#define PROBLEM "https://judge.yosupo.jp/problem/subset_convolution" // #include <immintrin.h> // #include <algorithm> #include <cassert> #include <chrono> #include <cstdint> #include <cstdio> #include <cstring> #include <iostream> #include <random> #include <type_traits> #include <utility> #include <vector> using namespace std; #include "../../misc/fastio.hpp" // #include "../../math-fast/subset-convolution.hpp" // #include "../../modint/montgomery-modint.hpp" int main() { using mint = LazyMontgomeryModInt<998244353>; using vm = vector<mint>; mmint::set_mod<mint>(); int N; rd(N); using vm = vector<mint>; vm a(1 << N), b(1 << N); unsigned int n; for (int i = 0; i < 1 << N; i++) { rd(n); a[i].a = mint::reduce(uint64_t(n) * mint::n2); } for (int i = 0; i < 1 << N; i++) { rd(n); b[i].a = mint::reduce(uint64_t(n) * mint::n2); } auto c = fast_multiply(a, b); for (int i = 0; i < 1 << N; i++) { if (i) wt(' '); wt(c[i].get()); } wt('\n'); }
#line 1 "verify/verify-yosupo-math/yosupo-subset-convolution-fast.test.cpp" #define PROBLEM "https://judge.yosupo.jp/problem/subset_convolution" // #include <immintrin.h> // #include <algorithm> #include <cassert> #include <chrono> #include <cstdint> #include <cstdio> #include <cstring> #include <iostream> #include <random> #include <type_traits> #include <utility> #include <vector> using namespace std; #line 2 "misc/fastio.hpp" #line 5 "misc/fastio.hpp" #include <string> #line 8 "misc/fastio.hpp" using namespace std; #line 2 "internal/internal-type-traits.hpp" #line 4 "internal/internal-type-traits.hpp" using namespace std; namespace internal { template <typename T> using is_broadly_integral = typename conditional_t<is_integral_v<T> || is_same_v<T, __int128_t> || is_same_v<T, __uint128_t>, true_type, false_type>::type; template <typename T> using is_broadly_signed = typename conditional_t<is_signed_v<T> || is_same_v<T, __int128_t>, true_type, false_type>::type; template <typename T> using is_broadly_unsigned = typename conditional_t<is_unsigned_v<T> || is_same_v<T, __uint128_t>, true_type, false_type>::type; #define ENABLE_VALUE(x) \ template <typename T> \ constexpr bool x##_v = x<T>::value; ENABLE_VALUE(is_broadly_integral); ENABLE_VALUE(is_broadly_signed); ENABLE_VALUE(is_broadly_unsigned); #undef ENABLE_VALUE #define ENABLE_HAS_TYPE(var) \ template <class, class = void> \ struct has_##var : false_type {}; \ template <class T> \ struct has_##var<T, void_t<typename T::var>> : true_type {}; \ template <class T> \ constexpr auto has_##var##_v = has_##var<T>::value; #define ENABLE_HAS_VAR(var) \ template <class, class = void> \ struct has_##var : false_type {}; \ template <class T> \ struct has_##var<T, void_t<decltype(T::var)>> : true_type {}; \ template <class T> \ constexpr auto has_##var##_v = has_##var<T>::value; } // namespace internal #line 12 "misc/fastio.hpp" namespace fastio { static constexpr int SZ = 1 << 17; static constexpr int offset = 64; char inbuf[SZ], outbuf[SZ]; int in_left = 0, in_right = 0, out_right = 0; struct Pre { char num[40000]; constexpr Pre() : num() { for (int i = 0; i < 10000; i++) { int n = i; for (int j = 3; j >= 0; j--) { num[i * 4 + j] = n % 10 + '0'; n /= 10; } } } } constexpr pre; void load() { int len = in_right - in_left; memmove(inbuf, inbuf + in_left, len); in_right = len + fread(inbuf + len, 1, SZ - len, stdin); in_left = 0; } void flush() { fwrite(outbuf, 1, out_right, stdout); out_right = 0; } void skip_space() { if (in_left + offset > in_right) load(); while (inbuf[in_left] <= ' ') in_left++; } void single_read(char& c) { if (in_left + offset > in_right) load(); skip_space(); c = inbuf[in_left++]; } void single_read(string& S) { skip_space(); while (true) { if (in_left == in_right) load(); int i = in_left; for (; i != in_right; i++) { if (inbuf[i] <= ' ') break; } copy(inbuf + in_left, inbuf + i, back_inserter(S)); in_left = i; if (i != in_right) break; } } template <typename T, enable_if_t<internal::is_broadly_integral_v<T>>* = nullptr> void single_read(T& x) { if (in_left + offset > in_right) load(); skip_space(); char c = inbuf[in_left++]; [[maybe_unused]] bool minus = false; if constexpr (internal::is_broadly_signed_v<T>) { if (c == '-') minus = true, c = inbuf[in_left++]; } x = 0; while (c >= '0') { x = x * 10 + (c & 15); c = inbuf[in_left++]; } if constexpr (internal::is_broadly_signed_v<T>) { if (minus) x = -x; } } void rd() {} template <typename Head, typename... Tail> void rd(Head& head, Tail&... tail) { single_read(head); rd(tail...); } void single_write(const char& c) { if (out_right > SZ - offset) flush(); outbuf[out_right++] = c; } void single_write(const bool& b) { if (out_right > SZ - offset) flush(); outbuf[out_right++] = b ? '1' : '0'; } void single_write(const string& S) { flush(), fwrite(S.data(), 1, S.size(), stdout); } void single_write(const char* p) { flush(), fwrite(p, 1, strlen(p), stdout); } template <typename T, enable_if_t<internal::is_broadly_integral_v<T>>* = nullptr> void single_write(const T& _x) { if (out_right > SZ - offset) flush(); if (_x == 0) { outbuf[out_right++] = '0'; return; } T x = _x; if constexpr (internal::is_broadly_signed_v<T>) { if (x < 0) outbuf[out_right++] = '-', x = -x; } constexpr int buffer_size = sizeof(T) * 10 / 4; char buf[buffer_size]; int i = buffer_size; while (x >= 10000) { i -= 4; memcpy(buf + i, pre.num + (x % 10000) * 4, 4); x /= 10000; } if (x < 100) { if (x < 10) { outbuf[out_right] = '0' + x; ++out_right; } else { uint32_t q = (uint32_t(x) * 205) >> 11; uint32_t r = uint32_t(x) - q * 10; outbuf[out_right] = '0' + q; outbuf[out_right + 1] = '0' + r; out_right += 2; } } else { if (x < 1000) { memcpy(outbuf + out_right, pre.num + (x << 2) + 1, 3); out_right += 3; } else { memcpy(outbuf + out_right, pre.num + (x << 2), 4); out_right += 4; } } memcpy(outbuf + out_right, buf + i, buffer_size - i); out_right += buffer_size - i; } void wt() {} template <typename Head, typename... Tail> void wt(const Head& head, const Tail&... tail) { single_write(head); wt(forward<const Tail>(tail)...); } template <typename... Args> void wtn(const Args&... x) { wt(forward<const Args>(x)...); wt('\n'); } struct Dummy { Dummy() { atexit(flush); } } dummy; } // namespace fastio using fastio::rd; using fastio::skip_space; using fastio::wt; using fastio::wtn; #line 20 "verify/verify-yosupo-math/yosupo-subset-convolution-fast.test.cpp" // #line 2 "math-fast/subset-convolution.hpp" #line 5 "math-fast/subset-convolution.hpp" using namespace std; #line 2 "modint/vectorize-modint.hpp" #pragma GCC optimize("O3,unroll-loops") #pragma GCC target("avx2") #line 8 "modint/vectorize-modint.hpp" using namespace std; using m256 = __m256i; struct alignas(32) mmint { m256 x; static mmint R, M0, M1, M2, N2; mmint() : x() {} inline mmint(const m256& _x) : x(_x) {} inline mmint(unsigned int a) : x(_mm256_set1_epi32(a)) {} inline mmint(unsigned int a0, unsigned int a1, unsigned int a2, unsigned int a3, unsigned int a4, unsigned int a5, unsigned int a6, unsigned int a7) : x(_mm256_set_epi32(a7, a6, a5, a4, a3, a2, a1, a0)) {} inline operator m256&() { return x; } inline operator const m256&() const { return x; } inline int& operator[](int i) { return *(reinterpret_cast<int*>(&x) + i); } inline const int& operator[](int i) const { return *(reinterpret_cast<const int*>(&x) + i); } friend ostream& operator<<(ostream& os, const mmint& m) { unsigned r = R[0], mod = M1[0]; auto reduce1 = [&](const uint64_t& b) { unsigned res = (b + uint64_t(unsigned(b) * unsigned(-r)) * mod) >> 32; return res >= mod ? res - mod : res; }; for (int i = 0; i < 8; i++) { os << reduce1(m[i]) << (i == 7 ? "" : " "); } return os; } template <typename mint> static void set_mod() { R = _mm256_set1_epi32(mint::r); M0 = _mm256_setzero_si256(); M1 = _mm256_set1_epi32(mint::get_mod()); M2 = _mm256_set1_epi32(mint::get_mod() * 2); N2 = _mm256_set1_epi32(mint::n2); } static inline mmint reduce(const mmint& prod02, const mmint& prod13) { 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 prodlohi = _mm256_shuffle_epi32(prodlo, 0xF5); m256 lmlr02 = _mm256_mul_epu32(prodlo, R); m256 lmlr13 = _mm256_mul_epu32(prodlohi, R); m256 prod02_ = _mm256_mul_epu32(lmlr02, M1); m256 prod13_ = _mm256_mul_epu32(lmlr13, M1); m256 unpalo_ = _mm256_unpacklo_epi32(prod02_, prod13_); m256 unpahi_ = _mm256_unpackhi_epi32(prod02_, prod13_); m256 prod = _mm256_unpackhi_epi64(unpalo_, unpahi_); return _mm256_sub_epi32(hiplm1, prod); } static inline mmint itom(const mmint& A) { return A * N2; } static inline mmint mtoi(const mmint& A) { m256 A13 = _mm256_shuffle_epi32(A, 0xF5); m256 lmlr02 = _mm256_mul_epu32(A, R); m256 lmlr13 = _mm256_mul_epu32(A13, R); m256 prod02_ = _mm256_mul_epu32(lmlr02, M1); m256 prod13_ = _mm256_mul_epu32(lmlr13, M1); m256 unpalo_ = _mm256_unpacklo_epi32(prod02_, prod13_); m256 unpahi_ = _mm256_unpackhi_epi32(prod02_, prod13_); m256 prod = _mm256_unpackhi_epi64(unpalo_, unpahi_); m256 cmp = _mm256_cmpgt_epi32(prod, M0); m256 dif = _mm256_and_si256(cmp, M1); return _mm256_sub_epi32(dif, prod); } friend inline mmint operator+(const mmint& A, const mmint& B) { m256 apb = _mm256_add_epi32(A, B); m256 ret = _mm256_sub_epi32(apb, M2); m256 cmp = _mm256_cmpgt_epi32(M0, ret); m256 add = _mm256_and_si256(cmp, M2); return _mm256_add_epi32(add, ret); } friend inline mmint operator-(const mmint& A, const mmint& B) { m256 ret = _mm256_sub_epi32(A, B); m256 cmp = _mm256_cmpgt_epi32(M0, ret); m256 add = _mm256_and_si256(cmp, M2); return _mm256_add_epi32(add, ret); } friend inline mmint operator*(const mmint& A, const mmint& 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); return reduce(prod02, prod13); } inline mmint& operator+=(const mmint& A) { return (*this) = (*this) + A; } inline mmint& operator-=(const mmint& A) { return (*this) = (*this) - A; } inline mmint& operator*=(const mmint& A) { return (*this) = (*this) * A; } bool operator==(const mmint& A) { m256 sub = _mm256_sub_epi32(x, A.x); return _mm256_testz_si256(sub, sub) == 1; } bool operator!=(const mmint& A) { return !((*this) == A); } }; __attribute__((aligned(32))) mmint mmint::R; __attribute__((aligned(32))) mmint mmint::M0, mmint::M1, mmint::M2, mmint::N2; /** * @brief vectorize modint */ #line 8 "math-fast/subset-convolution.hpp" template <typename mint> vector<mint> fast_multiply(const vector<mint>& a, const vector<mint>& b) { int n = a.size(); int d = __builtin_ctz(n); assert(d <= 23); mmint* a1 = new mmint[max(n, 8) * 3]; mmint* a2 = new mmint[max(n, 8) * 3]; memset((void*)a1, 0, max(n, 8) * 3 * sizeof(mmint)); memset((void*)a2, 0, max(n, 8) * 3 * sizeof(mmint)); mmint b1[24], b2[24], b3[24]; for (int i = 0; i < n; i++) { unsigned int pc = __builtin_popcount(i); a1[i * 3 + pc / 8][pc % 8] = a[i].a; a2[i * 3 + pc / 8][pc % 8] = b[i].a; } for (int j = 2; j <= n; j += 2) { unsigned int pc = __builtin_popcount(j); unsigned int ctz = __builtin_ctz(j); for (int h = 0; h < d; h++) { if (j & (1 << h)) break; int li = j - 2 * (1 << h), ri = j - (1 << h); if (pc + ctz <= 16) { for (int i = 0; i < 3 * (1 << h); i += 3) { a1[ri * 3 + i + 0] += a1[li * 3 + i + 0]; a2[ri * 3 + i + 0] += a2[li * 3 + i + 0]; a1[ri * 3 + i + 1] += a1[li * 3 + i + 1]; a2[ri * 3 + i + 1] += a2[li * 3 + i + 1]; } } else { for (int i = 0; i < 3 * (1 << h); i++) { a1[ri * 3 + i] += a1[li * 3 + i]; a2[ri * 3 + i] += a2[li * 3 + i]; } } } } mmint th = _mm256_set1_epi64x(4LL * mmint::M1[0] * mmint::M1[0]); for (int is = 0; is < n; is += 8) { int mpc = d; for (int i = is; i < is + 8; i++) { int pc = __builtin_popcount(i); mpc = min(mpc, pc); for (int j = 0; j <= d; j++) { b1[j][i - is] = a1[i * 3 + j / 8][j % 8]; b2[j][i - is] = a2[i * 3 + j / 8][j % 8]; b3[j][i - is] = 0; } } for (int j = 0; j <= d; j++) { m256 cmpB1 = _mm256_cmpgt_epi32(mmint::M1, b1[j]); m256 cmpB2 = _mm256_cmpgt_epi32(mmint::M1, b2[j]); m256 difB1 = _mm256_andnot_si256(cmpB1, mmint::M1); m256 difB2 = _mm256_andnot_si256(cmpB2, mmint::M1); b1[j] = _mm256_sub_epi32(b1[j], difB1); b2[j] = _mm256_sub_epi32(b2[j], difB2); } #define PROD(k) \ m256 A13##k = _mm256_shuffle_epi32(b1[j + k], 0xF5); \ m256 B13##k = _mm256_shuffle_epi32(b2[l - j - k], 0xF5); \ m256 p02##k = _mm256_mul_epi32(b1[j + k], b2[l - j - k]); \ m256 p13##k = _mm256_mul_epi32(A13##k, B13##k); \ prod02 = _mm256_add_epi64(prod02, p02##k); \ prod13 = _mm256_add_epi64(prod13, p13##k) #define COMP() \ do { \ m256 cmp02 = _mm256_cmpgt_epi64(prod02, th); \ m256 cmp13 = _mm256_cmpgt_epi64(prod13, th); \ m256 dif02 = _mm256_and_si256(cmp02, th); \ m256 dif13 = _mm256_and_si256(cmp13, th); \ prod02 = _mm256_sub_epi64(prod02, dif02); \ prod13 = _mm256_sub_epi64(prod13, dif13); \ } while (0) for (int l = mpc; l <= d; l++) { int j = 0; mmint prod02 = mmint::M0, prod13 = mmint::M0; for (; j <= l - 3; j += 4) { PROD(0); PROD(1); PROD(2); PROD(3); COMP(); } for (; j <= l; j++) { PROD(0); } COMP(); b3[l] = mmint::reduce(prod02, prod13); } #undef PROD #undef COMP for (int i = is; i < is + 8; i++) { for (unsigned j = mpc; j <= unsigned(d); j++) { a1[i * 3 + j / 8][j % 8] = b3[j][i - is]; } } } for (int j = 2; j <= n; j += 2) { for (int h = 0; h < d; h++) { if (j & (1 << h)) break; int li = j - 2 * (1 << h), ri = j - (1 << h); for (int i = 0; i < 3 * (1 << h); i++) { a1[ri * 3 + i] -= a1[li * 3 + i]; } } } vector<mint> c(n); for (int i = 0; i < n; i++) { unsigned int pc = __builtin_popcount(i); c[i].a = a1[i * 3 + pc / 8][pc % 8]; } delete[] (a1); delete[] (a2); return c; } #line 22 "verify/verify-yosupo-math/yosupo-subset-convolution-fast.test.cpp" // #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 24 "verify/verify-yosupo-math/yosupo-subset-convolution-fast.test.cpp" int main() { using mint = LazyMontgomeryModInt<998244353>; using vm = vector<mint>; mmint::set_mod<mint>(); int N; rd(N); using vm = vector<mint>; vm a(1 << N), b(1 << N); unsigned int n; for (int i = 0; i < 1 << N; i++) { rd(n); a[i].a = mint::reduce(uint64_t(n) * mint::n2); } for (int i = 0; i < 1 << N; i++) { rd(n); b[i].a = mint::reduce(uint64_t(n) * mint::n2); } auto c = fast_multiply(a, b); for (int i = 0; i < 1 << N; i++) { if (i) wt(' '); wt(c[i].get()); } wt('\n'); }