Tifa's CP Library

:heavy_check_mark: conv_ntt_large (src/code/conv/conv_ntt_large.hpp)

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#ifndef TIFALIBS_CONV_CONV_NTT_LARGE
#define TIFALIBS_CONV_CONV_NTT_LARGE

#include "conv_dft.hpp"

namespace tifa_libs::math {

template <ntt_c NTT_t, std::same_as<typename NTT_t::data_t> mint>
constexpr vec<mint> conv_ntt_large(NTT_t &ntt, vec<mint> l, vec<mint> r, u32 ans_size = 0) {
  const u32 n = (u32)l.size(), m = (u32)r.size();
  constexpr u32 len = NTT_t::max_size;
  if (n + m - 1 <= len) return conv_dft<NTT_t, mint>(ntt, l, r, ans_size);
  if (!ans_size) ans_size = n + m - 1;

  ntt.bzr(len);
  vvec<mint> as, bs;
  for (u32 i = 0; i < l.size(); i += len / 2) {
    vec<mint> v{l.begin() + i, l.begin() + std::min(i + len / 2, (u32)l.size())};
    ntt.dif(v);
    as.push_back(v);
  }
  for (u32 i = 0; i < r.size(); i += len / 2) {
    vec<mint> v{r.begin() + i, r.begin() + std::min(i + len / 2, (u32)r.size())};
    ntt.dif(v);
    bs.push_back(v);
  }
  vvec<mint> cs(as.size() + bs.size() - 1, vec<mint>(len));
  for (u32 i = 0; i < as.size(); ++i)
    for (u32 j = 0; j < bs.size(); ++j)
      for (u32 k = 0; k < len; ++k) cs[i + j][k] += as[i][k] * bs[j][k];
  for (auto &v : cs) ntt.dit(v);
  vec<mint> c(l.size() + r.size() - 1);
  for (u32 i = 0; i < cs.size(); ++i) {
    u32 ofs = len / 2 * i;
    for (u32 j = 0, je = std::min(len, (u32)c.size() - ofs); j < je; ++j) c[j + ofs] += cs[i][j];
  }
  c.resize(ans_size);
  return c;
}
template <class NTT_t, std::same_as<typename NTT_t::data_t> mint, class T = u64>
constexpr vec<mint> conv_ntt_large_u64(NTT_t &ntt, vec<T> const &l, vec<T> const &r, u32 ans_size = 0) {
  if (!ans_size) ans_size = u32(l.size() + r.size() - 1);
  vec<mint> l_, r_;
  l_.reserve(l.size());
  r_.reserve(r.size());
  for (auto i : l) l_.push_back(i);
  for (auto i : r) r_.push_back(i);
  return conv_ntt_large(ntt, l_, r_, ans_size);
}

}  // namespace tifa_libs::math

#endif
#line 1 "src/code/conv/conv_ntt_large.hpp"



#line 1 "src/code/conv/conv_dft.hpp"



#line 1 "src/code/conv/conv_naive.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&&...) {};


#line 5 "src/code/conv/conv_naive.hpp"

namespace tifa_libs::math {

template <class U, class T = U>
requires(sizeof(U) <= sizeof(T))
constexpr vec<T> conv_naive(vec<U> const &l, vec<U> const &r, u32 ans_size = 0) {
  if (l.empty() || r.empty()) return {};
  if (!ans_size) ans_size = u32(l.size() + r.size() - 1);
  u32 n = (u32)l.size(), m = (u32)r.size();
  vec<T> ans(ans_size);
  if (n < m)
    for (u32 j = 0; j < m; ++j)
      for (u32 i = 0; i < n; ++i) {
        if (i + j >= ans_size) break;
        ans[i + j] += (T)l[i] * (T)r[j];
      }
  else
    for (u32 i = 0; i < n; ++i)
      for (u32 j = 0; j < m; ++j) {
        if (i + j >= ans_size) break;
        ans[i + j] += (T)l[i] * (T)r[j];
      }
  return ans;
}

}  // namespace tifa_libs::math


#line 1 "src/code/conv/dft_traits.hpp"



#line 5 "src/code/conv/dft_traits.hpp"

namespace tifa_libs {

template <class T>
concept dft_c = requires(T x, vec<typename T::data_t> v, u32 n) {
  { x.size() } -> std::same_as<u32>;
  x.bzr(n);
  x.dif(v, n);
  x.dit(v, n);
};

template <class T>
concept ntt_c = dft_c<T> && requires(T x) {
  T::max_size;
  T::G;
};

}  // namespace tifa_libs


#line 6 "src/code/conv/conv_dft.hpp"

namespace tifa_libs::math {

template <dft_c DFT_t, std::same_as<typename DFT_t::data_t> DFT_data_t>
constexpr vec<DFT_data_t> conv_dft(DFT_t &dft, vec<DFT_data_t> l, vec<DFT_data_t> r, u32 ans_size = 0) {
  if (!ans_size) ans_size = u32(l.size() + r.size() - 1);
  if (ans_size < 32) return conv_naive(l, r, ans_size);
  dft.bzr(std::max({(u32)l.size(), (u32)r.size(), std::min(u32(l.size() + r.size() - 1), ans_size)}));
  dft.dif(l);
  dft.dif(r);
  for (u32 i = 0; i < dft.size(); ++i) l[i] *= r[i];
  dft.dit(l);
  l.resize(ans_size);
  return l;
}
template <class DFT_t, class mint, class T = u64>
constexpr vec<mint> conv_dft_u64(DFT_t &dft, vec<T> const &l, vec<T> const &r, u32 ans_size = 0) {
  if (!ans_size) ans_size = u32(l.size() + r.size() - 1);
  vec<mint> l_, r_;
  l_.reserve(l.size());
  r_.reserve(r.size());
  for (auto i : l) l_.push_back(i);
  for (auto i : r) r_.push_back(i);
  return conv_dft(dft, l_, r_, ans_size);
}

}  // namespace tifa_libs::math


#line 5 "src/code/conv/conv_ntt_large.hpp"

namespace tifa_libs::math {

template <ntt_c NTT_t, std::same_as<typename NTT_t::data_t> mint>
constexpr vec<mint> conv_ntt_large(NTT_t &ntt, vec<mint> l, vec<mint> r, u32 ans_size = 0) {
  const u32 n = (u32)l.size(), m = (u32)r.size();
  constexpr u32 len = NTT_t::max_size;
  if (n + m - 1 <= len) return conv_dft<NTT_t, mint>(ntt, l, r, ans_size);
  if (!ans_size) ans_size = n + m - 1;

  ntt.bzr(len);
  vvec<mint> as, bs;
  for (u32 i = 0; i < l.size(); i += len / 2) {
    vec<mint> v{l.begin() + i, l.begin() + std::min(i + len / 2, (u32)l.size())};
    ntt.dif(v);
    as.push_back(v);
  }
  for (u32 i = 0; i < r.size(); i += len / 2) {
    vec<mint> v{r.begin() + i, r.begin() + std::min(i + len / 2, (u32)r.size())};
    ntt.dif(v);
    bs.push_back(v);
  }
  vvec<mint> cs(as.size() + bs.size() - 1, vec<mint>(len));
  for (u32 i = 0; i < as.size(); ++i)
    for (u32 j = 0; j < bs.size(); ++j)
      for (u32 k = 0; k < len; ++k) cs[i + j][k] += as[i][k] * bs[j][k];
  for (auto &v : cs) ntt.dit(v);
  vec<mint> c(l.size() + r.size() - 1);
  for (u32 i = 0; i < cs.size(); ++i) {
    u32 ofs = len / 2 * i;
    for (u32 j = 0, je = std::min(len, (u32)c.size() - ofs); j < je; ++j) c[j + ofs] += cs[i][j];
  }
  c.resize(ans_size);
  return c;
}
template <class NTT_t, std::same_as<typename NTT_t::data_t> mint, class T = u64>
constexpr vec<mint> conv_ntt_large_u64(NTT_t &ntt, vec<T> const &l, vec<T> const &r, u32 ans_size = 0) {
  if (!ans_size) ans_size = u32(l.size() + r.size() - 1);
  vec<mint> l_, r_;
  l_.reserve(l.size());
  r_.reserve(r.size());
  for (auto i : l) l_.push_back(i);
  for (auto i : r) r_.push_back(i);
  return conv_ntt_large(ntt, l_, r_, ans_size);
}

}  // namespace tifa_libs::math


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