verify/verify-unit-test/strassen.test.cpp

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Last update: 2023-08-10 14:06:55+09:00
Problem: https://judge.yosupo.jp/problem/aplusb

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Code

#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#include "../../template/template.hpp"
//
#include "../../modulo/strassen.hpp"

namespace FastMatProd {
// for debug
template <typename fps>
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) vector<fps>
naive_mul(const vector<fps>& _a, const vector<fps>& _b) {
  int n = _a.size(), m = _b[0].size(), p = _b.size();
  assert(p == (int)_a[0].size());
  vector<fps> _c(n, fps(m, 0));
  for (int i = 0; i < n; i++)
    for (int k = 0; k < p; k++)
      for (int j = 0; j < m; j++) _c[i][j] += _a[i][k] * _b[k][j];
  return _c;
}

}  // namespace FastMatProd

#include "../../misc/rng.hpp"
#include "../../misc/timer.hpp"

using namespace FastMatProd;
using fps = vector<mint>;

void time_test() {
  int N = 1024;
  int P = N, M = N;
  vector<fps> s(N, fps(P)), t(P, fps(M));
  for (int i = 0; i < N; i++)
    for (int j = 0; j < P; j++) s[i][j] = rng() % 998244353;
  for (int i = 0; i < P; i++)
    for (int j = 0; j < M; j++) t[i][j] = rng() % 998244353;
  vector<fps> u, u2, u3;
  Timer timer;

  int loop = 5;
  timer.reset();
  for (int i = 0; i < loop; i++) u = FastMatProd::strassen(s, t);
  cerr << "strassen " << (timer.elapsed() / loop) << endl;

  timer.reset();
  u2 = FastMatProd::naive_mul(s, t);
  cerr << "naive " << timer.elapsed() << endl;

  timer.reset();
  for (int i = 0; i < loop; i++) u3 = FastMatProd::block_dec(s, t);
  cerr << "block dec " << (timer.elapsed() / loop) << endl;

  assert(u == u2);
  assert(u == u3);
}

void debug_test(int max = 500, int loop = 10) {
  int N, P, M;
  mt19937 rng(58);
  while (loop--) {
    N = rng() % max + 1;
    M = rng() % max + 1;
    P = rng() % max + 1;
    vector<fps> s(N, fps(P)), t(P, fps(M));
    for (int i = 0; i < N; i++)
      for (int j = 0; j < P; j++) s[i][j] = rng() % 998244353;
    for (int i = 0; i < P; i++)
      for (int j = 0; j < M; j++) t[i][j] = rng() % 998244353;
    auto u = strassen(s, t);
    auto u2 = naive_mul(s, t);
    auto u3 = block_dec(s, t);
    if (u != u2) {
      cerr << "ng u1 " << N << " " << P << " " << M << endl;
      exit(1);
    } else if (u != u3) {
      cerr << "ng u1 " << N << " " << P << " " << M << endl;
      exit(1);
    } 
  }
  cerr << "all ok" << endl;
}

void Nyaan::solve() {
  debug_test();
  debug_test(32, 2000);
  time_test();

  int a, b;
  cin >> a >> b;
  cout << a + b << endl;
}

#line 1 "verify/verify-unit-test/strassen.test.cpp"
#define PROBLEM "https://judge.yosupo.jp/problem/aplusb"

#line 2 "template/template.hpp"
using namespace std;

// intrinstic
#include <immintrin.h>

#include <algorithm>
#include <array>
#include <bitset>
#include <cassert>
#include <cctype>
#include <cfenv>
#include <cfloat>
#include <chrono>
#include <cinttypes>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdarg>
#include <cstddef>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <deque>
#include <fstream>
#include <functional>
#include <initializer_list>
#include <iomanip>
#include <ios>
#include <iostream>
#include <istream>
#include <iterator>
#include <limits>
#include <list>
#include <map>
#include <memory>
#include <new>
#include <numeric>
#include <ostream>
#include <queue>
#include <random>
#include <set>
#include <sstream>
#include <stack>
#include <streambuf>
#include <string>
#include <tuple>
#include <type_traits>
#include <typeinfo>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

// utility
#line 1 "template/util.hpp"
namespace Nyaan {
using ll = long long;
using i64 = long long;
using u64 = unsigned long long;
using i128 = __int128_t;
using u128 = __uint128_t;

template <typename T>
using V = vector<T>;
template <typename T>
using VV = vector<vector<T>>;
using vi = vector<int>;
using vl = vector<long long>;
using vd = V<double>;
using vs = V<string>;
using vvi = vector<vector<int>>;
using vvl = vector<vector<long long>>;
template <typename T>
using minpq = priority_queue<T, vector<T>, greater<T>>;

template <typename T, typename U>
struct P : pair<T, U> {
  template <typename... Args>
  P(Args... args) : pair<T, U>(args...) {}

  using pair<T, U>::first;
  using pair<T, U>::second;

  P &operator+=(const P &r) {
    first += r.first;
    second += r.second;
    return *this;
  }
  P &operator-=(const P &r) {
    first -= r.first;
    second -= r.second;
    return *this;
  }
  P &operator*=(const P &r) {
    first *= r.first;
    second *= r.second;
    return *this;
  }
  template <typename S>
  P &operator*=(const S &r) {
    first *= r, second *= r;
    return *this;
  }
  P operator+(const P &r) const { return P(*this) += r; }
  P operator-(const P &r) const { return P(*this) -= r; }
  P operator*(const P &r) const { return P(*this) *= r; }
  template <typename S>
  P operator*(const S &r) const {
    return P(*this) *= r;
  }
  P operator-() const { return P{-first, -second}; }
};

using pl = P<ll, ll>;
using pi = P<int, int>;
using vp = V<pl>;

constexpr int inf = 1001001001;
constexpr long long infLL = 4004004004004004004LL;

template <typename T>
int sz(const T &t) {
  return t.size();
}

template <typename T, typename U>
inline bool amin(T &x, U y) {
  return (y < x) ? (x = y, true) : false;
}
template <typename T, typename U>
inline bool amax(T &x, U y) {
  return (x < y) ? (x = y, true) : false;
}

template <typename T>
inline T Max(const vector<T> &v) {
  return *max_element(begin(v), end(v));
}
template <typename T>
inline T Min(const vector<T> &v) {
  return *min_element(begin(v), end(v));
}
template <typename T>
inline long long Sum(const vector<T> &v) {
  return accumulate(begin(v), end(v), 0LL);
}

template <typename T>
int lb(const vector<T> &v, const T &a) {
  return lower_bound(begin(v), end(v), a) - begin(v);
}
template <typename T>
int ub(const vector<T> &v, const T &a) {
  return upper_bound(begin(v), end(v), a) - begin(v);
}

constexpr long long TEN(int n) {
  long long ret = 1, x = 10;
  for (; n; x *= x, n >>= 1) ret *= (n & 1 ? x : 1);
  return ret;
}

template <typename T, typename U>
pair<T, U> mkp(const T &t, const U &u) {
  return make_pair(t, u);
}

template <typename T>
vector<T> mkrui(const vector<T> &v, bool rev = false) {
  vector<T> ret(v.size() + 1);
  if (rev) {
    for (int i = int(v.size()) - 1; i >= 0; i--) ret[i] = v[i] + ret[i + 1];
  } else {
    for (int i = 0; i < int(v.size()); i++) ret[i + 1] = ret[i] + v[i];
  }
  return ret;
};

template <typename T>
vector<T> mkuni(const vector<T> &v) {
  vector<T> ret(v);
  sort(ret.begin(), ret.end());
  ret.erase(unique(ret.begin(), ret.end()), ret.end());
  return ret;
}

template <typename F>
vector<int> mkord(int N, F f) {
  vector<int> ord(N);
  iota(begin(ord), end(ord), 0);
  sort(begin(ord), end(ord), f);
  return ord;
}

template <typename T>
vector<int> mkinv(vector<T> &v) {
  int max_val = *max_element(begin(v), end(v));
  vector<int> inv(max_val + 1, -1);
  for (int i = 0; i < (int)v.size(); i++) inv[v[i]] = i;
  return inv;
}

vector<int> mkiota(int n) {
  vector<int> ret(n);
  iota(begin(ret), end(ret), 0);
  return ret;
}

template <typename T>
T mkrev(const T &v) {
  T w{v};
  reverse(begin(w), end(w));
  return w;
}

template <typename T>
bool nxp(vector<T> &v) {
  return next_permutation(begin(v), end(v));
}

// 返り値の型は入力の T に依存
// i 要素目 : [0, a[i])
template <typename T>
vector<vector<T>> product(const vector<T> &a) {
  vector<vector<T>> ret;
  vector<T> v;
  auto dfs = [&](auto rc, int i) -> void {
    if (i == (int)a.size()) {
      ret.push_back(v);
      return;
    }
    for (int j = 0; j < a[i]; j++) v.push_back(j), rc(rc, i + 1), v.pop_back();
  };
  dfs(dfs, 0);
  return ret;
}

// F : function(void(T&)), mod を取る操作
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I, const function<void(T &)> &f) {
  T res = I;
  for (; n; f(a = a * a), n >>= 1) {
    if (n & 1) f(res = res * a);
  }
  return res;
}
// T : 整数型のときはオーバーフローに注意する
template <typename T>
T Power(T a, long long n, const T &I) {
  return Power(a, n, I, function<void(T &)>{[](T &) -> void {}});
}

}  // namespace Nyaan
#line 58 "template/template.hpp"

// bit operation
#line 1 "template/bitop.hpp"
namespace Nyaan {
__attribute__((target("popcnt"))) inline int popcnt(const u64 &a) {
  return _mm_popcnt_u64(a);
}
inline int lsb(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int ctz(const u64 &a) { return a ? __builtin_ctzll(a) : 64; }
inline int msb(const u64 &a) { return a ? 63 - __builtin_clzll(a) : -1; }
template <typename T>
inline int gbit(const T &a, int i) {
  return (a >> i) & 1;
}
template <typename T>
inline void sbit(T &a, int i, bool b) {
  if (gbit(a, i) != b) a ^= T(1) << i;
}
constexpr long long PW(int n) { return 1LL << n; }
constexpr long long MSK(int n) { return (1LL << n) - 1; }
}  // namespace Nyaan
#line 61 "template/template.hpp"

// inout
#line 1 "template/inout.hpp"
namespace Nyaan {

template <typename T, typename U>
ostream &operator<<(ostream &os, const pair<T, U> &p) {
  os << p.first << " " << p.second;
  return os;
}
template <typename T, typename U>
istream &operator>>(istream &is, pair<T, U> &p) {
  is >> p.first >> p.second;
  return is;
}

template <typename T>
ostream &operator<<(ostream &os, const vector<T> &v) {
  int s = (int)v.size();
  for (int i = 0; i < s; i++) os << (i ? " " : "") << v[i];
  return os;
}
template <typename T>
istream &operator>>(istream &is, vector<T> &v) {
  for (auto &x : v) is >> x;
  return is;
}

istream &operator>>(istream &is, __int128_t &x) {
  string S;
  is >> S;
  x = 0;
  int flag = 0;
  for (auto &c : S) {
    if (c == '-') {
      flag = true;
      continue;
    }
    x *= 10;
    x += c - '0';
  }
  if (flag) x = -x;
  return is;
}

istream &operator>>(istream &is, __uint128_t &x) {
  string S;
  is >> S;
  x = 0;
  for (auto &c : S) {
    x *= 10;
    x += c - '0';
  }
  return is;
}

ostream &operator<<(ostream &os, __int128_t x) {
  if (x == 0) return os << 0;
  if (x < 0) os << '-', x = -x;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}
ostream &operator<<(ostream &os, __uint128_t x) {
  if (x == 0) return os << 0;
  string S;
  while (x) S.push_back('0' + x % 10), x /= 10;
  reverse(begin(S), end(S));
  return os << S;
}

void in() {}
template <typename T, class... U>
void in(T &t, U &...u) {
  cin >> t;
  in(u...);
}

void out() { cout << "\n"; }
template <typename T, class... U, char sep = ' '>
void out(const T &t, const U &...u) {
  cout << t;
  if (sizeof...(u)) cout << sep;
  out(u...);
}

struct IoSetupNya {
  IoSetupNya() {
    cin.tie(nullptr);
    ios::sync_with_stdio(false);
    cout << fixed << setprecision(15);
    cerr << fixed << setprecision(7);
  }
} iosetupnya;

}  // namespace Nyaan
#line 64 "template/template.hpp"

// debug
#line 1 "template/debug.hpp"
namespace DebugImpl {

template <typename U, typename = void>
struct is_specialize : false_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, typename U::iterator, void>::type>
    : true_type {};
template <typename U>
struct is_specialize<
    U, typename conditional<false, decltype(U::first), void>::type>
    : true_type {};
template <typename U>
struct is_specialize<U, enable_if_t<is_integral<U>::value, void>> : true_type {
};

void dump(const char& t) { cerr << t; }

void dump(const string& t) { cerr << t; }

void dump(const bool& t) { cerr << (t ? "true" : "false"); }

void dump(__int128_t t) {
  if (t == 0) cerr << 0;
  if (t < 0) cerr << '-', t = -t;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

void dump(__uint128_t t) {
  if (t == 0) cerr << 0;
  string S;
  while (t) S.push_back('0' + t % 10), t /= 10;
  reverse(begin(S), end(S));
  cerr << S;
}

template <typename U,
          enable_if_t<!is_specialize<U>::value, nullptr_t> = nullptr>
void dump(const U& t) {
  cerr << t;
}

template <typename T>
void dump(const T& t, enable_if_t<is_integral<T>::value>* = nullptr) {
  string res;
  if (t == Nyaan::inf) res = "inf";
  if constexpr (is_signed<T>::value) {
    if (t == -Nyaan::inf) res = "-inf";
  }
  if constexpr (sizeof(T) == 8) {
    if (t == Nyaan::infLL) res = "inf";
    if constexpr (is_signed<T>::value) {
      if (t == -Nyaan::infLL) res = "-inf";
    }
  }
  if (res.empty()) res = to_string(t);
  cerr << res;
}

template <typename T, typename U>
void dump(const pair<T, U>&);
template <typename T>
void dump(const pair<T*, int>&);

template <typename T>
void dump(const T& t,
          enable_if_t<!is_void<typename T::iterator>::value>* = nullptr) {
  cerr << "[ ";
  for (auto it = t.begin(); it != t.end();) {
    dump(*it);
    cerr << (++it == t.end() ? "" : ", ");
  }
  cerr << " ]";
}

template <typename T, typename U>
void dump(const pair<T, U>& t) {
  cerr << "( ";
  dump(t.first);
  cerr << ", ";
  dump(t.second);
  cerr << " )";
}

template <typename T>
void dump(const pair<T*, int>& t) {
  cerr << "[ ";
  for (int i = 0; i < t.second; i++) {
    dump(t.first[i]);
    cerr << (i == t.second - 1 ? "" : ", ");
  }
  cerr << " ]";
}

void trace() { cerr << endl; }
template <typename Head, typename... Tail>
void trace(Head&& head, Tail&&... tail) {
  cerr << " ";
  dump(head);
  if (sizeof...(tail) != 0) cerr << ",";
  trace(forward<Tail>(tail)...);
}

}  // namespace DebugImpl

#ifdef NyaanDebug
#define trc(...)                            \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc(...) (void(0))
#endif

#ifdef NyaanLocal
#define trc2(...)                           \
  do {                                      \
    cerr << "## " << #__VA_ARGS__ << " = "; \
    DebugImpl::trace(__VA_ARGS__);          \
  } while (0)
#else
#define trc2(...) (void(0))
#endif
#line 67 "template/template.hpp"

// macro
#line 1 "template/macro.hpp"
#define each(x, v) for (auto&& x : v)
#define each2(x, y, v) for (auto&& [x, y] : v)
#define all(v) (v).begin(), (v).end()
#define rep(i, N) for (long long i = 0; i < (long long)(N); i++)
#define repr(i, N) for (long long i = (long long)(N)-1; i >= 0; i--)
#define rep1(i, N) for (long long i = 1; i <= (long long)(N); i++)
#define repr1(i, N) for (long long i = (N); (long long)(i) > 0; i--)
#define reg(i, a, b) for (long long i = (a); i < (b); i++)
#define regr(i, a, b) for (long long i = (b)-1; i >= (a); i--)
#define fi first
#define se second
#define ini(...)   \
  int __VA_ARGS__; \
  in(__VA_ARGS__)
#define inl(...)         \
  long long __VA_ARGS__; \
  in(__VA_ARGS__)
#define ins(...)      \
  string __VA_ARGS__; \
  in(__VA_ARGS__)
#define in2(s, t)                           \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i]);                         \
  }
#define in3(s, t, u)                        \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i]);                   \
  }
#define in4(s, t, u, v)                     \
  for (int i = 0; i < (int)s.size(); i++) { \
    in(s[i], t[i], u[i], v[i]);             \
  }
#define die(...)             \
  do {                       \
    Nyaan::out(__VA_ARGS__); \
    return;                  \
  } while (0)
#line 70 "template/template.hpp"

namespace Nyaan {
void solve();
}
int main() { Nyaan::solve(); }
#line 4 "verify/verify-unit-test/strassen.test.cpp"
//
#line 3 "modulo/strassen.hpp"
//

#line 2 "modint/montgomery-modint.hpp"

template <uint32_t mod>
struct LazyMontgomeryModInt {
  using mint = LazyMontgomeryModInt;
  using i32 = int32_t;
  using u32 = uint32_t;
  using u64 = uint64_t;

  static constexpr u32 get_r() {
    u32 ret = mod;
    for (i32 i = 0; i < 4; ++i) ret *= 2 - mod * ret;
    return ret;
  }

  static constexpr u32 r = get_r();
  static constexpr u32 n2 = -u64(mod) % mod;
  static_assert(mod < (1 << 30), "invalid, mod >= 2 ^ 30");
  static_assert((mod & 1) == 1, "invalid, mod % 2 == 0");
  static_assert(r * mod == 1, "this code has bugs.");

  u32 a;

  constexpr LazyMontgomeryModInt() : a(0) {}
  constexpr LazyMontgomeryModInt(const int64_t &b)
      : a(reduce(u64(b % mod + mod) * n2)){};

  static constexpr u32 reduce(const u64 &b) {
    return (b + u64(u32(b) * u32(-r)) * mod) >> 32;
  }

  constexpr mint &operator+=(const mint &b) {
    if (i32(a += b.a - 2 * mod) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator-=(const mint &b) {
    if (i32(a -= b.a) < 0) a += 2 * mod;
    return *this;
  }

  constexpr mint &operator*=(const mint &b) {
    a = reduce(u64(a) * b.a);
    return *this;
  }

  constexpr mint &operator/=(const mint &b) {
    *this *= b.inverse();
    return *this;
  }

  constexpr mint operator+(const mint &b) const { return mint(*this) += b; }
  constexpr mint operator-(const mint &b) const { return mint(*this) -= b; }
  constexpr mint operator*(const mint &b) const { return mint(*this) *= b; }
  constexpr mint operator/(const mint &b) const { return mint(*this) /= b; }
  constexpr bool operator==(const mint &b) const {
    return (a >= mod ? a - mod : a) == (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr bool operator!=(const mint &b) const {
    return (a >= mod ? a - mod : a) != (b.a >= mod ? b.a - mod : b.a);
  }
  constexpr mint operator-() const { return mint() - mint(*this); }
  constexpr mint operator+() const { return mint(*this); }

  constexpr mint pow(u64 n) const {
    mint ret(1), mul(*this);
    while (n > 0) {
      if (n & 1) ret *= mul;
      mul *= mul;
      n >>= 1;
    }
    return ret;
  }

  constexpr mint inverse() const {
    int x = get(), y = mod, u = 1, v = 0, t = 0, tmp = 0;
    while (y > 0) {
      t = x / y;
      x -= t * y, u -= t * v;
      tmp = x, x = y, y = tmp;
      tmp = u, u = v, v = tmp;
    }
    return mint{u};
  }

  friend ostream &operator<<(ostream &os, const mint &b) {
    return os << b.get();
  }

  friend istream &operator>>(istream &is, mint &b) {
    int64_t t;
    is >> t;
    b = LazyMontgomeryModInt<mod>(t);
    return (is);
  }

  constexpr u32 get() const {
    u32 ret = reduce(a);
    return ret >= mod ? ret - mod : ret;
  }

  static constexpr u32 get_mod() { return mod; }
};
#line 2 "modint/simd-montgomery.hpp"

#line 4 "modint/simd-montgomery.hpp"

__attribute__((target("sse4.2"))) inline __m128i my128_mullo_epu32(
    const __m128i &a, const __m128i &b) {
  return _mm_mullo_epi32(a, b);
}

__attribute__((target("sse4.2"))) inline __m128i my128_mulhi_epu32(
    const __m128i &a, const __m128i &b) {
  __m128i a13 = _mm_shuffle_epi32(a, 0xF5);
  __m128i b13 = _mm_shuffle_epi32(b, 0xF5);
  __m128i prod02 = _mm_mul_epu32(a, b);
  __m128i prod13 = _mm_mul_epu32(a13, b13);
  __m128i prod = _mm_unpackhi_epi64(_mm_unpacklo_epi32(prod02, prod13),
                                    _mm_unpackhi_epi32(prod02, prod13));
  return prod;
}

__attribute__((target("sse4.2"))) inline __m128i montgomery_mul_128(
    const __m128i &a, const __m128i &b, const __m128i &r, const __m128i &m1) {
  return _mm_sub_epi32(
      _mm_add_epi32(my128_mulhi_epu32(a, b), m1),
      my128_mulhi_epu32(my128_mullo_epu32(my128_mullo_epu32(a, b), r), m1));
}

__attribute__((target("sse4.2"))) inline __m128i montgomery_add_128(
    const __m128i &a, const __m128i &b, const __m128i &m2, const __m128i &m0) {
  __m128i ret = _mm_sub_epi32(_mm_add_epi32(a, b), m2);
  return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}

__attribute__((target("sse4.2"))) inline __m128i montgomery_sub_128(
    const __m128i &a, const __m128i &b, const __m128i &m2, const __m128i &m0) {
  __m128i ret = _mm_sub_epi32(a, b);
  return _mm_add_epi32(_mm_and_si128(_mm_cmpgt_epi32(m0, ret), m2), ret);
}

__attribute__((target("avx2"))) inline __m256i my256_mullo_epu32(
    const __m256i &a, const __m256i &b) {
  return _mm256_mullo_epi32(a, b);
}

__attribute__((target("avx2"))) inline __m256i my256_mulhi_epu32(
    const __m256i &a, const __m256i &b) {
  __m256i a13 = _mm256_shuffle_epi32(a, 0xF5);
  __m256i b13 = _mm256_shuffle_epi32(b, 0xF5);
  __m256i prod02 = _mm256_mul_epu32(a, b);
  __m256i prod13 = _mm256_mul_epu32(a13, b13);
  __m256i prod = _mm256_unpackhi_epi64(_mm256_unpacklo_epi32(prod02, prod13),
                                       _mm256_unpackhi_epi32(prod02, prod13));
  return prod;
}

__attribute__((target("avx2"))) inline __m256i montgomery_mul_256(
    const __m256i &a, const __m256i &b, const __m256i &r, const __m256i &m1) {
  return _mm256_sub_epi32(
      _mm256_add_epi32(my256_mulhi_epu32(a, b), m1),
      my256_mulhi_epu32(my256_mullo_epu32(my256_mullo_epu32(a, b), r), m1));
}

__attribute__((target("avx2"))) inline __m256i montgomery_add_256(
    const __m256i &a, const __m256i &b, const __m256i &m2, const __m256i &m0) {
  __m256i ret = _mm256_sub_epi32(_mm256_add_epi32(a, b), m2);
  return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
                          ret);
}

__attribute__((target("avx2"))) inline __m256i montgomery_sub_256(
    const __m256i &a, const __m256i &b, const __m256i &m2, const __m256i &m0) {
  __m256i ret = _mm256_sub_epi32(a, b);
  return _mm256_add_epi32(_mm256_and_si256(_mm256_cmpgt_epi32(m0, ret), m2),
                          ret);
}
#line 7 "modulo/strassen.hpp"

namespace FastMatProd {

using mint = LazyMontgomeryModInt<998244353>;
using u32 = uint32_t;
using i32 = int32_t;
using u64 = uint64_t;
using m256 = __m256i;

constexpr u32 SHIFT_ = 6;
u32 a[1 << (SHIFT_ * 2)] __attribute__((aligned(64)));
u32 b[1 << (SHIFT_ * 2)] __attribute__((aligned(64)));
u32 c[1 << (SHIFT_ * 2)] __attribute__((aligned(64)));

__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline m256
normalize_m256(const m256& x, const m256& M1) {
  m256 CMP = _mm256_cmpgt_epi32(x, M1);
  return _mm256_sub_epi32(x, _mm256_and_si256(CMP, M1));
}

__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline m256
simd_mulhi(const m256& _a, const m256& _b) {
  m256 a13 = _mm256_shuffle_epi32(_a, 0xF5);
  m256 b13 = _mm256_shuffle_epi32(_b, 0xF5);
  m256 prod02 = _mm256_mul_epu32(_a, _b);
  m256 prod13 = _mm256_mul_epu32(a13, b13);
  m256 unpalo = _mm256_unpacklo_epi32(prod02, prod13);
  m256 unpahi = _mm256_unpackhi_epi32(prod02, prod13);
  m256 prod = _mm256_unpackhi_epi64(unpalo, unpahi);
  return prod;
}

__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline m256
simd_reduct(const m256& prod02, const m256& prod13, const m256& R,
            const m256& M1) {
  m256 unpalo = _mm256_unpacklo_epi32(prod02, prod13);
  m256 unpahi = _mm256_unpackhi_epi32(prod02, prod13);
  m256 prodlo = _mm256_unpacklo_epi64(unpalo, unpahi);
  m256 prodhi = _mm256_unpackhi_epi64(unpalo, unpahi);
  m256 hiplm1 = _mm256_add_epi32(prodhi, M1);
  m256 lomulr = _mm256_mullo_epi32(prodlo, R);
  m256 lomulrmulm1 = simd_mulhi(lomulr, M1);
  return _mm256_sub_epi32(hiplm1, lomulrmulm1);
}

__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline m256
mul4(const m256& A00, const m256& A01, const m256& A02, const m256& A03,
     const m256& B00, const m256& B10, const m256& B20, const m256& B30,
     const m256& R, const m256& M1) {
  const m256 A00n = normalize_m256(A00, M1);
  const m256 A01n = normalize_m256(A01, M1);
  const m256 A02n = normalize_m256(A02, M1);
  const m256 A03n = normalize_m256(A03, M1);
  const m256 B00n = normalize_m256(B00, M1);
  const m256 B10n = normalize_m256(B10, M1);
  const m256 B20n = normalize_m256(B20, M1);
  const m256 B30n = normalize_m256(B30, M1);

  m256 a013 = _mm256_shuffle_epi32(A00n, 0xF5);
  m256 b013 = _mm256_shuffle_epi32(B00n, 0xF5);
  m256 a113 = _mm256_shuffle_epi32(A01n, 0xF5);
  m256 b113 = _mm256_shuffle_epi32(B10n, 0xF5);
  m256 a213 = _mm256_shuffle_epi32(A02n, 0xF5);
  m256 b213 = _mm256_shuffle_epi32(B20n, 0xF5);
  m256 a313 = _mm256_shuffle_epi32(A03n, 0xF5);
  m256 b313 = _mm256_shuffle_epi32(B30n, 0xF5);
  m256 p0_02 = _mm256_mul_epu32(A00n, B00n);
  m256 p0_13 = _mm256_mul_epu32(a013, b013);
  m256 p1_02 = _mm256_mul_epu32(A01n, B10n);
  m256 p1_13 = _mm256_mul_epu32(a113, b113);
  m256 p2_02 = _mm256_mul_epu32(A02n, B20n);
  m256 p2_13 = _mm256_mul_epu32(a213, b213);
  m256 p3_02 = _mm256_mul_epu32(A03n, B30n);
  m256 p3_13 = _mm256_mul_epu32(a313, b313);
  m256 p02_02 = _mm256_add_epi64(p0_02, p2_02);
  m256 p13_02 = _mm256_add_epi64(p1_02, p3_02);
  m256 prod02 = _mm256_add_epi64(p02_02, p13_02);
  m256 p02_13 = _mm256_add_epi64(p0_13, p2_13);
  m256 p13_13 = _mm256_add_epi64(p1_13, p3_13);
  m256 prod13 = _mm256_add_epi64(p02_13, p13_13);
  return simd_reduct(prod02, prod13, R, M1);
}

__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
inner_simd_mul(u32 n, u32 m, u32 p) {
  memset(c, 0, sizeof(c));
  const m256 R = _mm256_set1_epi32(mint::r);
  const m256 M0 = _mm256_set1_epi32(0);
  const m256 M1 = _mm256_set1_epi32(mint::get_mod());
  const m256 M2 = _mm256_set1_epi32(mint::get_mod() << 1);

  u32 k0 = 0;
  for (; i32(k0) < i32(p) - 3; k0 += 4) {
    const u32 k1 = k0 + 1;
    const u32 k2 = k0 + 2;
    const u32 k3 = k0 + 3;
    u32 j0 = 0;
    for (; i32(j0) < i32(m) - 7; j0 += 8) {
      const m256 B00 = _mm256_load_si256((m256*)(b + (k0 << SHIFT_) + j0));
      const m256 B10 = _mm256_load_si256((m256*)(b + (k1 << SHIFT_) + j0));
      const m256 B20 = _mm256_load_si256((m256*)(b + (k2 << SHIFT_) + j0));
      const m256 B30 = _mm256_load_si256((m256*)(b + (k3 << SHIFT_) + j0));
      for (u32 i0 = 0; i0 < n; ++i0) {
        const m256 A00 = _mm256_set1_epi32(a[(i0 << SHIFT_) | k0]);
        const m256 A01 = _mm256_set1_epi32(a[(i0 << SHIFT_) | k1]);
        const m256 A02 = _mm256_set1_epi32(a[(i0 << SHIFT_) | k2]);
        const m256 A03 = _mm256_set1_epi32(a[(i0 << SHIFT_) | k3]);
        const u32* pc00 = c + (i0 << SHIFT_) + j0;
        const m256 C00 = _mm256_load_si256((m256*)pc00);
        const m256 C00_ad = mul4(A00, A01, A02, A03, B00, B10, B20, B30, R, M1);
        const m256 C00sum = montgomery_add_256(C00, C00_ad, M2, M0);
        _mm256_store_si256((m256*)pc00, C00sum);
      }
    }
    for (; j0 < m; j0++) {
      for (u32 i0 = 0; i0 < n; ++i0) {
        u32 ab0 =
            mint::reduce(u64(a[(i0 << SHIFT_) | k0]) * b[(k0 << SHIFT_) | j0]);
        u32 ab1 =
            mint::reduce(u64(a[(i0 << SHIFT_) | k1]) * b[(k1 << SHIFT_) | j0]);
        u32 ab2 =
            mint::reduce(u64(a[(i0 << SHIFT_) | k2]) * b[(k2 << SHIFT_) | j0]);
        u32 ab3 =
            mint::reduce(u64(a[(i0 << SHIFT_) | k3]) * b[(k3 << SHIFT_) | j0]);
        if ((ab0 += ab1) >= 2 * mint::get_mod()) ab0 -= 2 * mint::get_mod();
        if ((ab2 += ab3) >= 2 * mint::get_mod()) ab2 -= 2 * mint::get_mod();
        if ((ab0 += ab2) >= 2 * mint::get_mod()) ab0 -= 2 * mint::get_mod();
        if ((c[(i0 << SHIFT_) | j0] += ab0) >= 2 * mint::get_mod())
          c[(i0 << SHIFT_) | j0] -= 2 * mint::get_mod();
      }
    }
  }

  for (; k0 < p; k0++) {
    u32 j0 = 0;
    for (; i32(j0) < i32(m) - 7; j0 += 8) {
      const m256 B00 = _mm256_load_si256((m256*)(b + (k0 << SHIFT_) + j0));
      for (u32 i0 = 0; i0 < n; ++i0) {
        const m256 A00 = _mm256_set1_epi32(a[(i0 << SHIFT_) | k0]);
        const m256 A00B00 = montgomery_mul_256(A00, B00, R, M1);
        const u32* pc00 = c + (i0 << SHIFT_) + j0;
        const m256 C00 = _mm256_load_si256((m256*)pc00);
        const m256 C00_ad = montgomery_add_256(C00, A00B00, M2, M0);
        _mm256_store_si256((m256*)pc00, C00_ad);
      }
    }
    for (; j0 < m; j0++) {
      for (u32 i0 = 0; i0 < n; ++i0) {
        u32 ab0 =
            mint::reduce(u64(a[(i0 << SHIFT_) | k0]) * b[(k0 << SHIFT_) | j0]);
        if ((c[(i0 << SHIFT_) | j0] += ab0) >= 2 * mint::get_mod())
          c[(i0 << SHIFT_) | j0] -= 2 * mint::get_mod();
      }
    }
  }
}

struct Mat {
  int H, W, HM, WM;
  mint* a;

  Mat(int H_, int W_, mint* a_) : H(H_), W(W_), a(a_) {
    HM = (H >> 1) + (H & 1);
    WM = (W >> 1) + (W & 1);
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
  range_add(mint* _b, int as, int ae, int bs) const {
    const m256 M0 = _mm256_set1_epi32(0);
    const m256 M2 = _mm256_set1_epi32(mint::get_mod() * 2);
    for (; as < ae - 31; as += 32, bs += 32) {
      int a0 = as;
      int a1 = as + 8;
      int a2 = as + 16;
      int a3 = as + 24;
      int b0 = bs;
      int b1 = bs + 8;
      int b2 = bs + 16;
      int b3 = bs + 24;
      const m256 A0 = _mm256_loadu_si256((m256*)(a + a0));
      const m256 A1 = _mm256_loadu_si256((m256*)(a + a1));
      const m256 A2 = _mm256_loadu_si256((m256*)(a + a2));
      const m256 A3 = _mm256_loadu_si256((m256*)(a + a3));
      const m256 B0 = _mm256_loadu_si256((m256*)(_b + b0));
      const m256 B1 = _mm256_loadu_si256((m256*)(_b + b1));
      const m256 B2 = _mm256_loadu_si256((m256*)(_b + b2));
      const m256 B3 = _mm256_loadu_si256((m256*)(_b + b3));
      const m256 BA0 = montgomery_add_256(B0, A0, M2, M0);
      const m256 BA1 = montgomery_add_256(B1, A1, M2, M0);
      const m256 BA2 = montgomery_add_256(B2, A2, M2, M0);
      const m256 BA3 = montgomery_add_256(B3, A3, M2, M0);
      _mm256_storeu_si256((m256*)(_b + b0), BA0);
      _mm256_storeu_si256((m256*)(_b + b1), BA1);
      _mm256_storeu_si256((m256*)(_b + b2), BA2);
      _mm256_storeu_si256((m256*)(_b + b3), BA3);
    }
    for (; as < ae; ++as, ++bs) _b[bs] += a[as];
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
  range_sub(mint* _b, int as, int ae, int bs) const {
    const m256 M0 = _mm256_set1_epi32(0);
    const m256 M2 = _mm256_set1_epi32(mint::get_mod() * 2);
    for (; as < ae - 31; as += 32, bs += 32) {
      int a0 = as;
      int a1 = as + 8;
      int a2 = as + 16;
      int a3 = as + 24;
      int b0 = bs;
      int b1 = bs + 8;
      int b2 = bs + 16;
      int b3 = bs + 24;
      const m256 A0 = _mm256_loadu_si256((m256*)(a + a0));
      const m256 A1 = _mm256_loadu_si256((m256*)(a + a1));
      const m256 A2 = _mm256_loadu_si256((m256*)(a + a2));
      const m256 A3 = _mm256_loadu_si256((m256*)(a + a3));
      const m256 B0 = _mm256_loadu_si256((m256*)(_b + b0));
      const m256 B1 = _mm256_loadu_si256((m256*)(_b + b1));
      const m256 B2 = _mm256_loadu_si256((m256*)(_b + b2));
      const m256 B3 = _mm256_loadu_si256((m256*)(_b + b3));
      const m256 BA0 = montgomery_sub_256(B0, A0, M2, M0);
      const m256 BA1 = montgomery_sub_256(B1, A1, M2, M0);
      const m256 BA2 = montgomery_sub_256(B2, A2, M2, M0);
      const m256 BA3 = montgomery_sub_256(B3, A3, M2, M0);
      _mm256_storeu_si256((m256*)(_b + b0), BA0);
      _mm256_storeu_si256((m256*)(_b + b1), BA1);
      _mm256_storeu_si256((m256*)(_b + b2), BA2);
      _mm256_storeu_si256((m256*)(_b + b3), BA3);
    }
    for (; as < ae; ++as, ++bs) _b[bs] -= a[as];
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
  op_range_add(mint* _b, int as, int ae, int bs) const {
    const m256 M0 = _mm256_set1_epi32(0);
    const m256 M2 = _mm256_set1_epi32(mint::get_mod() * 2);
    for (; as < ae - 31; as += 32, bs += 32) {
      int a0 = as;
      int a1 = as + 8;
      int a2 = as + 16;
      int a3 = as + 24;
      int b0 = bs;
      int b1 = bs + 8;
      int b2 = bs + 16;
      int b3 = bs + 24;
      const m256 A0 = _mm256_loadu_si256((m256*)(a + a0));
      const m256 A1 = _mm256_loadu_si256((m256*)(a + a1));
      const m256 A2 = _mm256_loadu_si256((m256*)(a + a2));
      const m256 A3 = _mm256_loadu_si256((m256*)(a + a3));
      const m256 B0 = _mm256_loadu_si256((m256*)(_b + b0));
      const m256 B1 = _mm256_loadu_si256((m256*)(_b + b1));
      const m256 B2 = _mm256_loadu_si256((m256*)(_b + b2));
      const m256 B3 = _mm256_loadu_si256((m256*)(_b + b3));
      const m256 BA0 = montgomery_add_256(B0, A0, M2, M0);
      const m256 BA1 = montgomery_add_256(B1, A1, M2, M0);
      const m256 BA2 = montgomery_add_256(B2, A2, M2, M0);
      const m256 BA3 = montgomery_add_256(B3, A3, M2, M0);
      _mm256_storeu_si256((m256*)(a + a0), BA0);
      _mm256_storeu_si256((m256*)(a + a1), BA1);
      _mm256_storeu_si256((m256*)(a + a2), BA2);
      _mm256_storeu_si256((m256*)(a + a3), BA3);
    }
    for (; as < ae; ++as, ++bs) a[as] += _b[bs];
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
  op_range_sub(mint* _b, int as, int ae, int bs) const {
    const m256 M0 = _mm256_set1_epi32(0);
    const m256 M2 = _mm256_set1_epi32(mint::get_mod() * 2);
    for (; as < ae - 31; as += 32, bs += 32) {
      int a0 = as;
      int a1 = as + 8;
      int a2 = as + 16;
      int a3 = as + 24;
      int b0 = bs;
      int b1 = bs + 8;
      int b2 = bs + 16;
      int b3 = bs + 24;
      const m256 A0 = _mm256_loadu_si256((m256*)(a + a0));
      const m256 A1 = _mm256_loadu_si256((m256*)(a + a1));
      const m256 A2 = _mm256_loadu_si256((m256*)(a + a2));
      const m256 A3 = _mm256_loadu_si256((m256*)(a + a3));
      const m256 B0 = _mm256_loadu_si256((m256*)(_b + b0));
      const m256 B1 = _mm256_loadu_si256((m256*)(_b + b1));
      const m256 B2 = _mm256_loadu_si256((m256*)(_b + b2));
      const m256 B3 = _mm256_loadu_si256((m256*)(_b + b3));
      const m256 BA0 = montgomery_sub_256(A0, B0, M2, M0);
      const m256 BA1 = montgomery_sub_256(A1, B1, M2, M0);
      const m256 BA2 = montgomery_sub_256(A2, B2, M2, M0);
      const m256 BA3 = montgomery_sub_256(A3, B3, M2, M0);
      _mm256_storeu_si256((m256*)(a + a0), BA0);
      _mm256_storeu_si256((m256*)(a + a1), BA1);
      _mm256_storeu_si256((m256*)(a + a2), BA2);
      _mm256_storeu_si256((m256*)(a + a3), BA3);
    }
    for (; as < ae; ++as, ++bs) a[as] -= _b[bs];
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  A11(mint* _b) const {
    for (int i = 0; i < HM; i++)
      memcpy(_b + i * WM, a + i * W, WM * sizeof(int));
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  A12(mint* _b) const {
    for (int i = 0; i < HM; i++)
      memcpy(_b + i * WM, a + i * W + WM, (W - WM) * sizeof(int));
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  A21(mint* _b) const {
    for (int i = 0; i < H - HM; i++)
      memcpy(_b + i * WM, a + (i + HM) * W, WM * sizeof(int));
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  A22(mint* _b) const {
    for (int i = 0; i < H - HM; i++)
      memcpy(_b + i * WM, a + (i + HM) * W + WM, (W - WM) * sizeof(int));
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  subA11(mint* _b) const {
    for (int i = 0; i < HM; i++) {
      int as = i * W;
      int ae = i * W + WM;
      int bs = i * WM;
      range_sub(_b, as, ae, bs);
    }
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  addA12(mint* _b) const {
    for (int i = 0; i < HM; i++) {
      int as = i * W + WM;
      int ae = i * W + W;
      int bs = i * WM;
      range_add(_b, as, ae, bs);
    }
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  addA22(mint* _b) const {
    for (int i = 0; i < H - HM; i++) {
      int as = (i + HM) * W + WM;
      int ae = as + W - WM;
      int bs = i * WM;
      range_add(_b, as, ae, bs);
    }
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  subA22(mint* _b) const {
    for (int i = 0; i < H - HM; i++) {
      int as = (i + HM) * W + WM;
      int ae = as + W - WM;
      int bs = i * WM;
      range_sub(_b, as, ae, bs);
    }
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  updA11(mint* _b) const {
    for (int i = 0; i < HM; i++)
      memcpy(a + i * W, _b + i * WM, WM * sizeof(int));
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  updA12(mint* _b) const {
    for (int i = 0; i < HM; i++)
      memcpy(a + i * W + WM, _b + i * WM, (W - WM) * sizeof(int));
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  updA21(mint* _b) const {
    for (int i = 0; i < H - HM; i++)
      memcpy(a + (i + HM) * W, _b + i * WM, WM * sizeof(int));
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  updA22(mint* _b) const {
    for (int i = 0; i < H - HM; i++)
      memcpy(a + (i + HM) * W + WM, _b + i * WM, (W - WM) * sizeof(int));
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  opaddA11(mint* _b) const {
    for (int i = 0; i < HM; i++) {
      int as = i * W;
      int ae = i * W + WM;
      int bs = i * WM;
      op_range_add(_b, as, ae, bs);
    }
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  opaddA12(mint* _b) const {
    for (int i = 0; i < HM; i++) {
      int as = i * W + WM;
      int ae = i * W + W;
      int bs = i * WM;
      op_range_add(_b, as, ae, bs);
    }
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  opaddA21(mint* _b) const {
    for (int i = 0; i < H - HM; i++) {
      int as = (i + HM) * W;
      int ae = (i + HM) * W + WM;
      int bs = i * WM;
      op_range_add(_b, as, ae, bs);
    }
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  opaddA22(mint* _b) const {
    for (int i = 0; i < H - HM; i++) {
      int as = (i + HM) * W + WM;
      int ae = (i + HM) * W + W;
      int bs = i * WM;
      op_range_add(_b, as, ae, bs);
    }
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  opsubA11(mint* _b) const {
    for (int i = 0; i < HM; i++) {
      int as = i * W;
      int ae = i * W + WM;
      int bs = i * WM;
      op_range_sub(_b, as, ae, bs);
    }
  }

  __attribute__((target("avx2"), optimize("O3", "unroll-loops"))) inline void
  opsubA22(mint* _b) const {
    for (int i = 0; i < H - HM; i++) {
      int as = (i + HM) * W + WM;
      int ae = (i + HM) * W + W;
      int bs = i * WM;
      op_range_sub(_b, as, ae, bs);
    }
  }

  void dump() const {
    cerr << "[ " << endl << " ";
    for (int i = 0; i < H; i++)
      for (int j = 0; j < W; j++)
        cerr << a[i * W + j] << (j == W - 1 ? ",\n " : " ");
    cerr << "] " << endl;
  }
};

#ifndef BUFFER_SIZE
#define BUFFER_SIZE (1 << 23)
#endif
mint A[BUFFER_SIZE] __attribute__((aligned(64)));
mint B[BUFFER_SIZE] __attribute__((aligned(64)));
mint C[BUFFER_SIZE] __attribute__((aligned(64)));

__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
inner_fast_mul(const Mat* s, const Mat* t, const Mat* u) {
  int n = s->H, m = t->W, p = s->W;
  for (int i = 0; i < n; i++)
    memcpy((mint*)(a + (i << SHIFT_)), s->a + i * p, p * sizeof(int));
  for (int i = 0; i < p; i++)
    memcpy((mint*)(b + (i << SHIFT_)), t->a + i * m, m * sizeof(int));
  inner_simd_mul(n, m, p);
  for (int i = 0; i < n; i++)
    memcpy(u->a + i * m, (mint*)(c + (i << SHIFT_)), m * sizeof(int));
}

__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
inner_block_dec_mul(const Mat* s, const Mat* t, const Mat* u) {
  int n = s->H, m = t->W, p = s->W;
  memset((int*)(u->a), 0, n * m * sizeof(int));
  for (int is = 0; is < n; is += (1 << SHIFT_))
    for (int ks = 0; ks < p; ks += (1 << SHIFT_))
      for (int js = 0; js < m; js += (1 << SHIFT_)) {
        int ie = min(is + (1 << SHIFT_), n);
        int je = min(js + (1 << SHIFT_), m);
        int ke = min(ks + (1 << SHIFT_), p);
        for (int l = is; l < ie; l++)
          memcpy((mint*)(a + ((l - is) << SHIFT_)), s->a + l * p + ks,
                 (ke - ks) * sizeof(int));
        for (int l = ks; l < ke; l++)
          memcpy((mint*)(b + ((l - ks) << SHIFT_)), t->a + l * m + js,
                 (je - js) * sizeof(int));
        inner_simd_mul(ie - is, je - js, ke - ks);
        for (int l = is; l < ie; l++) {
          for (int ll = js; ll < je; ll++) {
            u->a[l * m + ll] +=
                *reinterpret_cast<mint*>(c + ((l - is) << SHIFT_) + (ll - js));
          }
        }
      }
}

__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) void
inner_strassen(const Mat* _a, const Mat* _b, const Mat* _c) {
  int n = _a->H, m = _b->W, p = _a->W;
  if (max({n, m, p}) <= (1 << SHIFT_)) {
    inner_fast_mul(_a, _b, _c);
    return;
  }
  if (min({n, m, p}) <= (1 << (SHIFT_ - 2))) {
    inner_block_dec_mul(_a, _b, _c);
    return;
  }
  int nm = n / 2 + (n & 1);
  int mm = m / 2 + (m & 1);
  int pm = p / 2 + (p & 1);

  Mat s(nm, pm, _a->a + n * p);
  Mat t(pm, mm, _b->a + p * m);
  Mat u(nm, mm, _c->a + n * m);

  // P1 = (A11 + A22) * (B11 + B22)
  _a->A11(s.a);
  _a->addA22(s.a);
  _b->A11(t.a);
  _b->addA22(t.a);
  inner_strassen(&s, &t, &u);
  _c->updA11(u.a);
  _c->updA22(u.a);

  // P2 = (A21 + A22) * B11
  memset((int*)s.a, 0, nm * pm * sizeof(int));
  _a->A21(s.a);
  _a->addA22(s.a);
  _b->A11(t.a);
  inner_strassen(&s, &t, &u);
  _c->updA21(u.a);
  _c->opsubA22(u.a);

  // P3 = A11 (B12 - B22)
  _a->A11(s.a);
  memset((int*)t.a, 0, pm * mm * sizeof(int));
  _b->A12(t.a);
  _b->subA22(t.a);
  inner_strassen(&s, &t, &u);
  _c->updA12(u.a);
  _c->opaddA22(u.a);

  // P4 = A22 (B21 - B11)
  memset((int*)s.a, 0, nm * pm * sizeof(int));
  _a->A22(s.a);
  memset((int*)t.a + (pm - 1) * mm, 0, mm * sizeof(int));
  _b->A21(t.a);
  _b->subA11(t.a);
  inner_strassen(&s, &t, &u);
  _c->opaddA11(u.a);
  _c->opaddA21(u.a);

  // P5 = (A11 + A12) B22
  memset((int*)t.a, 0, pm * mm * sizeof(int));
  _a->A11(s.a);
  _a->addA12(s.a);
  _b->A22(t.a);
  inner_strassen(&s, &t, &u);
  _c->opsubA11(u.a);
  _c->opaddA12(u.a);

  // P6 = (A21 - A11) (B11 + B12)
  memset((int*)s.a + (nm - 1) * pm, 0, pm * sizeof(int));
  _a->A21(s.a);
  _a->subA11(s.a);
  _b->A11(t.a);
  _b->addA12(t.a);
  inner_strassen(&s, &t, &u);
  _c->opaddA22(u.a);

  // P7 = (A12 - A22) (B21 + B22)
  memset((int*)s.a, 0, nm * pm * sizeof(int));
  _a->A12(s.a);
  _a->subA22(s.a);
  memset((int*)t.a + (pm - 1) * mm, 0, mm * sizeof(int));
  _b->A21(t.a);
  _b->addA22(t.a);
  inner_strassen(&s, &t, &u);
  _c->opaddA11(u.a);
}

template <typename fps>
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) vector<fps>
block_dec(const vector<fps>& s, const vector<fps>& t) {
  int n = s.size(), p = s[0].size(), m = t[0].size();
  assert(int(n * p * 1.4) <= BUFFER_SIZE);
  assert(int(p * m * 1.4) <= BUFFER_SIZE);
  assert(int(n * m * 1.4) <= BUFFER_SIZE);
  memset(A, 0, int(n * p * 1.4) * sizeof(int));
  memset(B, 0, int(p * m * 1.4) * sizeof(int));
  memset(C, 0, int(m * n * 1.4) * sizeof(int));

  for (int i = 0; i < n; i++) memcpy(A + i * p, s[i].data(), p * sizeof(int));
  for (int i = 0; i < p; i++) memcpy(B + i * m, t[i].data(), m * sizeof(int));

  Mat S(n, p, A), T(p, m, B), U(n, m, C);
  inner_block_dec_mul(&S, &T, &U);
  vector<fps> u(n, fps(m));
  for (int i = 0; i < n; i++) memcpy(u[i].data(), C + i * m, m * sizeof(int));
  return std::move(u);
}

template <typename fps>
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) vector<fps>
strassen(const vector<fps>& s, const vector<fps>& t) {
  int n = s.size(), p = s[0].size(), m = t[0].size();
  assert(int(n * p * 1.4) <= BUFFER_SIZE);
  assert(int(p * m * 1.4) <= BUFFER_SIZE);
  assert(int(n * m * 1.4) <= BUFFER_SIZE);
  memset(A, 0, int(n * p * 1.4) * sizeof(int));
  memset(B, 0, int(p * m * 1.4) * sizeof(int));
  memset(C, 0, int(m * n * 1.4) * sizeof(int));

  for (int i = 0; i < n; i++) memcpy(A + i * p, s[i].data(), p * sizeof(int));
  for (int i = 0; i < p; i++) memcpy(B + i * m, t[i].data(), m * sizeof(int));

  Mat S(n, p, A), T(p, m, B), U(n, m, C);
  inner_strassen(&S, &T, &U);
  vector<fps> u(n, fps(m));
  for (int i = 0; i < n; i++) memcpy(u[i].data(), C + i * m, m * sizeof(int));
  return std::move(u);
}

#ifdef BUFFER_SIZE
#undef BUFFER_SIZE
#endif
}  // namespace FastMatProd
#line 6 "verify/verify-unit-test/strassen.test.cpp"

namespace FastMatProd {
// for debug
template <typename fps>
__attribute__((target("avx2"), optimize("O3", "unroll-loops"))) vector<fps>
naive_mul(const vector<fps>& _a, const vector<fps>& _b) {
  int n = _a.size(), m = _b[0].size(), p = _b.size();
  assert(p == (int)_a[0].size());
  vector<fps> _c(n, fps(m, 0));
  for (int i = 0; i < n; i++)
    for (int k = 0; k < p; k++)
      for (int j = 0; j < m; j++) _c[i][j] += _a[i][k] * _b[k][j];
  return _c;
}

}  // namespace FastMatProd

#line 2 "misc/rng.hpp"

#line 2 "internal/internal-seed.hpp"

#line 4 "internal/internal-seed.hpp"
using namespace std;

namespace internal {
unsigned long long non_deterministic_seed() {
  unsigned long long m =
      chrono::duration_cast<chrono::nanoseconds>(
          chrono::high_resolution_clock::now().time_since_epoch())
          .count();
  m ^= 9845834732710364265uLL;
  m ^= m << 24, m ^= m >> 31, m ^= m << 35;
  return m;
}
unsigned long long deterministic_seed() { return 88172645463325252UL; }

// 64 bit の seed 値を生成 (手元では seed 固定)
// 連続で呼び出すと同じ値が何度も返ってくるので注意
// #define RANDOMIZED_SEED するとシードがランダムになる
unsigned long long seed() {
#if defined(NyaanLocal) && !defined(RANDOMIZED_SEED)
  return deterministic_seed();
#else
  return non_deterministic_seed();
#endif
}

}  // namespace internal
#line 4 "misc/rng.hpp"

namespace my_rand {
using i64 = long long;
using u64 = unsigned long long;

// [0, 2^64 - 1)
u64 rng() {
  static u64 _x = internal::seed();
  return _x ^= _x << 7, _x ^= _x >> 9;
}

// [l, r]
i64 rng(i64 l, i64 r) {
  assert(l <= r);
  return l + rng() % u64(r - l + 1);
}

// [l, r)
i64 randint(i64 l, i64 r) {
  assert(l < r);
  return l + rng() % u64(r - l);
}

// choose n numbers from [l, r) without overlapping
vector<i64> randset(i64 l, i64 r, i64 n) {
  assert(l <= r && n <= r - l);
  unordered_set<i64> s;
  for (i64 i = n; i; --i) {
    i64 m = randint(l, r + 1 - i);
    if (s.find(m) != s.end()) m = r - i;
    s.insert(m);
  }
  vector<i64> ret;
  for (auto& x : s) ret.push_back(x);
  return ret;
}

// [0.0, 1.0)
double rnd() { return rng() * 5.42101086242752217004e-20; }
// [l, r)
double rnd(double l, double r) {
  assert(l < r);
  return l + rnd() * (r - l);
}

template <typename T>
void randshf(vector<T>& v) {
  int n = v.size();
  for (int i = 1; i < n; i++) swap(v[i], v[randint(0, i + 1)]);
}

}  // namespace my_rand

using my_rand::randint;
using my_rand::randset;
using my_rand::randshf;
using my_rand::rnd;
using my_rand::rng;
#line 2 "misc/timer.hpp"

#line 4 "misc/timer.hpp"
using namespace std;

struct Timer {
  chrono::high_resolution_clock::time_point st;

  Timer() { reset(); }
  void reset() { st = chrono::high_resolution_clock::now(); }

  long long elapsed() {
    auto ed = chrono::high_resolution_clock::now();
    return chrono::duration_cast<chrono::milliseconds>(ed - st).count();
  }
  long long operator()() { return elapsed(); }
};
#line 25 "verify/verify-unit-test/strassen.test.cpp"

using namespace FastMatProd;
using fps = vector<mint>;

void time_test() {
  int N = 1024;
  int P = N, M = N;
  vector<fps> s(N, fps(P)), t(P, fps(M));
  for (int i = 0; i < N; i++)
    for (int j = 0; j < P; j++) s[i][j] = rng() % 998244353;
  for (int i = 0; i < P; i++)
    for (int j = 0; j < M; j++) t[i][j] = rng() % 998244353;
  vector<fps> u, u2, u3;
  Timer timer;

  int loop = 5;
  timer.reset();
  for (int i = 0; i < loop; i++) u = FastMatProd::strassen(s, t);
  cerr << "strassen " << (timer.elapsed() / loop) << endl;

  timer.reset();
  u2 = FastMatProd::naive_mul(s, t);
  cerr << "naive " << timer.elapsed() << endl;

  timer.reset();
  for (int i = 0; i < loop; i++) u3 = FastMatProd::block_dec(s, t);
  cerr << "block dec " << (timer.elapsed() / loop) << endl;

  assert(u == u2);
  assert(u == u3);
}

void debug_test(int max = 500, int loop = 10) {
  int N, P, M;
  mt19937 rng(58);
  while (loop--) {
    N = rng() % max + 1;
    M = rng() % max + 1;
    P = rng() % max + 1;
    vector<fps> s(N, fps(P)), t(P, fps(M));
    for (int i = 0; i < N; i++)
      for (int j = 0; j < P; j++) s[i][j] = rng() % 998244353;
    for (int i = 0; i < P; i++)
      for (int j = 0; j < M; j++) t[i][j] = rng() % 998244353;
    auto u = strassen(s, t);
    auto u2 = naive_mul(s, t);
    auto u3 = block_dec(s, t);
    if (u != u2) {
      cerr << "ng u1 " << N << " " << P << " " << M << endl;
      exit(1);
    } else if (u != u3) {
      cerr << "ng u1 " << N << " " << P << " " << M << endl;
      exit(1);
    } 
  }
  cerr << "all ok" << endl;
}

void Nyaan::solve() {
  debug_test();
  debug_test(32, 2000);
  time_test();

  int a, b;
  cin >> a >> b;
  cout << a + b << endl;
}

Nyaan's Library

This documentation is automatically generated by online-judge-tools/verification-helper

verify/verify-unit-test/strassen.test.cpp

Depends on

Code