8, 16, 32, 64, 128,
            1, 2, 4, 8, 16, 32, 64, 128,
            1, 2, 4, 8, 16, 32, 64, 128
        };
        for(int z = 0; z < 32; z++) {
            p[z] = shuffled[z] & mask[z] ? '1' : '0';
        }
    }
    [[gnu::target("avx2")]] inline void write_bits64(char *p, uint64_t bits) {
        write_bits(p, uint32_t(bits));
        write_bits(p + 32, uint32_t(bits >> 32));
    }
}

#line 4 "cp-algo/util/sort.hpp"
#include <algorithm>
#include <numeric>
#include <ranges>
#include <vector>
namespace cp_algo {
    template<size_t maxc>
    void count_sort(auto &a, auto &&proj = std::identity{}) {
        std::array<int, maxc> cnt = {};
        for(auto &x: a) {
            cnt[proj(x)]++;
        }
        std::partial_sum(begin(cnt), end(cnt), begin(cnt));
        auto res = a;
        for(auto const& it: a | std::views::reverse) {
            res[--cnt[proj(it)]] = it;
        }
        a = std::move(res);
    }

    void radix_sort(auto &a) {
        if(empty(a)) {
            return;
        }
        auto [mn, mx] = std::ranges::minmax(a);
        with_bit_floor<1>(size(a), [&]<size_t floor>() {
            constexpr int base = std::min<size_t>(floor, 1 << 16);
            for(int64_t i = 1; i <= mx - mn; i *= base) {
                count_sort<base>(a, [&](auto x) {
                    return (x - mn) / i % base;
                });
            }
        });
    }
}
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