#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; }