CP-Algorithms Library
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Wildcard Pattern Matching (verify/poly/wildcard.test.cpp)
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- Last update: 2026-10-16 14:16:08+02:00
- Problem: https://judge.yosupo.jp/problem/wildcard_pattern_matching
Depends on
- cp-algo/math/cvector.hpp
- cp-algo/random/rng.hpp
- cp-algo/util/big_alloc.hpp
- cp-algo/util/checkpoint.hpp
- cp-algo/util/complex.hpp
- cp-algo/util/simd.hpp
Code
// @brief Wildcard Pattern Matching
#define PROBLEM "https://judge.yosupo.jp/problem/wildcard_pattern_matching"
#pragma GCC optimize("O3,unroll-loops")
#define CP_ALGO_CHECKPOINT
#pragma GCC target("avx2")
#include <bits/stdc++.h>
#include "cp-algo/math/cvector.hpp"
#include "cp-algo/random/rng.hpp"
using namespace std;
using namespace cp_algo::math;
using fft::ftype;
using fft::point;
using fft::vftype;
using fft::cvector;
void semicorr(auto &a, auto &b) {
a.fft();
b.fft();
a.dot(b);
a.ifft();
}
auto is_integer(auto a) {
static const ftype eps = 1e-9;
return cp_algo::abs(a - cp_algo::round(a)) < eps;
}
cp_algo::big_string matches(cp_algo::big_string const& A, cp_algo::big_string const& B, char wild = '*') {
static ftype project[2][128];
static bool init = false;
if(!init) {
init = true;
std::uniform_real_distribution<> dis(.5, 2.);
for(int i = 0; i < 128; i++) {
ftype x = dis(cp_algo::random::gen);
project[0][i] = x;
project[1][i] = 1. / x;
}
}
project[0][(int)wild] = project[1][(int)wild] = 0;
cp_algo::big_vector<cvector> P;
P.emplace_back((size(A) + 1) / 2);
P.emplace_back((size(A) + 1) / 2);
auto N = P[0].size();
auto assign = [&](int z) {
return [&, z](auto ic) {
auto [i, c] = ic;
if(i < (int)N) {
real(P[z].r[i / fft::flen])[i % fft::flen] = project[z][(int)c];
} else {
i -= N;
imag(P[z].r[i / fft::flen])[i % fft::flen] = project[z][(int)c];
}
};
};
ranges::for_each(A | views::enumerate, assign(0));
ranges::for_each(B | views::reverse | views::enumerate, assign(1));
cp_algo::checkpoint("cvector fill");
semicorr(P[0], P[1]);
cp_algo::big_string ans(2 * size(P[0]), '0');
auto start = (ssize(B) - 1) / fft::flen * fft::flen;
for(auto j = start; j < size(ans); j += fft::flen) {
decltype(is_integer(real(P[0].at(j)))) check;
if(j < N) {
check = is_integer(real(P[0].at(j)));
} else {
check = is_integer(imag(P[0].at(j - N)));
}
for(int z = 0; z < 4; z++) {
ans[j + z] ^= (bool)check[z];
}
}
cp_algo::checkpoint("fill answer");
return ans.substr(size(B) - 1, size(A) - size(B) + 1);
}
void solve() {
cp_algo::big_string a, b;
cin >> a >> b;
cp_algo::checkpoint("input");
cout << matches(a, b) << "\n";
cp_algo::checkpoint("output");
cp_algo::checkpoint<true>("done");
}
signed main() {
//freopen("input.txt", "r", stdin);
ios::sync_with_stdio(0);
cin.tie(0);
int t = 1;
//cin >> t;
while(t--) {
solve();
}
}
#line 1 "verify/poly/wildcard.test.cpp"
// @brief Wildcard Pattern Matching
#define PROBLEM "https://judge.yosupo.jp/problem/wildcard_pattern_matching"
#pragma GCC optimize("O3,unroll-loops")
#define CP_ALGO_CHECKPOINT
#pragma GCC target("avx2")
#include <bits/stdc++.h>
#line 1 "cp-algo/math/cvector.hpp"
#line 1 "cp-algo/util/simd.hpp"
#include <experimental/simd>
#line 7 "cp-algo/util/simd.hpp"
#if defined(__x86_64__) && !defined(CP_ALGO_DISABLE_AVX2)
#define CP_ALGO_SIMD_AVX2_TARGET _Pragma("GCC target(\"avx2,fma\")")
#else
#define CP_ALGO_SIMD_AVX2_TARGET
#endif
#define CP_ALGO_SIMD_PRAGMA_PUSH \
_Pragma("GCC push_options") \
CP_ALGO_SIMD_AVX2_TARGET
CP_ALGO_SIMD_PRAGMA_PUSH
namespace cp_algo {
template<typename T, size_t len>
using simd [[gnu::vector_size(len * sizeof(T))]] = T;
using u64x8 = simd<uint64_t, 8>;
using u32x16 = simd<uint32_t, 16>;
using i64x4 = simd<int64_t, 4>;
using u64x4 = simd<uint64_t, 4>;
using u32x8 = simd<uint32_t, 8>;
using u16x16 = simd<uint16_t, 16>;
using i32x4 = simd<int32_t, 4>;
using u32x4 = simd<uint32_t, 4>;
using u16x8 = simd<uint16_t, 8>;
using u16x4 = simd<uint16_t, 4>;
using i16x4 = simd<int16_t, 4>;
using u8x32 = simd<uint8_t, 32>;
using u8x16 = simd<uint8_t, 16>;
using u8x8 = simd<uint8_t, 8>;
using u8x4 = simd<uint8_t, 4>;
using dx4 = simd<double, 4>;
inline dx4 abs(dx4 a) {
return dx4{
std::abs(a[0]),
std::abs(a[1]),
std::abs(a[2]),
std::abs(a[3])
};
}
// https://stackoverflow.com/a/77376595
// works for ints in (-2^51, 2^51)
static constexpr dx4 magic = dx4() + (3ULL << 51);
inline i64x4 lround(dx4 x) {
return i64x4(x + magic) - i64x4(magic);
}
inline dx4 to_double(i64x4 x) {
return dx4(x + i64x4(magic)) - magic;
}
inline dx4 round(dx4 a) {
return dx4{
std::nearbyint(a[0]),
std::nearbyint(a[1]),
std::nearbyint(a[2]),
std::nearbyint(a[3])
};
}
inline u64x4 low32(u64x4 x) {
return x & uint32_t(-1);
}
inline auto swap_bytes(auto x) {
return decltype(x)(__builtin_shufflevector(u32x8(x), u32x8(x), 1, 0, 3, 2, 5, 4, 7, 6));
}
inline u64x4 montgomery_reduce(u64x4 x, uint32_t mod, uint32_t imod) {
#ifdef __AVX2__
auto x_ninv = u64x4(_mm256_mul_epu32(__m256i(x), __m256i() + imod));
x += u64x4(_mm256_mul_epu32(__m256i(x_ninv), __m256i() + mod));
#else
auto x_ninv = u64x4(u32x8(low32(x)) * imod);
x += x_ninv * uint64_t(mod);
#endif
return swap_bytes(x);
}
// x - mod where x >= mod, for x in [0, 2 mod). Unsigned, so it holds up to mod < 2^31;
// zero upper halves of 64-bit lanes stay zero.
inline u32x8 reduce_once(u32x8 x, uint32_t mod) {
auto y = x - mod;
return x < y ? x : y;
}
inline u64x4 reduce_once(u64x4 x, uint32_t mod) {
return u64x4(reduce_once(u32x8(x), mod));
}
inline u64x4 montgomery_mul(u64x4 x, u64x4 y, uint32_t mod, uint32_t imod) {
#ifdef __AVX2__
return montgomery_reduce(u64x4(_mm256_mul_epu32(__m256i(x), __m256i(y))), mod, imod);
#else
return montgomery_reduce(x * y, mod, imod);
#endif
}
inline u32x8 montgomery_mul(u32x8 x, u32x8 y, uint32_t mod, uint32_t imod) {
return u32x8(montgomery_mul(u64x4(x), u64x4(y), mod, imod)) |
u32x8(swap_bytes(montgomery_mul(u64x4(swap_bytes(x)), u64x4(swap_bytes(y)), mod, imod)));
}
inline dx4 rotate_right(dx4 x) {
static constexpr u64x4 shuffler = {3, 0, 1, 2};
return __builtin_shuffle(x, shuffler);
}
template<std::size_t Align = 32>
inline bool is_aligned(const auto *p) noexcept {
return (reinterpret_cast<std::uintptr_t>(p) % Align) == 0;
}
template<class Target>
inline Target& vector_cast(auto &&p) {
return *reinterpret_cast<Target*>(std::assume_aligned<alignof(Target)>(&p));
}
}
#pragma GCC pop_options
#line 1 "cp-algo/util/complex.hpp"
#line 7 "cp-algo/util/complex.hpp"
CP_ALGO_SIMD_PRAGMA_PUSH
namespace cp_algo {
// Custom implementation, since std::complex is UB on non-floating types
template<typename T>
struct complex {
using value_type = T;
T x, y;
inline constexpr complex(): x(), y() {}
inline constexpr complex(T const& x): x(x), y() {}
inline constexpr complex(T const& x, T const& y): x(x), y(y) {}
inline complex& operator *= (T const& t) {x *= t; y *= t; return *this;}
inline complex& operator /= (T const& t) {x /= t; y /= t; return *this;}
inline complex operator * (T const& t) const {return complex(*this) *= t;}
inline complex operator / (T const& t) const {return complex(*this) /= t;}
inline complex& operator += (complex const& t) {x += t.x; y += t.y; return *this;}
inline complex& operator -= (complex const& t) {x -= t.x; y -= t.y; return *this;}
inline complex operator * (complex const& t) const {return {x * t.x - y * t.y, x * t.y + y * t.x};}
inline complex operator / (complex const& t) const {return *this * t.conj() / t.norm();}
inline complex operator + (complex const& t) const {return complex(*this) += t;}
inline complex operator - (complex const& t) const {return complex(*this) -= t;}
inline complex& operator *= (complex const& t) {return *this = *this * t;}
inline complex& operator /= (complex const& t) {return *this = *this / t;}
inline complex operator - () const {return {-x, -y};}
inline complex conj() const {return {x, -y};}
inline T norm() const {return x * x + y * y;}
inline T abs() const {return std::sqrt(norm());}
inline T const real() const {return x;}
inline T const imag() const {return y;}
inline T& real() {return x;}
inline T& imag() {return y;}
inline static constexpr complex polar(T r, T theta) {return {T(r * cos(theta)), T(r * sin(theta))};}
inline auto operator <=> (complex const& t) const = default;
};
template<typename T> inline complex<T> conj(complex<T> const& x) {return x.conj();}
template<typename T> inline T norm(complex<T> const& x) {return x.norm();}
template<typename T> inline T abs(complex<T> const& x) {return x.abs();}
template<typename T> inline T& real(complex<T> &x) {return x.real();}
template<typename T> inline T& imag(complex<T> &x) {return x.imag();}
template<typename T> inline T const real(complex<T> const& x) {return x.real();}
template<typename T> inline T const imag(complex<T> const& x) {return x.imag();}
template<typename T>
inline constexpr complex<T> polar(T r, T theta) {
return complex<T>::polar(r, theta);
}
template<typename T>
inline std::ostream& operator << (std::ostream &out, complex<T> const& x) {
return out << x.real() << ' ' << x.imag();
}
}
#pragma GCC pop_options
#line 1 "cp-algo/util/checkpoint.hpp"
#line 1 "cp-algo/util/big_alloc.hpp"
#line 15 "cp-algo/util/big_alloc.hpp"
// Single macro to detect POSIX platforms (Linux, Unix, macOS)
#if defined(__linux__) || defined(__unix__) || (defined(__APPLE__) && defined(__MACH__))
#define CP_ALGO_USE_MMAP 1
#include <sys/mman.h>
#else
#define CP_ALGO_USE_MMAP 0
#endif
namespace cp_algo {
template<typename T, size_t Align = 32>
class big_alloc {
static_assert(Align >= alignof(void*), "Align must be at least pointer-size");
static_assert(std::has_single_bit(Align), "Align must be a power of two");
public:
using value_type = T;
template<class U>
struct rebind {
using other = big_alloc<U, Align>;
};
constexpr bool operator==(const big_alloc&) const = default;
big_alloc() noexcept = default;
template<typename U, std::size_t A>
big_alloc(const big_alloc<U, A>&) noexcept {}
[[nodiscard]] T* allocate(std::size_t n) {
std::size_t padded = round_up(n * sizeof(T));
std::size_t align = std::max<std::size_t>(alignof(T), Align);
#if CP_ALGO_USE_MMAP
if(padded >= MEGABYTE) {
void* raw = mmap(nullptr, padded, PROT_READ | PROT_WRITE, MAP_PRIVATE | MAP_ANONYMOUS, -1, 0);
madvise(raw, padded, MADV_HUGEPAGE);
return static_cast<T*>(raw);
}
#endif
return static_cast<T*>(::operator new(padded, std::align_val_t(align)));
}
void deallocate(T* p, std::size_t n) noexcept {
if(!p) {
return;
}
std::size_t padded = round_up(n * sizeof(T));
std::size_t align = std::max<std::size_t>(alignof(T), Align);
#if CP_ALGO_USE_MMAP
if(padded >= MEGABYTE) {
munmap(p, padded);
return;
}
#endif
::operator delete(p, padded, std::align_val_t(align));
}
private:
static constexpr std::size_t MEGABYTE = 1 << 20;
static constexpr std::size_t round_up(std::size_t x) noexcept {
return (x + Align - 1) / Align * Align;
}
};
template<typename T>
using big_vector = std::vector<T, big_alloc<T>>;
template<typename T>
using big_basic_string = std::basic_string<T, std::char_traits<T>, big_alloc<T>>;
template<typename T>
using big_deque = std::deque<T, big_alloc<T>>;
template<typename T>
using big_stack = std::stack<T, big_deque<T>>;
template<typename T>
using big_queue = std::queue<T, big_deque<T>>;
template<typename T>
using big_priority_queue = std::priority_queue<T, big_vector<T>>;
template<typename T>
using big_forward_list = std::forward_list<T, big_alloc<T>>;
using big_string = big_basic_string<char>;
template<typename Key, typename Value, typename Compare = std::less<Key>>
using big_map = std::map<Key, Value, Compare, big_alloc<std::pair<const Key, Value>>>;
template<typename T, typename Compare = std::less<T>>
using big_multiset = std::multiset<T, Compare, big_alloc<T>>;
template<typename T, typename Compare = std::less<T>>
using big_set = std::set<T, Compare, big_alloc<T>>;
}
#line 8 "cp-algo/util/checkpoint.hpp"
namespace cp_algo {
#ifdef CP_ALGO_CHECKPOINT
big_map<big_string, double> checkpoints;
double last;
#endif
template<bool final = false>
void checkpoint([[maybe_unused]] auto const& _msg) {
#ifdef CP_ALGO_CHECKPOINT
big_string msg = _msg;
double now = (double)clock() / CLOCKS_PER_SEC;
double delta = now - last;
last = now;
if(msg.size() && !final) {
checkpoints[msg] += delta;
}
if(final) {
for(auto const& [key, value] : checkpoints) {
std::cerr << key << ": " << value * 1000 << " ms\n";
}
std::cerr << "Total: " << now * 1000 << " ms\n";
}
#endif
}
template<bool final = false>
void checkpoint() {
checkpoint<final>("");
}
}
#line 7 "cp-algo/math/cvector.hpp"
#include <immintrin.h>
#line 13 "cp-algo/math/cvector.hpp"
CP_ALGO_SIMD_PRAGMA_PUSH
namespace stdx = std::experimental;
namespace cp_algo::math::fft {
static constexpr size_t flen = 4;
using ftype = double;
using vftype = dx4;
using point = complex<ftype>;
using vpoint = complex<vftype>;
static constexpr vftype vz = {};
vpoint vi(vpoint const& r) {
return {-imag(r), real(r)};
}
// Spectrum storage skips zero-filling on resize; every user writes before reading.
template<class T>
struct spectrum_alloc: big_alloc<T> {
using big_alloc<T>::big_alloc;
template<class U>
struct rebind {
using other = spectrum_alloc<U>;
};
template<class U>
requires(std::is_same_v<U, vpoint>)
void construct(U*) noexcept {}
};
using spectrum_vector = std::vector<vpoint, spectrum_alloc<vpoint>>;
struct cvector {
spectrum_vector r;
cvector(size_t n) {
n = std::max(flen, std::bit_ceil(n));
r.assign(n / flen, vpoint{});
prepare_roots(n / 16);
checkpoint("cvector create");
}
vpoint& at(size_t k) { return r[k / flen]; }
vpoint at(size_t k) const { return r[k / flen]; }
template<class pt = point>
inline void set(size_t k, pt const& t) {
if constexpr(std::is_same_v<pt, point>) {
real(r[k / flen])[k % flen] = real(t);
imag(r[k / flen])[k % flen] = imag(t);
} else {
at(k) = t;
}
}
template<class pt = point>
inline pt get(size_t k) const {
if constexpr(std::is_same_v<pt, point>) {
return {real(r[k / flen])[k % flen], imag(r[k / flen])[k % flen]};
} else {
return at(k);
}
}
size_t size() const {
return flen * r.size();
}
static constexpr size_t eval_arg(size_t n) {
if(n < pre_evals) {
return eval_args[n];
} else {
return eval_arg(n / 2) | (n & 1) << (std::bit_width(n) - 1);
}
}
static constexpr point eval_point(size_t n) {
if(n % 2) {
return -eval_point(n - 1);
} else if(n % 4) {
return eval_point(n - 2) * point(0, 1);
} else if(n / 4 < pre_evals) {
return evalp[n / 4];
} else if(n / 4 - pre_evals < extra.size()) {
return extra[n / 4 - pre_evals];
} else {
return polar<ftype>(1., std::numbers::pi / (ftype)std::bit_floor(n) * (ftype)eval_arg(n));
}
}
static constexpr std::array<point, 32> roots = []() {
std::array<point, 32> res;
for(size_t i = 2; i < 32; i++) {
res[i] = polar<ftype>(1., std::numbers::pi / (1ull << (i - 2)));
}
return res;
}();
static constexpr point root(size_t n) {
return roots[std::bit_width(n)];
}
template<int step>
static void exec_on_eval(size_t n, size_t k, auto &&callback) {
callback(k, root(4 * step * n) * eval_point(step * k));
}
template<int step>
static void exec_on_evals(size_t n, auto &&callback) {
point factor = root(4 * step * n);
if constexpr(step == 1 || step == 2 || step == 4) {
prepare_roots((step * n + 3) / 4);
size_t i = 0;
if constexpr(step == 1) {
for(; i + 4 <= n; i += 4) {
size_t k = i / 4;
point e = k < pre_evals ? evalp[k] : extra[k - pre_evals];
point v = factor * e;
callback(i, v);
callback(i + 1, -v);
point iv(-imag(v), real(v));
callback(i + 2, iv);
callback(i + 3, -iv);
}
} else if constexpr(step == 2) {
for(; i + 2 <= n; i += 2) {
size_t k = i / 2;
point e = k < pre_evals ? evalp[k] : extra[k - pre_evals];
point v = factor * e;
callback(i, v);
callback(i + 1, point(-imag(v), real(v)));
}
}
for(; i < n; i++) {
size_t index = step * i, k = index / 4;
point e = k < pre_evals ? evalp[k] : extra[k - pre_evals];
if(index & 2) {
e = e * point(0, 1);
}
if(index & 1) {
e = -e;
}
callback(i, factor * e);
}
} else {
for(size_t i = 0; i < n; i++) {
callback(i, factor * eval_point(step * i));
}
}
}
static void do_dot_iter(point rt, vpoint& Bv, vpoint const& Av, vpoint& res) {
res += Av * Bv;
real(Bv) = rotate_right(real(Bv));
imag(Bv) = rotate_right(imag(Bv));
auto x = real(Bv)[0], y = imag(Bv)[0];
real(Bv)[0] = x * real(rt) - y * imag(rt);
imag(Bv)[0] = x * imag(rt) + y * real(rt);
}
template<size_t fixed = 0>
void dot(cvector const& t) {
size_t n = fixed ? fixed : this->size();
exec_on_evals<1>(n / flen, [&] [[gnu::always_inline]] (size_t k, point rt) {
k *= flen;
auto [Ax, Ay] = at(k);
auto Cv = t.at(k);
vpoint vrt = {vz + real(rt), vz + imag(rt)};
auto Cr = Cv * vrt;
vpoint res = vz;
auto iter = [&]<int i> [[gnu::always_inline]] () {
auto wrap = [&](vftype original, vftype rotated) {
if constexpr(i == 0) {
return original;
} else {
return __builtin_shufflevector(rotated, original, 4 - i, 5 - i, 6 - i, 7 - i);
}
};
vpoint Cw = {wrap(real(Cv), real(Cr)), wrap(imag(Cv), imag(Cr))};
vpoint Av = {vz + Ax[i], vz + Ay[i]};
return Av * Cw;
};
auto p0 = iter.template operator()<0>(), p1 = iter.template operator()<1>();
auto p2 = iter.template operator()<2>(), p3 = iter.template operator()<3>();
res = (p0 + p1) + (p2 + p3);
set(k, res);
});
checkpoint("dot");
}
// normalize=false leaves the inverse-transform scale for the caller.
template<bool partial = true, bool normalize = true, size_t fixed = 0>
void ifft() {
size_t n = fixed ? fixed : size();
if constexpr(!partial) {
prepare_roots(n / 4);
point pi(0, 1);
exec_on_evals<4>(n / 4, [&] [[gnu::always_inline]] (size_t k, point rt) {
k *= 4;
point v1 = conj(rt);
point v2 = v1 * v1;
point v3 = v1 * v2;
auto A = get(k);
auto B = get(k + 1);
auto C = get(k + 2);
auto D = get(k + 3);
set(k, (A + B) + (C + D));
set(k + 2, ((A + B) - (C + D)) * v2);
set(k + 1, ((A - B) - pi * (C - D)) * v1);
set(k + 3, ((A - B) + pi * (C - D)) * v3);
});
}
bool parity = std::countr_zero(n) % 2;
if(parity) {
exec_on_evals<2>(n / (2 * flen), [&] [[gnu::always_inline]] (size_t k, point rt) {
k *= 2 * flen;
vpoint cvrt = {vz + real(rt), vz - imag(rt)};
auto B = at(k) - at(k + flen);
at(k) += at(k + flen);
at(k + flen) = B * cvrt;
});
}
transform<true, fixed>(n, parity);
checkpoint("ifft");
if constexpr(normalize) {
auto scale = vz + ftype(partial ? flen : 1) / ftype(n);
for(size_t k = 0; k < n; k += flen) {
set(k, get<vpoint>(k) * scale);
}
}
}
template<bool partial = true, size_t fixed = 0>
void fft() {
size_t n = fixed ? fixed : size();
prepare_roots(n / (partial ? 16 : 4));
bool parity = std::countr_zero(n) % 2;
transform<false, fixed>(n, parity);
if(parity) {
exec_on_evals<2>(n / (2 * flen), [&] [[gnu::always_inline]] (size_t k, point rt) {
k *= 2 * flen;
vpoint vrt = {vz + real(rt), vz + imag(rt)};
auto t = at(k + flen) * vrt;
at(k + flen) = at(k) - t;
at(k) += t;
});
}
if constexpr(!partial) {
prepare_roots(n / 4);
point pi(0, 1);
exec_on_evals<4>(n / 4, [&] [[gnu::always_inline]] (size_t k, point rt) {
k *= 4;
point v1 = rt;
point v2 = v1 * v1;
point v3 = v1 * v2;
auto A = get(k);
auto B = get(k + 1) * v1;
auto C = get(k + 2) * v2;
auto D = get(k + 3) * v3;
set(k, (A + C) + (B + D));
set(k + 1, (A + C) - (B + D));
set(k + 2, (A - C) + pi * (B - D));
set(k + 3, (A - C) - pi * (B - D));
});
}
checkpoint("fft");
}
static std::array<vpoint, 4> transpose(std::array<vpoint, 4> const& a) {
auto half = [](auto part) {
auto a0 = __m256d(part(0)), a1 = __m256d(part(1)), a2 = __m256d(part(2)), a3 = __m256d(part(3));
auto t0 = _mm256_unpacklo_pd(a0, a1), t1 = _mm256_unpackhi_pd(a0, a1), t2 = _mm256_unpacklo_pd(a2, a3),
t3 = _mm256_unpackhi_pd(a2, a3);
return std::array<vftype, 4>{
vftype(_mm256_permute2f128_pd(t0, t2, 0x20)), vftype(_mm256_permute2f128_pd(t1, t3, 0x20)),
vftype(_mm256_permute2f128_pd(t0, t2, 0x31)), vftype(_mm256_permute2f128_pd(t1, t3, 0x31))};
};
auto re = half([&](int k) { return real(a[k]); }), im = half([&](int k) { return imag(a[k]); });
return {vpoint{re[0], im[0]}, vpoint{re[1], im[1]}, vpoint{re[2], im[2]}, vpoint{re[3], im[3]}};
}
// Multiply groups of 16 points as polynomials modulo x^16 - rt: one radix-4 level on
// each operand, a lane-parallel 4-coefficient Karatsuba product, one inverse level.
// The weights rt, rt^2, rt^3 of a tile of groups are computed four groups per SIMD
// operation ahead of the tile, so the product loop only broadcasts them from memory.
static constexpr size_t dot_tile = 64;
template<size_t fixed, bool square = false>
void dot_fused16(cvector const& t, size_t offset, size_t length) {
constexpr size_t T = dot_tile;
const size_t n = fixed ? fixed : size();
point factor = root(n);
auto fr = _mm256_set1_pd(real(factor)), fi = _mm256_set1_pd(imag(factor));
alignas(32) double tw[6][T];
const bool ahead = offset + length < n;
auto cmadd = [] [[gnu::always_inline]] (vpoint x, vpoint y, vpoint c) {
auto re = _mm256_fmadd_pd(__m256d(real(x)), __m256d(real(y)),
_mm256_fnmadd_pd(__m256d(imag(x)), __m256d(imag(y)), __m256d(real(c))));
auto im = _mm256_fmadd_pd(__m256d(real(x)), __m256d(imag(y)),
_mm256_fmadd_pd(__m256d(imag(x)), __m256d(real(y)), __m256d(imag(c))));
return vpoint{vftype(re), vftype(im)};
};
auto cmcross = [] [[gnu::always_inline]] (vpoint x, vpoint y, vpoint p, vpoint q) {
auto re = _mm256_sub_pd(_mm256_fmsub_pd(__m256d(real(x)), __m256d(real(y)), __m256d(real(p))),
_mm256_fmadd_pd(__m256d(imag(x)), __m256d(imag(y)), __m256d(real(q))));
auto im = _mm256_add_pd(_mm256_fmsub_pd(__m256d(real(x)), __m256d(imag(y)), __m256d(imag(p))),
_mm256_fmsub_pd(__m256d(imag(x)), __m256d(real(y)), __m256d(imag(q))));
return vpoint{vftype(re), vftype(im)};
};
// z * conj(v)
auto mulconj = [] [[gnu::always_inline]] (vpoint z, vpoint v) {
auto re = _mm256_fmadd_pd(__m256d(real(z)), __m256d(real(v)),
_mm256_mul_pd(__m256d(imag(z)), __m256d(imag(v))));
auto im = _mm256_fmsub_pd(__m256d(imag(z)), __m256d(real(v)),
_mm256_mul_pd(__m256d(real(z)), __m256d(imag(v))));
return vpoint{vftype(re), vftype(im)};
};
for(size_t tile = offset; tile < offset + length; tile += 16 * T) {
size_t k0 = tile / 16;
auto const* e = reinterpret_cast<double const*>(k0 < pre_evals ? evalp.data() + k0
: extra.data() + (k0 - pre_evals));
for(size_t g = 0; g < T; g += 4) {
auto x = _mm256_loadu_pd(e + 2 * g), y = _mm256_loadu_pd(e + 2 * g + 4);
auto er = _mm256_permute4x64_pd(_mm256_unpacklo_pd(x, y), 0xD8),
ei = _mm256_permute4x64_pd(_mm256_unpackhi_pd(x, y), 0xD8);
auto r1 = _mm256_fmsub_pd(fr, er, _mm256_mul_pd(fi, ei)),
i1 = _mm256_fmadd_pd(fr, ei, _mm256_mul_pd(fi, er));
auto r2 = _mm256_fmsub_pd(r1, r1, _mm256_mul_pd(i1, i1)),
i2 = _mm256_fmadd_pd(r1, i1, _mm256_mul_pd(i1, r1));
auto r3 = _mm256_fmsub_pd(r1, r2, _mm256_mul_pd(i1, i2)),
i3 = _mm256_fmadd_pd(r1, i2, _mm256_mul_pd(i1, r2));
_mm256_store_pd(tw[0] + g, r1);
_mm256_store_pd(tw[1] + g, i1);
_mm256_store_pd(tw[2] + g, r2);
_mm256_store_pd(tw[3] + g, i2);
_mm256_store_pd(tw[4] + g, r3);
_mm256_store_pd(tw[5] + g, i3);
}
for(size_t g = 0; g < T; g++) {
size_t pos = tile + 16 * g;
if(ahead) {
// Pull the next block of both operands towards the cache while this one is multiplied.
auto const* pa = reinterpret_cast<char const*>(r.data() + (pos + length) / flen);
auto const* pb = reinterpret_cast<char const*>(t.r.data() + (pos + length) / flen);
for(size_t c = 0; c < 4; c++) {
_mm_prefetch(pa + 64 * c, _MM_HINT_T2);
_mm_prefetch(pb + 64 * c, _MM_HINT_T2);
}
}
auto bc = [&] [[gnu::always_inline]] (size_t c) {
return vftype(_mm256_broadcast_sd(tw[c] + g));
};
vpoint v1 = {bc(0), bc(1)}, v2 = {bc(2), bc(3)}, v3 = {bc(4), bc(5)};
auto forward = [&] [[gnu::always_inline]] (cvector const& a) {
auto A = a.at(pos), B = a.at(pos + 4) * v1, C = a.at(pos + 8) * v2, D = a.at(pos + 12) * v3;
return std::array<vpoint, 4>{(A + C) + (B + D), (A + C) - (B + D), (A - C) + vi(B - D),
(A - C) - vi(B - D)};
};
auto a = transpose(forward(*this));
auto b = [&] {
if constexpr(square) {
return a;
} else {
return transpose(forward(t));
}
}();
// The four residues are taken modulo x^4 - rt * {1, -1, i, -i}.
const auto flip_re = _mm256_set_pd(0., -0., -0., 0.), flip_im = _mm256_set_pd(-0., 0., -0., 0.);
vpoint w = {
vftype(_mm256_xor_pd(_mm256_blend_pd(__m256d(real(v1)), __m256d(imag(v1)), 0b1100), flip_re)),
vftype(_mm256_xor_pd(_mm256_blend_pd(__m256d(imag(v1)), __m256d(real(v1)), 0b1100), flip_im))};
auto mul = [&] [[gnu::always_inline]] (vpoint a0, vpoint a1, vpoint b0, vpoint b1) {
auto p = a0 * b0, q = a1 * b1;
return std::array<vpoint, 2>{cmadd(w, q, p), cmcross(a0 + a1, b0 + b1, p, q)};
};
auto p = mul(a[0], a[2], b[0], b[2]), q = mul(a[1], a[3], b[1], b[3]);
auto m = mul(a[0] + a[1], a[2] + a[3], b[0] + b[1], b[2] + b[3]);
auto c = transpose({cmadd(w, q[1], p[0]), (m[0] - p[0]) - q[0], p[1] + q[0], (m[1] - p[1]) - q[1]});
auto A = c[0], B = c[1], C = c[2], D = c[3];
at(pos) = (A + B) + (C + D);
at(pos + 8) = mulconj((A + B) - (C + D), v2);
at(pos + 4) = mulconj((A - B) - vi(C - D), v1);
at(pos + 12) = mulconj((A - B) + vi(C - D), v3);
}
}
}
// A product in two steps, this <- this * t modulo x^n - i up to the factor n / flen:
// forward() on both operands, then multiply(t), which may be *this for a square.
// The forward transform stops at groups of 16 points and dot_fused16 multiplies those,
// which saves a pass over each operand and one over the result. That needs powers of
// four, so a length 2 * 4^k takes its radix-two level at the top, modulo
// x^(n/2) -+ sqrt(i); short lengths take the complete transform and the 4-point product.
void forward() {
if(!fused_leaves()) {
return fft();
}
size_t n = size(), part = fused_part();
if(part < n) {
vpoint vrt = {vz + real(roots[4]), vz + imag(roots[4])};
for(size_t k = 0; k < part; k += flen) {
auto t = at(k + part) * vrt;
at(k + part) = at(k) - t;
at(k) += t;
}
}
for(size_t offset = 0; offset < n; offset += part) {
transform<false, 0, 0, true>(n, false, offset, part);
}
checkpoint("fft");
}
void multiply(cvector const& t) {
if(!fused_leaves()) {
dot(t);
return ifft<true, false>();
}
size_t n = size(), part = fused_part();
dot_fused16<0>(t, 0, n);
checkpoint("dot");
for(size_t offset = 0; offset < n; offset += part) {
transform<true, 0, 0, true>(n, false, offset, part);
}
if(part < n) {
vpoint cvrt = {vz + real(roots[4]), vz - imag(roots[4])};
for(size_t k = 0; k < part; k += flen) {
auto t = at(k) - at(k + part);
at(k) += at(k + part);
at(k + part) = t * cvrt;
}
}
checkpoint("ifft");
}
// Radix-64 out-of-cache pass for n = 2^24, run as two tiled radix-8 stages.
// With Fuse=1 (forward only) the first stage lifts u32 residues to Gaussian
// coordinates on load, so the spectrum buffer is written once and never re-read
// before the in-cache block phase. The index-keyed noise makes both branches see
// the same representatives.
struct fuse_args {
const uint32_t* src = nullptr;
size_t count = 0;
uint64_t seed = 0;
double a = 0, b = 0, a_over_p = 0, b_over_p = 0;
};
static constexpr size_t sweep_tile = 256;
template<bool inverse, int Mode, size_t Tile, int Fuse = 0, bool Neg = false>
void sweep8(fuse_args const& fa = {}) {
constexpr size_t n = 1 << 24;
static const std::array<std::array<point, 7>, 9> weights = []() {
std::array<std::array<point, 7>, 9> table;
for(size_t count: {size_t(1), size_t(8)}) {
for(size_t k = 0; k < count; k++) {
size_t rev = 0, x = k;
for(size_t c = count; c > 1; c >>= 1) {
rev = (rev << 1) | (x & 1);
x >>= 1;
}
long double angle = std::numbers::pi_v<long double> * (1 + 4 * rev) / (16 * count);
if(k & 1) {
angle -= std::numbers::pi_v<long double> / 4;
}
for(size_t j = 1; j < 8; j++) {
long double a = j * angle;
if constexpr(Mode == 0) {
table[(count - 1) / 7 + k][j - 1] = {double(cosl(a)), double(sinl(a))};
} else {
table[(count - 1) / 7 + k][j - 1] = {double(sinl(a)), double(tanl(a / 2))};
}
}
}
}
return table;
}();
auto lift = [&] [[gnu::always_inline]] (size_t idx) -> vpoint {
i32x4 bits{};
if(idx + 4 <= fa.count) {
std::memcpy(&bits, fa.src + idx, sizeof(bits));
} else if(idx < fa.count) {
for(size_t j = 0; j < fa.count - idx; j++) {
bits[j] = int32_t(fa.src[idx + j]);
}
} else {
return vpoint{vz, vz};
}
auto x = __builtin_convertvector(bits, vftype);
u32x4 h =
u32x4{uint32_t(idx), uint32_t(idx + 1), uint32_t(idx + 2), uint32_t(idx + 3)} ^ uint32_t(fa.seed);
h *= 0x9E3779B1u;
h ^= h >> 15;
h *= 0x85EBCA77u;
h ^= h >> 13;
h *= 0xC2B2AE3Du;
h ^= h >> 16;
auto noise = __builtin_convertvector(i32x4(h), vftype) * 0x1p-32;
auto q = round(x * fa.a_over_p + noise), t = round(x * fa.b_over_p + noise);
auto re = x - q * fa.a - t * fa.b, im = t * fa.a - q * fa.b;
return vpoint{re, Neg ? -im : im};
};
auto stage = [&]<bool top> [[gnu::always_inline]] (size_t offset, size_t length, size_t begin, size_t end) {
size_t step = length / 8, k = offset / length;
auto const& w = weights[(n / length - 1) / 7 + k];
auto rot = [&]<size_t J> [[gnu::always_inline]] (vpoint z) {
auto c = w[J - 1];
if constexpr(Mode == 0) {
return z * vpoint{vz + real(c), inverse ? vz - imag(c) : vz + imag(c)};
} else {
auto s = inverse ? vz - real(c) : vz + real(c), t = inverse ? vz - imag(c) : vz + imag(c);
auto x = vftype(_mm256_fnmadd_pd(__m256d(t), __m256d(imag(z)), __m256d(real(z))));
auto y = vftype(_mm256_fmadd_pd(__m256d(s), __m256d(x), __m256d(imag(z))));
return vpoint{vftype(_mm256_fnmadd_pd(__m256d(t), __m256d(y), __m256d(x))), y};
}
};
auto add = [] [[gnu::always_inline]] (vpoint a, vpoint b) {
if constexpr(Mode != 2) {
return a + b;
} else {
return vpoint{vftype(_mm256_fmadd_pd(__m256d(real(a)), _mm256_set1_pd(1), __m256d(real(b)))),
vftype(_mm256_fmadd_pd(__m256d(imag(a)), _mm256_set1_pd(1), __m256d(imag(b))))};
}
};
auto sub = [] [[gnu::always_inline]] (vpoint a, vpoint b) {
if constexpr(Mode != 2) {
return a - b;
} else {
return vpoint{vftype(_mm256_fmsub_pd(__m256d(real(a)), _mm256_set1_pd(1), __m256d(real(b)))),
vftype(_mm256_fmsub_pd(__m256d(imag(a)), _mm256_set1_pd(1), __m256d(imag(b))))};
}
};
auto d4 = [] [[gnu::always_inline]] (vpoint a, vpoint b, vpoint c, vpoint d) {
auto s = a + c, t = a - c, u = b + d, v = vi(b - d);
if constexpr(inverse) {
return std::array<vpoint, 4>{s + u, t - v, s - u, t + v};
} else {
return std::array<vpoint, 4>{s + u, t + v, s - u, t - v};
}
};
constexpr double q = 0.707106781186547524400844362104849039;
auto r1 = [] [[gnu::always_inline]] (vpoint z) {
if constexpr(inverse) {
return vpoint{(real(z) + imag(z)) * q, (imag(z) - real(z)) * q};
} else {
return vpoint{(real(z) - imag(z)) * q, (real(z) + imag(z)) * q};
}
};
auto r3 = [] [[gnu::always_inline]] (vpoint z) {
if constexpr(inverse) {
return vpoint{(imag(z) - real(z)) * q, (-imag(z) - real(z)) * q};
} else {
return vpoint{(-real(z) - imag(z)) * q, (real(z) - imag(z)) * q};
}
};
std::array<vpoint*, 8> input, output;
for(size_t j = 0; j < 8; j++) {
input[j] = output[j] = r.data() + (offset + begin + j * step) / flen;
}
if(k & 1) {
constexpr std::array<size_t, 8> perm = {7, 6, 4, 5, 0, 1, 2, 3};
for(size_t j = 0; j < 8; j++) {
if constexpr(inverse) {
input[j] = output[perm[j]];
} else {
output[j] = input[perm[j]];
}
}
}
constexpr bool fused_in = top && Fuse == 1 && !inverse;
for(size_t j = 0; j < (end - begin) / flen; j++) {
size_t base = offset + begin + j * flen;
auto in = [&]<size_t S> [[gnu::always_inline]] () {
if constexpr(fused_in) {
return lift(base + S * step);
} else {
return input[S][j];
}
};
if constexpr(!inverse) {
auto E =
d4(in.template operator()<0>(), rot.template operator()<2>(in.template operator()<2>()),
rot.template operator()<4>(in.template operator()<4>()),
rot.template operator()<6>(in.template operator()<6>()));
auto O = d4(rot.template operator()<1>(in.template operator()<1>()),
rot.template operator()<3>(in.template operator()<3>()),
rot.template operator()<5>(in.template operator()<5>()),
rot.template operator()<7>(in.template operator()<7>()));
auto a = O[0], b = r1(O[1]), c = vi(O[2]), d = r3(O[3]);
output[0][j] = add(E[0], a);
output[1][j] = sub(E[0], a);
output[2][j] = add(E[2], c);
output[3][j] = sub(E[2], c);
output[4][j] = add(E[1], b);
output[5][j] = sub(E[1], b);
output[6][j] = add(E[3], d);
output[7][j] = sub(E[3], d);
} else {
auto E = d4(add(input[0][j], input[1][j]), add(input[4][j], input[5][j]),
add(input[2][j], input[3][j]), add(input[6][j], input[7][j]));
auto O = d4(sub(input[0][j], input[1][j]), r1(sub(input[4][j], input[5][j])),
-vi(sub(input[2][j], input[3][j])), r3(sub(input[6][j], input[7][j])));
output[0][j] = E[0];
output[1][j] = rot.template operator()<1>(O[0]);
output[2][j] = rot.template operator()<2>(E[1]);
output[3][j] = rot.template operator()<3>(O[1]);
output[4][j] = rot.template operator()<4>(E[2]);
output[5][j] = rot.template operator()<5>(O[2]);
output[6][j] = rot.template operator()<6>(E[3]);
output[7][j] = rot.template operator()<7>(O[3]);
}
}
};
constexpr size_t h = n / 64;
for(size_t j = 0; j < h; j += Tile) {
size_t end = std::min(h, j + Tile);
auto first = [&]() {
for(size_t t = 0; t < 8; t++) {
stage.template operator()<true>(0, n, j + t * h, end + t * h);
}
};
auto second = [&]() {
for(size_t k = 0; k < 8; k++) {
stage.template operator()<false>(k * n / 8, n / 8, j, end);
}
};
if constexpr(inverse) {
second();
first();
} else {
first();
second();
}
}
}
// Product for n = 2^24: the top three stages split each input into 64 independent
// blocks. Both forward transforms read the u32 inputs directly; each block then
// completes its two forward transforms, the product, and the inverse before the
// final three inverse stages combine the results.
// Fusing the Gaussian lift into the first pass saves a write and a read of each
// spectrum, but makes that pass compute-bound on the judge (measured slower there),
// so it stays opt-in; by default both spectra are filled first and swept in place.
static constexpr bool fuse_forward = false;
template<bool Neg, bool Fused = fuse_forward, bool Square = false>
void cache_product(cvector& b, fuse_args const& fa = {}, fuse_args const& fb = {}) {
constexpr size_t n = 1 << 24, block = 1 << 18;
prepare_roots(n / 16);
prepare_shear_roots();
if constexpr(Fused) {
sweep8<false, 2, sweep_tile, 1, Neg>(fa);
if constexpr(!Square) {
b.sweep8<false, 2, sweep_tile, 1, Neg>(fb);
}
} else {
sweep8<false, 2, sweep_tile>();
if constexpr(!Square) {
b.sweep8<false, 2, sweep_tile>();
}
}
checkpoint("sweep forward");
for(size_t offset = 0; offset < n; offset += block) {
transform<false, n, block, true>(n, false, offset, block);
if constexpr(!Square) {
b.transform<false, n, block, true>(n, false, offset, block);
}
dot_fused16<n, Square>(b, offset, block);
transform<true, n, block, true>(n, false, offset, block);
}
checkpoint("blocks");
sweep8<true, 2, sweep_tile>();
checkpoint("sweep inverse");
}
static constexpr size_t pre_evals = 1 << 16;
static const std::array<size_t, pre_evals> eval_args;
static const std::array<point, pre_evals> evalp;
private:
// The power of four that the fused product works on: all of n = 4^k, half of n = 2 * 4^k.
size_t fused_part() const {
return size() >> (std::countr_zero(size()) % 2);
}
bool fused_leaves() const {
return fused_part() >= 16 * dot_tile;
}
// Tile two radix-four stages together before descending into each child.
template<bool inverse, size_t fixed = 0, size_t range_fixed = 0, bool omit16 = false>
void transform(size_t input_n, bool parity, size_t range_offset = 0, size_t range_length = 0) {
if constexpr(range_fixed) {
range_length = range_fixed;
}
const size_t n = fixed ? fixed : input_n;
if constexpr(!range_fixed) {
prepare_roots(n / 16);
if constexpr(fixed == (1 << 24)) {
prepare_shear_roots();
}
}
size_t log_n = std::countr_zero(n);
auto butterfly = [&] [[gnu::always_inline]] (size_t offset, size_t length, size_t begin, size_t end) {
if constexpr(omit16) {
if(length == 16) {
return;
}
}
size_t step = length / 4, log_length = std::countr_zero(length), k = offset >> log_length;
auto *p0 = r.data() + (offset + begin) / flen, *p1 = r.data() + (offset + begin + step) / flen,
*p2 = r.data() + (offset + begin + 2 * step) / flen,
*p3 = r.data() + (offset + begin + 3 * step) / flen;
auto run = [&]<bool shear> [[gnu::always_inline]] () {
vpoint v1, v2, v3;
vftype t1{}, t2{}, t3{};
if constexpr(shear && fixed == (1 << 24)) {
auto const& c = shear_roots[((n >> log_length) - 1) / 3 + k];
v1 = {vz, inverse ? vz - real(c[0]) : vz + real(c[0])};
v2 = {vz, inverse ? vz - real(c[1]) : vz + real(c[1])};
v3 = {vz, inverse ? vz - real(c[2]) : vz + real(c[2])};
t1 = inverse ? vz - imag(c[0]) : vz + imag(c[0]);
t2 = inverse ? vz - imag(c[1]) : vz + imag(c[1]);
t3 = inverse ? vz - imag(c[2]) : vz + imag(c[2]);
} else {
point e = k < pre_evals ? evalp[k] : extra[k - pre_evals];
point rt = roots[log_n + 5 - log_length] * e;
v1 = {vz + real(rt), inverse ? vz - imag(rt) : vz + imag(rt)};
if constexpr(shear) {
if(k & 1) {
if constexpr(inverse) {
v1 = vi(v1);
} else {
v1 = -vi(v1);
}
}
}
v2 = v1 * v1;
v3 = v1 * v2;
if constexpr(shear) {
t1 = imag(v1) / (vz + 1.0 + real(v1));
t2 = imag(v2) / (vz + 1.0 + real(v2));
t3 = imag(v3) / (vz + 1.0 + real(v3));
}
}
auto rotate = [] [[gnu::always_inline]] (vpoint z, vpoint v, vftype t) {
if constexpr(!shear) {
return z * v;
} else {
auto x = vftype(_mm256_fnmadd_pd(__m256d(t), __m256d(imag(z)), __m256d(real(z))));
auto y = vftype(_mm256_fmadd_pd(__m256d(imag(v)), __m256d(x), __m256d(imag(z))));
return vpoint{vftype(_mm256_fnmadd_pd(__m256d(t), __m256d(y), __m256d(x))), y};
}
};
auto *i0 = p0, *i1 = p1, *i2 = p2, *i3 = p3, *o0 = p0, *o1 = p1, *o2 = p2, *o3 = p3;
if constexpr(shear) {
if(k & 1) {
if constexpr(inverse) {
i0 = p3;
i1 = p2;
i2 = p0;
i3 = p1;
} else {
o0 = p3;
o1 = p2;
o2 = p0;
o3 = p1;
}
}
}
for(size_t j = 0; j < (end - begin) / flen; j++) {
auto A = i0[j], B = i1[j], C = i2[j], D = i3[j];
if constexpr(inverse) {
o0[j] = (A + B) + (C + D);
o2[j] = rotate((A + B) - (C + D), v2, t2);
o1[j] = rotate((A - B) - vi(C - D), v1, t1);
o3[j] = rotate((A - B) + vi(C - D), v3, t3);
} else {
B = rotate(B, v1, t1);
C = rotate(C, v2, t2);
D = rotate(D, v3, t3);
o0[j] = (A + C) + (B + D);
o1[j] = (A + C) - (B + D);
o2[j] = (A - C) + vi(B - D);
o3[j] = (A - C) - vi(B - D);
}
}
};
if(length >= shear_min<fixed>) {
run.template operator()<true>();
} else {
run.template operator()<false>();
}
};
auto recurse = [&](this auto const& self, size_t offset, size_t length) -> void {
if(length < 4 * flen) {
return;
}
if(length >= (1 << 15)) {
size_t step = length / 16;
if constexpr(inverse) {
for(size_t t = 0; t < 16; t++) {
self(offset + t * step, step);
}
}
for(size_t j = 0; j < step; j += 256) {
size_t end = std::min(step, j + 256);
if constexpr(inverse) {
for(size_t t = 0; t < 4; t++) {
butterfly(offset + t * length / 4, length / 4, j, end);
}
for(size_t t = 0; t < 4; t++) {
butterfly(offset, length, j + t * step, end + t * step);
}
} else {
for(size_t t = 0; t < 4; t++) {
butterfly(offset, length, j + t * step, end + t * step);
}
for(size_t t = 0; t < 4; t++) {
butterfly(offset + t * length / 4, length / 4, j, end);
}
}
}
if constexpr(!inverse) {
for(size_t t = 0; t < 16; t++) {
self(offset + t * step, step);
}
}
} else if(length >= (size_t(1) << (6 + parity))) {
auto finish = [&]<bool par>() {
constexpr size_t chunk = size_t(1) << (6 + par);
constexpr size_t bottom = size_t(1) << (4 + par);
auto small = [&]<size_t L> [[gnu::always_inline]] (this auto const& self, size_t pos) -> void {
if constexpr(inverse && L > bottom) {
for(size_t q = 0; q < 4; q++) {
self.template operator()<L / 4>(pos + q * (L / 4));
}
}
butterfly(pos, L, 0, L / 4);
if constexpr(!inverse && L > bottom) {
for(size_t q = 0; q < 4; q++) {
self.template operator()<L / 4>(pos + q * (L / 4));
}
}
};
for(size_t leaf = offset; leaf < offset + length; leaf += chunk) {
if constexpr(inverse) {
small.template operator()<chunk>(leaf);
size_t level =
std::min<size_t>(std::countr_one(leaf + chunk - 1), std::countr_zero(length));
for(size_t lvl = 6 + 2 + par; lvl <= level; lvl += 2) {
size_t len = size_t(1) << lvl;
butterfly(leaf & ~(len - 1), len, 0, len / 4);
}
} else {
size_t level = std::min<size_t>(std::countr_zero(n + leaf), std::countr_zero(length));
level -= level % 2 != par;
for(size_t lvl = level; lvl >= 6 + 2 + par; lvl -= 2) {
size_t len = size_t(1) << lvl;
butterfly(leaf & ~(len - 1), len, 0, len / 4);
}
small.template operator()<chunk>(leaf);
}
}
};
if(parity) {
finish.template operator()<true>();
} else {
finish.template operator()<false>();
}
} else {
if constexpr(inverse) {
for(size_t leaf = offset + 3 * flen; leaf < offset + length; leaf += 4 * flen) {
size_t level = std::min<size_t>(std::countr_one(leaf + 3), std::countr_zero(length));
for(size_t lvl = 4 + parity; lvl <= level; lvl += 2) {
size_t len = size_t(1) << lvl;
butterfly(leaf & ~(len - 1), len, 0, len / 4);
}
}
} else {
for(size_t leaf = offset; leaf < offset + length; leaf += 4 * flen) {
size_t level = std::min<size_t>(std::countr_zero(n + leaf), std::countr_zero(length));
level -= level % 2 != parity;
for(size_t lvl = level; lvl >= 4; lvl -= 2) {
size_t len = size_t(1) << lvl;
butterfly(leaf & ~(len - 1), len, 0, len / 4);
}
}
}
}
};
// Radix two is performed separately at the leaves.
recurse(range_offset, range_length ? range_length : n);
}
// Shortest butterfly that uses the shear rotation; the fixed 2^24 transform reads its
// shear roots from a table, so they are worth using down to the last in-block level.
template<size_t fixed>
static constexpr size_t shear_min = fixed == (1 << 24) ? 64 : 256;
static big_vector<std::array<point, 3>> shear_roots;
static void prepare_shear_roots() {
constexpr size_t n = 1 << 24;
if(!shear_roots.empty()) {
return;
}
shear_roots.resize((n / 16 - 1) / 3, std::array<point, 3>{});
for(size_t len = n; len >= shear_min<n>; len /= 4) {
size_t count = n / len, base = (count - 1) / 3;
point factor = roots[29 - std::countr_zero(len)];
for(size_t k = 0; k < count; k++) {
point rt = factor * (k < pre_evals ? evalp[k] : extra[k - pre_evals]);
vpoint v1 = {vz + real(rt), vz + imag(rt)};
if(k & 1) {
v1 = -vi(v1);
}
vpoint v2 = v1 * v1, v3 = v1 * v2;
vftype t1 = imag(v1) / (vz + 1.0 + real(v1)), t2 = imag(v2) / (vz + 1.0 + real(v2)),
t3 = imag(v3) / (vz + 1.0 + real(v3));
shear_roots[base + k] = {point(imag(v1)[0], t1[0]), point(imag(v2)[0], t2[0]),
point(imag(v3)[0], t3[0])};
}
}
}
static big_vector<point> extra;
// Keep the usual table small; cache additional roots for large transforms.
static void prepare_roots(size_t n) {
if(n <= pre_evals + extra.size()) {
return;
}
size_t old = extra.size();
extra.resize(std::bit_ceil(n) - pre_evals);
static const std::array<point, 256> coarse = []() {
std::array<point, 256> out;
for(size_t i = 0; i < 256; i++) {
out[i] = polar<ftype>(1., std::numbers::pi * double((eval_args[256 + i] - 1) / 2) / 512.0);
}
return out;
}();
for(size_t h = pre_evals + old; h < pre_evals + extra.size(); h *= 2) {
for(size_t i = h; i < 2 * h; i += 256) {
point fine = polar<ftype>(1., std::numbers::pi / double(4 * h) * double(eval_arg(4 * i)));
for(size_t j = 0; j < 256; j++) {
extra[i + j - pre_evals] = coarse[j] * fine;
}
}
}
}
};
big_vector<std::array<point, 3>> cvector::shear_roots;
big_vector<point> cvector::extra;
const std::array<size_t, cvector::pre_evals> cvector::eval_args = []() {
std::array<size_t, pre_evals> res = {};
for(size_t i = 1; i < pre_evals; i++) {
res[i] = res[i >> 1] | (i & 1) << (std::bit_width(i) - 1);
}
return res;
}();
const std::array<point, cvector::pre_evals> cvector::evalp = []() {
std::array<point, pre_evals> res = {};
res[0] = 1;
for(size_t n = 1; n < pre_evals; n++) {
res[n] = polar<ftype>(1., std::numbers::pi * ftype(eval_args[n]) / ftype(4 * std::bit_floor(n)));
}
return res;
}();
}
#pragma GCC pop_options
#line 1 "cp-algo/random/rng.hpp"
#line 5 "cp-algo/random/rng.hpp"
namespace cp_algo::random {
std::mt19937_64 gen(
std::chrono::steady_clock::now().time_since_epoch().count()
);
uint64_t rng() {
return gen();
}
}
#line 9 "verify/poly/wildcard.test.cpp"
using namespace std;
using namespace cp_algo::math;
using fft::ftype;
using fft::point;
using fft::vftype;
using fft::cvector;
void semicorr(auto &a, auto &b) {
a.fft();
b.fft();
a.dot(b);
a.ifft();
}
auto is_integer(auto a) {
static const ftype eps = 1e-9;
return cp_algo::abs(a - cp_algo::round(a)) < eps;
}
cp_algo::big_string matches(cp_algo::big_string const& A, cp_algo::big_string const& B, char wild = '*') {
static ftype project[2][128];
static bool init = false;
if(!init) {
init = true;
std::uniform_real_distribution<> dis(.5, 2.);
for(int i = 0; i < 128; i++) {
ftype x = dis(cp_algo::random::gen);
project[0][i] = x;
project[1][i] = 1. / x;
}
}
project[0][(int)wild] = project[1][(int)wild] = 0;
cp_algo::big_vector<cvector> P;
P.emplace_back((size(A) + 1) / 2);
P.emplace_back((size(A) + 1) / 2);
auto N = P[0].size();
auto assign = [&](int z) {
return [&, z](auto ic) {
auto [i, c] = ic;
if(i < (int)N) {
real(P[z].r[i / fft::flen])[i % fft::flen] = project[z][(int)c];
} else {
i -= N;
imag(P[z].r[i / fft::flen])[i % fft::flen] = project[z][(int)c];
}
};
};
ranges::for_each(A | views::enumerate, assign(0));
ranges::for_each(B | views::reverse | views::enumerate, assign(1));
cp_algo::checkpoint("cvector fill");
semicorr(P[0], P[1]);
cp_algo::big_string ans(2 * size(P[0]), '0');
auto start = (ssize(B) - 1) / fft::flen * fft::flen;
for(auto j = start; j < size(ans); j += fft::flen) {
decltype(is_integer(real(P[0].at(j)))) check;
if(j < N) {
check = is_integer(real(P[0].at(j)));
} else {
check = is_integer(imag(P[0].at(j - N)));
}
for(int z = 0; z < 4; z++) {
ans[j + z] ^= (bool)check[z];
}
}
cp_algo::checkpoint("fill answer");
return ans.substr(size(B) - 1, size(A) - size(B) + 1);
}
void solve() {
cp_algo::big_string a, b;
cin >> a >> b;
cp_algo::checkpoint("input");
cout << matches(a, b) << "\n";
cp_algo::checkpoint("output");
cp_algo::checkpoint<true>("done");
}
signed main() {
//freopen("input.txt", "r", stdin);
ios::sync_with_stdio(0);
cin.tie(0);
int t = 1;
//cin >> t;
while(t--) {
solve();
}
}
Test cases
| Env | Name | Status | Elapsed | Memory |
|---|---|---|---|---|
| g++ | alternating_00 |
AC |
11 ms | 13 MB |
| g++ | alternating_01 |
AC |
12 ms | 13 MB |
| g++ | alternating_02 |
AC |
4 ms | 5 MB |
| g++ | alternating_03 |
AC |
10 ms | 13 MB |
| g++ | alternating_04 |
AC |
10 ms | 13 MB |
| g++ | example_00 |
AC |
2 ms | 4 MB |
| g++ | hack_998244353_00 |
AC |
11 ms | 14 MB |
| g++ | hack_998244353_01 |
AC |
11 ms | 14 MB |
| g++ | hack_998244353_02 |
AC |
11 ms | 14 MB |
| g++ | random_00 |
AC |
11 ms | 13 MB |
| g++ | random_01 |
AC |
11 ms | 13 MB |
| g++ | random_02 |
AC |
3 ms | 5 MB |
| g++ | random_03 |
AC |
10 ms | 13 MB |
| g++ | random_04 |
AC |
10 ms | 13 MB |
| g++ | random_ab_00 |
AC |
10 ms | 13 MB |
| g++ | random_ab_01 |
AC |
11 ms | 13 MB |
| g++ | random_ab_02 |
AC |
3 ms | 5 MB |
| g++ | random_ab_03 |
AC |
11 ms | 13 MB |
| g++ | random_ab_04 |
AC |
10 ms | 13 MB |