Tifa's CP Library

:heavy_check_mark: lsieve_func (src/code/nt/lsieve_func.hpp)

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#ifndef TIFALIBS_MATH_LSIEVE_FUNC
#define TIFALIBS_MATH_LSIEVE_FUNC

#include "lsieve.hpp"

namespace tifa_libs::math {

enum lsieve_state { ls_mpf = 1,
                    ls_phi = 2,
                    ls_mu = 4,
                    ls_sigma = 8,
                    ls_tau = 16 };

struct lsieve_func {
  vecu prime, mpf, phi;
  veci mu;
  vecuu sigma, tau;

  template <int state>
  CEXP lsieve_func& reset_lsieve_func(u32 n) {
    if CEXP (state | ls_mpf) mpf = vecu(n), mpf[1] = 1;
    if CEXP (state | ls_phi) phi = vecu(n), phi[1] = 1;
    if CEXP (state | ls_mu) mu = veci(n), mu[1] = 1;
    if CEXP (state | ls_sigma) pw = vecuu(n), sigma = vecuu(n), sigma[1] = 1;
    if CEXP (state | ls_tau) pc = vecu(n, 1), tau = vecuu(n), tau[1] = 1;

    prime = lsieve(n, [&](u32 p) {
          if CEXP (state | ls_mpf) mpf[p] = p;
          if CEXP (state | ls_phi) phi[p] = p - 1;
          if CEXP (state | ls_mu) mu[p] = -1;
          if CEXP (state | ls_sigma) pw[p] = (u64)p * p, sigma[p] = p + 1;
          if CEXP (state | ls_tau) tau[p] = 2; }, [&](u32 i, u32 j) {
          if CEXP (state | ls_mpf) mpf[i * j] = j;
          if CEXP (state | ls_phi) phi[i * j] = phi[i] * (j - 1);
          if CEXP (state | ls_mu) mu[i * j] = -mu[i];
          if CEXP (state | ls_sigma) pw[i * j] = (u64)j * j, sigma[i * j] = sigma[i] * (j + 1);
          if CEXP (state | ls_tau) tau[i * j] = tau[i] * 2; }, [&](u32 i, u32 j) {
          if CEXP (state | ls_mpf) mpf[i * j] = j;
          if CEXP (state | ls_phi) phi[i * j] = phi[i] * j;
          if CEXP (state | ls_sigma) sigma[i * j] = sigma[i] * ((pw[i * j] = pw[i] * j) - 1) / (pw[i] - 1);
          if CEXP (state | ls_tau) tau[i * j] = tau[i] + tau[i] / (pc[i * j] = pc[i] + 1); });
    return *this;
  }

 private:
  vecuu pw;
  vecu pc;
};

}  // namespace tifa_libs::math

#endif
#line 1 "src/code/nt/lsieve_func.hpp"



#line 1 "src/code/nt/lsieve.hpp"



#line 1 "src/code/util/util.hpp"



#include <bits/extc++.h>

#define CEXP constexpr
#define CEXPE constexpr explicit
#define TPN typename
#define CR const&

#define cT_(...) std::conditional_t<sizeof(__VA_ARGS__) <= sizeof(size_t), __VA_ARGS__, __VA_ARGS__ CR>
#define fle_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i <= i##e; ++i)
#define flt_(T, i, l, r, ...) for (T i = (l), i##e = (r)__VA_OPT__(, ) __VA_ARGS__; i < i##e; ++i)

#ifdef ONLINE_JUDGE
#undef assert
#define assert(x) 42
#endif

using i8 = int8_t;
using i16 = int16_t;
using i32 = int32_t;
using i64 = int64_t;
using i128 = __int128_t;
using isz = ptrdiff_t;
using u8 = uint8_t;
using u16 = uint16_t;
using u32 = uint32_t;
using u64 = uint64_t;
using u128 = __uint128_t;
using usz = size_t;
using f32 = float;
using f64 = double;
using f128 = long double;
using strn = std::string;
using strnv = std::string_view;

// clang-format off
template <class T, T v> using ic = std::integral_constant<T, v>;
template <class T> using ptt = std::pair<T, T>;
template <class T> struct edge_t {
  T w; u32 u, v;
  CEXP auto operator<=>(edge_t CR) const = default;
};
template <class T> struct pt3 {
  T _0, _1, _2;
  CEXP auto operator<=>(pt3 CR) const = default;
};
template <class T> struct pt4 {
  T _0, _1, _2, _3;
  CEXP auto operator<=>(pt4 CR) const = default;
};
template <class E> using itl = std::initializer_list<E>;
template <class T> using vec = std::vector<T>;
template <class T> using vvec = vec<vec<T>>;
template <class T> using v3ec = vec<vvec<T>>;
template <class T> using vecpt = vec<ptt<T>>;
template <class T> using vvecpt = vvec<ptt<T>>;
template <class T> using ptvec = ptt<vec<T>>;
template <class T> using ptvvec = ptt<vvec<T>>;

template <class T, usz ext = std::dynamic_extent> using spn = std::span<T const, ext>;
template <class T, usz N> using arr = std::array<T, N>;
template <class U, class T> using vecp = vec<std::pair<U, T>>;
template <class U, class T> using vvecp = vvec<std::pair<U, T>>;

template <class T, class C = std::less<T>> using pq = std::priority_queue<T, vec<T>, C>;
template <class T> using pqg = std::priority_queue<T, vec<T>, std::greater<T>>;
// clang-format on

#define mk_(V, A, T) using V##A = V<T>;
#define mk(A, T) mk_(edge_t, A, T) mk_(ptt, A, T) mk_(pt3, A, T) mk_(pt4, A, T) mk_(vec, A, T) mk_(vvec, A, T) mk_(v3ec, A, T) mk_(vecpt, A, T) mk_(vvecpt, A, T) mk_(ptvec, A, T) mk_(ptvvec, A, T) mk_(spn, A, T) mk_(itl, A, T)
mk(b, bool) mk(i, i32) mk(u, u32) mk(ii, i64) mk(uu, u64);
#undef mk
#undef mk_

using namespace std::literals;
CEXP i8 operator""_i8(unsigned long long x) { return (i8)x; }
CEXP i16 operator""_i16(unsigned long long x) { return (i16)x; }
CEXP i32 operator""_i32(unsigned long long x) { return (i32)x; }
CEXP i64 operator""_i64(unsigned long long x) { return (i64)x; }
CEXP isz operator""_iz(unsigned long long x) { return (isz)x; }
CEXP u8 operator""_u8(unsigned long long x) { return (u8)x; }
CEXP u16 operator""_u16(unsigned long long x) { return (u16)x; }
CEXP u32 operator""_u32(unsigned long long x) { return (u32)x; }
CEXP u64 operator""_u64(unsigned long long x) { return (u64)x; }
CEXP usz operator""_uz(unsigned long long x) { return (usz)x; }

using std::numbers::pi_v;
template <std::floating_point FP>
inline FP eps_v = std::sqrt(std::numeric_limits<FP>::epsilon());
template <std::floating_point FP>
CEXP void set_eps(FP v) { eps_v<FP> = v; }

inline const auto fn_0 = [](auto&&...) {};
inline const auto fn_is0 = [](auto x) { return x == 0; };

namespace tifa_libs {
using std::min, std::max, std::swap;
template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }
}  // namespace tifa_libs


#line 5 "src/code/nt/lsieve.hpp"

namespace tifa_libs::math {

template <class F1, class F2, class F3>
requires requires(F1 cb_prime, F2 cb_coprime, F3 cb_not_coprime, u32 p, u32 q) {
  cb_prime(p);
  cb_coprime(p, q);
  cb_not_coprime(p, q);
}
CEXP vecu lsieve(u32 n, F1 cb_prime, F2 cb_coprime, F3 cb_not_coprime) {
  vecb vis(n);
  vecu p;
  p.reserve(n <= 170 ? 16 : n / 10);
  flt_ (u32, i, 2, n) {
    if (!vis[i]) p.push_back(i), cb_prime(i);
    for (u32 j : p) {
      if (i * j >= n) break;
      if (vis[i * j] = true; i % j) cb_coprime(i, j);
      else {
        cb_not_coprime(i, j);
        break;
      }
    }
  }
  return p;
}

}  // namespace tifa_libs::math


#line 5 "src/code/nt/lsieve_func.hpp"

namespace tifa_libs::math {

enum lsieve_state { ls_mpf = 1,
                    ls_phi = 2,
                    ls_mu = 4,
                    ls_sigma = 8,
                    ls_tau = 16 };

struct lsieve_func {
  vecu prime, mpf, phi;
  veci mu;
  vecuu sigma, tau;

  template <int state>
  CEXP lsieve_func& reset_lsieve_func(u32 n) {
    if CEXP (state | ls_mpf) mpf = vecu(n), mpf[1] = 1;
    if CEXP (state | ls_phi) phi = vecu(n), phi[1] = 1;
    if CEXP (state | ls_mu) mu = veci(n), mu[1] = 1;
    if CEXP (state | ls_sigma) pw = vecuu(n), sigma = vecuu(n), sigma[1] = 1;
    if CEXP (state | ls_tau) pc = vecu(n, 1), tau = vecuu(n), tau[1] = 1;

    prime = lsieve(n, [&](u32 p) {
          if CEXP (state | ls_mpf) mpf[p] = p;
          if CEXP (state | ls_phi) phi[p] = p - 1;
          if CEXP (state | ls_mu) mu[p] = -1;
          if CEXP (state | ls_sigma) pw[p] = (u64)p * p, sigma[p] = p + 1;
          if CEXP (state | ls_tau) tau[p] = 2; }, [&](u32 i, u32 j) {
          if CEXP (state | ls_mpf) mpf[i * j] = j;
          if CEXP (state | ls_phi) phi[i * j] = phi[i] * (j - 1);
          if CEXP (state | ls_mu) mu[i * j] = -mu[i];
          if CEXP (state | ls_sigma) pw[i * j] = (u64)j * j, sigma[i * j] = sigma[i] * (j + 1);
          if CEXP (state | ls_tau) tau[i * j] = tau[i] * 2; }, [&](u32 i, u32 j) {
          if CEXP (state | ls_mpf) mpf[i * j] = j;
          if CEXP (state | ls_phi) phi[i * j] = phi[i] * j;
          if CEXP (state | ls_sigma) sigma[i * j] = sigma[i] * ((pw[i * j] = pw[i] * j) - 1) / (pw[i] - 1);
          if CEXP (state | ls_tau) tau[i * j] = tau[i] + tau[i] / (pc[i * j] = pc[i] + 1); });
    return *this;
  }

 private:
  vecuu pw;
  vecu pc;
};

}  // namespace tifa_libs::math


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