Tifa's CP Library

:heavy_check_mark: pi_34log (src/code/nt/pi_34log.hpp)

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#ifndef TIFALIBS_MATH_PI_34LOG
#define TIFALIBS_MATH_PI_34LOG

#include "../math/div64.hpp"
#include "../math/isqrt.hpp"

namespace tifa_libs::math {

constexpr u64 pi_34log(u64 n) {
  if (n < 2) return 0;
  u64 n2 = isqrt(n), ndn2 = div_u64d(n, n2);
  vecu64 hl(ndn2);
  for (u32 i = 1; i < ndn2; ++i) hl[i] = div_u64d(n, i) - 1;
  vecu hs(n2 + 1);
  std::iota(hs.begin(), hs.end(), -1_u32);
  for (u64 x = 2, pi = 0; x <= n2; ++x) {
    if (hs[x] == hs[x - 1]) continue;
    u64 x2 = x * x, mx = std::min(ndn2, div_u64d(n, x2) + 1), ix = x;
    for (u64 i = 1; i < mx; ++i) {
      hl[i] -= (ix < ndn2 ? hl[ix] : hs[div_u64d(n, ix)]) - pi;
      ix += x;
    }
    for (u64 n = n2; n >= x2; --n) hs[n] -= hs[div_u64d(n, x)] - pi;
    ++pi;
  }
  return hl[1];
}

}  // namespace tifa_libs::math

#endif
#line 1 "src/code/nt/pi_34log.hpp"



#line 1 "src/code/math/div64.hpp"



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



#include <bits/stdc++.h>

template <class T>
constexpr T abs(T x) { return x < 0 ? -x : x; }

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;

template <class T>
using ptt = std::pair<T, T>;
template <class T>
using pt3 = std::tuple<T, T, T>;
template <class T>
using pt4 = std::tuple<T, T, T, T>;

template <class T, usz N>
using arr = std::array<T, N>;
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 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>
using vecpt = vec<ptt<T>>;
template <class T>
using vvecpt = vvec<ptt<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>>;

using strn = std::string;
using strnv = std::string_view;

using vecu = vec<u32>;
using vvecu = vvec<u32>;
using v3ecu = v3ec<u32>;
using vecu64 = vec<u64>;
using vecb = vec<bool>;
using vvecb = vvec<bool>;

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

using namespace std::literals;

constexpr i8 operator""_i8(unsigned long long x) { return (i8)x; }
constexpr i16 operator""_i16(unsigned long long x) { return (i16)x; }
constexpr i32 operator""_i32(unsigned long long x) { return (i32)x; }
constexpr i64 operator""_i64(unsigned long long x) { return (i64)x; }
constexpr isz operator""_iz(unsigned long long x) { return (isz)x; }

constexpr u8 operator""_u8(unsigned long long x) { return (u8)x; }
constexpr u16 operator""_u16(unsigned long long x) { return (u16)x; }
constexpr u32 operator""_u32(unsigned long long x) { return (u32)x; }
constexpr u64 operator""_u64(unsigned long long x) { return (u64)x; }
constexpr usz operator""_uz(unsigned long long x) { return (usz)x; }

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


#line 5 "src/code/math/div64.hpp"

namespace tifa_libs::math {

constexpr i64 div_i64d(i64 a, i64 b) { return i64(f64(a) / f64(b)); }
constexpr u64 div_u64d(u64 a, u64 b) { return u64(f64(a) / f64(b)); }
constexpr i64 div_i64(i64 a, i64 b) { return a <= 1000000000000 ? div_i64d(a, b) : a / b; }
constexpr u64 div_u64(u64 a, u64 b) { return a <= 1000000000000 ? div_u64d(a, b) : a / b; }

}  // namespace tifa_libs::math


#line 1 "src/code/math/isqrt.hpp"



#line 5 "src/code/math/isqrt.hpp"

namespace tifa_libs::math {

constexpr u32 isqrt(u64 x) {
  if (!x) return 0;
  int c = i32(std::bit_width(x) - 1) / 2, sh = 31 - c;
  u32 u = [](u64 x) {
    constexpr u8 TAB[192] = {128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 144, 145, 146, 147, 148, 149, 150, 151, 151, 152, 153, 154, 155, 156, 156, 157, 158, 159, 160, 160, 161, 162, 163, 164, 164, 165, 166, 167, 167, 168, 169, 170, 170, 171, 172, 173, 173, 174, 175, 176, 176, 177, 178, 179, 179, 180, 181, 181, 182, 183, 183, 184, 185, 186, 186, 187, 188, 188, 189, 190, 190, 191, 192, 192, 193, 194, 194, 195, 196, 196, 197, 198, 198, 199, 200, 200, 201, 201, 202, 203, 203, 204, 205, 205, 206, 206, 207, 208, 208, 209, 210, 210, 211, 211, 212, 213, 213, 214, 214, 215, 216, 216, 217, 217, 218, 219, 219, 220, 220, 221, 221, 222, 223, 223, 224, 224, 225, 225, 226, 227, 227, 228, 228, 229, 229, 230, 230, 231, 232, 232, 233, 233, 234, 234, 235, 235, 236, 237, 237, 238, 238, 239, 239, 240, 240, 241, 241, 242, 242, 243, 243, 244, 244, 245, 246, 246, 247, 247, 248, 248, 249, 249, 250, 250, 251, 251, 252, 252, 253, 253, 254, 254, 255, 255, 255};
    u32 u = TAB[(x >> 56) - 64];
    u = (u << 7) + (u32)(x >> 41) / u;
    return (u << 15) + (u32)((x >> 17) / u);
  }(x << 2 * sh);
  u >>= sh;
  u -= (u64)u * u > x;
  return u;
}

}  // namespace tifa_libs::math


#line 6 "src/code/nt/pi_34log.hpp"

namespace tifa_libs::math {

constexpr u64 pi_34log(u64 n) {
  if (n < 2) return 0;
  u64 n2 = isqrt(n), ndn2 = div_u64d(n, n2);
  vecu64 hl(ndn2);
  for (u32 i = 1; i < ndn2; ++i) hl[i] = div_u64d(n, i) - 1;
  vecu hs(n2 + 1);
  std::iota(hs.begin(), hs.end(), -1_u32);
  for (u64 x = 2, pi = 0; x <= n2; ++x) {
    if (hs[x] == hs[x - 1]) continue;
    u64 x2 = x * x, mx = std::min(ndn2, div_u64d(n, x2) + 1), ix = x;
    for (u64 i = 1; i < mx; ++i) {
      hl[i] -= (ix < ndn2 ? hl[ix] : hs[div_u64d(n, ix)]) - pi;
      ix += x;
    }
    for (u64 n = n2; n >= x2; --n) hs[n] -= hs[div_u64d(n, x)] - pi;
    ++pi;
  }
  return hl[1];
}

}  // namespace tifa_libs::math


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