CP-Algorithms Library
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cp-algo/math/fft64.hpp
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- Last update: 2025-05-31 15:35:36+02:00
- Include:
#include "cp-algo/math/fft64.hpp"
Depends on
- cp-algo/math/common.hpp
- 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
Verified with
Code
#ifndef CP_ALGO_MATH_FFT64_HPP
#define CP_ALGO_MATH_FFT64_HPP
#include "../random/rng.hpp"
#include "../math/common.hpp"
#include "../math/cvector.hpp"
namespace cp_algo::math::fft {
struct dft64 {
std::vector<cp_algo::math::fft::cvector> cv;
static uint64_t factor, ifactor;
static bool _init;
static void init() {
if(_init) return;
_init = true;
factor = random::rng();
if(factor % 2 == 0) {factor++;}
ifactor = inv2(factor);
}
dft64(auto const& a, size_t n): cv(4, n) {
init();
uint64_t cur = 1, step = bpow(factor, n);
for(size_t i = 0; i < std::min(std::size(a), n); i++) {
auto split = [&](size_t i, uint64_t mul) -> std::array<int16_t, 4> {
uint64_t x = i < std::size(a) ? a[i] * mul : 0;
std::array<int16_t, 4> res;
for(int z = 0; z < 4; z++) {
res[z] = int16_t(x);
x = (x >> 16) + (res[z] < 0);
}
return res;
};
auto re = split(i, cur);
auto im = split(n + i, cur * step);
for(int z = 0; z < 4; z++) {
real(cv[z].at(i))[i % 4] = re[z];
imag(cv[z].at(i))[i % 4] = im[z];
}
cur *= factor;
}
checkpoint("dft64 init");
for(auto &x: cv) {
x.fft();
}
}
void dot(dft64 const& t) {
size_t N = cv[0].size();
cvector::exec_on_evals<1>(N / flen, [&](size_t k, point rt) {
k *= flen;
auto [A0x, A0y] = cv[0].at(k);
auto [A1x, A1y] = cv[1].at(k);
auto [A2x, A2y] = cv[2].at(k);
auto [A3x, A3y] = cv[3].at(k);
std::array B = {
t.cv[0].at(k),
t.cv[1].at(k),
t.cv[2].at(k),
t.cv[3].at(k)
};
std::array<vpoint, 4> C = {vz, vz, vz, vz};
for (size_t i = 0; i < flen; i++) {
std::array A = {
vpoint{vz + A0x[i], vz + A0y[i]},
vpoint{vz + A1x[i], vz + A1y[i]},
vpoint{vz + A2x[i], vz + A2y[i]},
vpoint{vz + A3x[i], vz + A3y[i]}
};
for(size_t k = 0; k < 4; k++) {
for(size_t i = 0; i <= k; i++) {
C[k] += A[i] * B[k - i];
}
}
for(size_t k = 0; k < 4; k++) {
real(B[k]) = rotate_right(real(B[k]));
imag(B[k]) = rotate_right(imag(B[k]));
auto bx = real(B[k])[0], by = imag(B[k])[0];
real(B[k])[0] = bx * real(rt) - by * imag(rt);
imag(B[k])[0] = bx * imag(rt) + by * real(rt);
}
}
cv[0].at(k) = C[0];
cv[1].at(k) = C[1];
cv[2].at(k) = C[2];
cv[3].at(k) = C[3];
});
checkpoint("dot");
for(auto &x: cv) {
x.ifft();
}
}
void recover_mod(auto &res, size_t k) {
size_t n = cv[0].size();
uint64_t cur = 1, step = bpow(ifactor, n);
for(size_t i = 0; i < std::min(k, n); i++) {
std::array re = {real(cv[0].get(i)), real(cv[1].get(i)), real(cv[2].get(i)), real(cv[3].get(i))};
std::array im = {imag(cv[0].get(i)), imag(cv[1].get(i)), imag(cv[2].get(i)), imag(cv[3].get(i))};
auto set_i = [&](size_t i, auto &x, auto mul) {
if (i >= k) return;
res[i] = llround(x[0]) + (llround(x[1]) << 16) + (llround(x[2]) << 32) + (llround(x[3]) << 48);
res[i] *= mul;
};
set_i(i, re, cur);
set_i(n + i, im, cur * step);
cur *= ifactor;
}
cp_algo::checkpoint("recover mod");
}
};
uint64_t dft64::factor = 1, dft64::ifactor = 1;
bool dft64::_init = false;
void conv64(auto& a, auto const& b) {
size_t n = a.size(), m = b.size();
size_t N = std::max(flen, std::bit_ceil(n + m - 1) / 2);
dft64 A(a, N), B(b, N);
A.dot(B);
a.resize(n + m - 1);
A.recover_mod(a, n + m - 1);
}
}
#endif // CP_ALGO_MATH_FFT64_HPP
#line 1 "cp-algo/math/fft64.hpp"
#line 1 "cp-algo/random/rng.hpp"
#include <chrono>
#include <random>
namespace cp_algo::random {
uint64_t rng() {
static std::mt19937_64 rng(
std::chrono::steady_clock::now().time_since_epoch().count()
);
return rng();
}
}
#line 1 "cp-algo/math/common.hpp"
#include <functional>
#include <cstdint>
#include <cassert>
namespace cp_algo::math {
#ifdef CP_ALGO_MAXN
const int maxn = CP_ALGO_MAXN;
#else
const int maxn = 1 << 19;
#endif
const int magic = 64; // threshold for sizes to run the naive algo
auto bpow(auto const& x, auto n, auto const& one, auto op) {
if(n == 0) {
return one;
} else {
auto t = bpow(x, n / 2, one, op);
t = op(t, t);
if(n % 2) {
t = op(t, x);
}
return t;
}
}
auto bpow(auto x, auto n, auto ans) {
return bpow(x, n, ans, std::multiplies{});
}
template<typename T>
T bpow(T const& x, auto n) {
return bpow(x, n, T(1));
}
inline constexpr auto inv2(auto x) {
assert(x % 2);
std::make_unsigned_t<decltype(x)> y = 1;
while(y * x != 1) {
y *= 2 - x * y;
}
return y;
}
}
#line 1 "cp-algo/math/cvector.hpp"
#line 1 "cp-algo/util/simd.hpp"
#include <experimental/simd>
#line 5 "cp-algo/util/simd.hpp"
#include <cstddef>
#include <memory>
namespace cp_algo {
template<typename T, size_t len>
using simd [[gnu::vector_size(len * sizeof(T))]] = T;
using i64x4 = simd<int64_t, 4>;
using u64x4 = simd<uint64_t, 4>;
using u32x8 = simd<uint32_t, 8>;
using i32x4 = simd<int32_t, 4>;
using u32x4 = simd<uint32_t, 4>;
using i16x4 = simd<int16_t, 4>;
using u8x32 = simd<uint8_t, 32>;
using dx4 = simd<double, 4>;
[[gnu::target("avx2")]] inline dx4 abs(dx4 a) {
return a < 0 ? -a : a;
}
// https://stackoverflow.com/a/77376595
// works for ints in (-2^51, 2^51)
static constexpr dx4 magic = dx4() + (3ULL << 51);
[[gnu::target("avx2")]] inline i64x4 lround(dx4 x) {
return i64x4(x + magic) - i64x4(magic);
}
[[gnu::target("avx2")]] inline dx4 to_double(i64x4 x) {
return dx4(x + i64x4(magic)) - magic;
}
[[gnu::target("avx2")]] inline dx4 round(dx4 a) {
return dx4{
std::nearbyint(a[0]),
std::nearbyint(a[1]),
std::nearbyint(a[2]),
std::nearbyint(a[3])
};
}
[[gnu::target("avx2")]] inline u64x4 low32(u64x4 x) {
return x & uint32_t(-1);
}
[[gnu::target("avx2")]] inline auto swap_bytes(auto x) {
return decltype(x)(__builtin_shufflevector(u32x8(x), u32x8(x), 1, 0, 3, 2, 5, 4, 7, 6));
}
[[gnu::target("avx2")]] inline u64x4 montgomery_reduce(u64x4 x, uint32_t mod, uint32_t imod) {
auto x_ninv = u64x4(_mm256_mul_epu32(__m256i(x), __m256i() + imod));
x += u64x4(_mm256_mul_epu32(__m256i(x_ninv), __m256i() + mod));
return swap_bytes(x);
}
[[gnu::target("avx2")]] inline u64x4 montgomery_mul(u64x4 x, u64x4 y, uint32_t mod, uint32_t imod) {
return montgomery_reduce(u64x4(_mm256_mul_epu32(__m256i(x), __m256i(y))), mod, imod);
}
[[gnu::target("avx2")]] 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)));
}
[[gnu::target("avx2")]] 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>
[[gnu::target("avx2")]] inline bool is_aligned(const auto* p) noexcept {
return (reinterpret_cast<std::uintptr_t>(p) % Align) == 0;
}
template<class Target>
[[gnu::target("avx2")]] inline Target& vector_cast(auto &&p) {
return *reinterpret_cast<Target*>(std::assume_aligned<alignof(Target)>(&p));
}
}
#line 1 "cp-algo/util/complex.hpp"
#include <iostream>
#include <cmath>
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;
constexpr complex(): x(), y() {}
constexpr complex(T x): x(x), y() {}
constexpr complex(T x, T y): x(x), y(y) {}
complex& operator *= (T t) {x *= t; y *= t; return *this;}
complex& operator /= (T t) {x /= t; y /= t; return *this;}
complex operator * (T t) const {return complex(*this) *= t;}
complex operator / (T t) const {return complex(*this) /= t;}
complex& operator += (complex t) {x += t.x; y += t.y; return *this;}
complex& operator -= (complex t) {x -= t.x; y -= t.y; return *this;}
complex operator * (complex t) const {return {x * t.x - y * t.y, x * t.y + y * t.x};}
complex operator / (complex t) const {return *this * t.conj() / t.norm();}
complex operator + (complex t) const {return complex(*this) += t;}
complex operator - (complex t) const {return complex(*this) -= t;}
complex& operator *= (complex t) {return *this = *this * t;}
complex& operator /= (complex t) {return *this = *this / t;}
complex operator - () const {return {-x, -y};}
complex conj() const {return {x, -y};}
T norm() const {return x * x + y * y;}
T abs() const {return std::sqrt(norm());}
T const real() const {return x;}
T const imag() const {return y;}
T& real() {return x;}
T& imag() {return y;}
static constexpr complex polar(T r, T theta) {return {T(r * cos(theta)), T(r * sin(theta))};}
auto operator <=> (complex const& t) const = default;
};
template<typename T>
complex<T> operator * (auto x, complex<T> y) {return y *= x;}
template<typename T> complex<T> conj(complex<T> x) {return x.conj();}
template<typename T> T norm(complex<T> x) {return x.norm();}
template<typename T> T abs(complex<T> x) {return x.abs();}
template<typename T> T& real(complex<T> &x) {return x.real();}
template<typename T> T& imag(complex<T> &x) {return x.imag();}
template<typename T> T const real(complex<T> const& x) {return x.real();}
template<typename T> T const imag(complex<T> const& x) {return x.imag();}
template<typename T>
constexpr complex<T> polar(T r, T theta) {
return complex<T>::polar(r, theta);
}
template<typename T>
std::ostream& operator << (std::ostream &out, complex<T> x) {
return out << x.real() << ' ' << x.imag();
}
}
#line 1 "cp-algo/util/checkpoint.hpp"
#line 5 "cp-algo/util/checkpoint.hpp"
#include <string>
#include <map>
namespace cp_algo {
std::map<std::string, double> checkpoints;
template<bool final = false>
void checkpoint([[maybe_unused]] std::string const& msg = "") {
#ifdef CP_ALGO_CHECKPOINT
static double last = 0;
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
}
}
#line 1 "cp-algo/util/big_alloc.hpp"
#line 6 "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, std::size_t Align = 32>
class big_alloc {
static_assert( Align >= alignof(void*), "Align must be at least pointer-size");
static_assert(std::popcount(Align) == 1, "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;
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);
madvise(raw, padded, MADV_POPULATE_WRITE);
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;
}
};
}
#line 7 "cp-algo/math/cvector.hpp"
#include <ranges>
#include <bit>
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)};
}
struct cvector {
std::vector<vpoint, big_alloc<vpoint>> r;
cvector(size_t n) {
n = std::max(flen, std::bit_ceil(n));
r.resize(n / flen);
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>
void set(size_t k, pt 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>
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 {
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);
for(size_t i = 0; i < n; i++) {
callback(i, factor * eval_point(step * i));
}
}
void dot(cvector const& t) {
size_t n = this->size();
exec_on_evals<1>(n / flen, [&](size_t k, point rt) {
k *= flen;
auto [Ax, Ay] = at(k);
auto Bv = t.at(k);
vpoint res = vz;
for (size_t i = 0; i < flen; i++) {
res += vpoint(vz + Ax[i], vz + Ay[i]) * 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);
}
set(k, res);
});
checkpoint("dot");
}
template<bool partial = true>
void ifft() {
size_t n = size();
if constexpr (!partial) {
point pi(0, 1);
exec_on_evals<4>(n / 4, [&](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), [&](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;
});
}
for(size_t leaf = 3 * flen; leaf < n; leaf += 4 * flen) {
size_t level = std::countr_one(leaf + 3);
for(size_t lvl = 4 + parity; lvl <= level; lvl += 2) {
size_t i = (1 << lvl) / 4;
exec_on_eval<4>(n >> lvl, leaf >> lvl, [&](size_t k, point rt) {
k <<= lvl;
vpoint v1 = {vz + real(rt), vz - imag(rt)};
vpoint v2 = v1 * v1;
vpoint v3 = v1 * v2;
for(size_t j = k; j < k + i; j += flen) {
auto A = at(j);
auto B = at(j + i);
auto C = at(j + 2 * i);
auto D = at(j + 3 * i);
at(j) = ((A + B) + (C + D));
at(j + 2 * i) = ((A + B) - (C + D)) * v2;
at(j + i) = ((A - B) - vi(C - D)) * v1;
at(j + 3 * i) = ((A - B) + vi(C - D)) * v3;
}
});
}
}
checkpoint("ifft");
for(size_t k = 0; k < n; k += flen) {
if constexpr (partial) {
set(k, get<vpoint>(k) /= vz + ftype(n / flen));
} else {
set(k, get<vpoint>(k) /= vz + ftype(n));
}
}
}
template<bool partial = true>
void fft() {
size_t n = size();
bool parity = std::countr_zero(n) % 2;
for(size_t leaf = 0; leaf < n; leaf += 4 * flen) {
size_t level = std::countr_zero(n + leaf);
level -= level % 2 != parity;
for(size_t lvl = level; lvl >= 4; lvl -= 2) {
size_t i = (1 << lvl) / 4;
exec_on_eval<4>(n >> lvl, leaf >> lvl, [&](size_t k, point rt) {
k <<= lvl;
vpoint v1 = {vz + real(rt), vz + imag(rt)};
vpoint v2 = v1 * v1;
vpoint v3 = v1 * v2;
for(size_t j = k; j < k + i; j += flen) {
auto A = at(j);
auto B = at(j + i) * v1;
auto C = at(j + 2 * i) * v2;
auto D = at(j + 3 * i) * v3;
at(j) = (A + C) + (B + D);
at(j + i) = (A + C) - (B + D);
at(j + 2 * i) = (A - C) + vi(B - D);
at(j + 3 * i) = (A - C) - vi(B - D);
}
});
}
}
if(parity) {
exec_on_evals<2>(n / (2 * flen), [&](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) {
point pi(0, 1);
exec_on_evals<4>(n / 4, [&](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 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;
};
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;
}();
}
#line 6 "cp-algo/math/fft64.hpp"
namespace cp_algo::math::fft {
struct dft64 {
std::vector<cp_algo::math::fft::cvector> cv;
static uint64_t factor, ifactor;
static bool _init;
static void init() {
if(_init) return;
_init = true;
factor = random::rng();
if(factor % 2 == 0) {factor++;}
ifactor = inv2(factor);
}
dft64(auto const& a, size_t n): cv(4, n) {
init();
uint64_t cur = 1, step = bpow(factor, n);
for(size_t i = 0; i < std::min(std::size(a), n); i++) {
auto split = [&](size_t i, uint64_t mul) -> std::array<int16_t, 4> {
uint64_t x = i < std::size(a) ? a[i] * mul : 0;
std::array<int16_t, 4> res;
for(int z = 0; z < 4; z++) {
res[z] = int16_t(x);
x = (x >> 16) + (res[z] < 0);
}
return res;
};
auto re = split(i, cur);
auto im = split(n + i, cur * step);
for(int z = 0; z < 4; z++) {
real(cv[z].at(i))[i % 4] = re[z];
imag(cv[z].at(i))[i % 4] = im[z];
}
cur *= factor;
}
checkpoint("dft64 init");
for(auto &x: cv) {
x.fft();
}
}
void dot(dft64 const& t) {
size_t N = cv[0].size();
cvector::exec_on_evals<1>(N / flen, [&](size_t k, point rt) {
k *= flen;
auto [A0x, A0y] = cv[0].at(k);
auto [A1x, A1y] = cv[1].at(k);
auto [A2x, A2y] = cv[2].at(k);
auto [A3x, A3y] = cv[3].at(k);
std::array B = {
t.cv[0].at(k),
t.cv[1].at(k),
t.cv[2].at(k),
t.cv[3].at(k)
};
std::array<vpoint, 4> C = {vz, vz, vz, vz};
for (size_t i = 0; i < flen; i++) {
std::array A = {
vpoint{vz + A0x[i], vz + A0y[i]},
vpoint{vz + A1x[i], vz + A1y[i]},
vpoint{vz + A2x[i], vz + A2y[i]},
vpoint{vz + A3x[i], vz + A3y[i]}
};
for(size_t k = 0; k < 4; k++) {
for(size_t i = 0; i <= k; i++) {
C[k] += A[i] * B[k - i];
}
}
for(size_t k = 0; k < 4; k++) {
real(B[k]) = rotate_right(real(B[k]));
imag(B[k]) = rotate_right(imag(B[k]));
auto bx = real(B[k])[0], by = imag(B[k])[0];
real(B[k])[0] = bx * real(rt) - by * imag(rt);
imag(B[k])[0] = bx * imag(rt) + by * real(rt);
}
}
cv[0].at(k) = C[0];
cv[1].at(k) = C[1];
cv[2].at(k) = C[2];
cv[3].at(k) = C[3];
});
checkpoint("dot");
for(auto &x: cv) {
x.ifft();
}
}
void recover_mod(auto &res, size_t k) {
size_t n = cv[0].size();
uint64_t cur = 1, step = bpow(ifactor, n);
for(size_t i = 0; i < std::min(k, n); i++) {
std::array re = {real(cv[0].get(i)), real(cv[1].get(i)), real(cv[2].get(i)), real(cv[3].get(i))};
std::array im = {imag(cv[0].get(i)), imag(cv[1].get(i)), imag(cv[2].get(i)), imag(cv[3].get(i))};
auto set_i = [&](size_t i, auto &x, auto mul) {
if (i >= k) return;
res[i] = llround(x[0]) + (llround(x[1]) << 16) + (llround(x[2]) << 32) + (llround(x[3]) << 48);
res[i] *= mul;
};
set_i(i, re, cur);
set_i(n + i, im, cur * step);
cur *= ifactor;
}
cp_algo::checkpoint("recover mod");
}
};
uint64_t dft64::factor = 1, dft64::ifactor = 1;
bool dft64::_init = false;
void conv64(auto& a, auto const& b) {
size_t n = a.size(), m = b.size();
size_t N = std::max(flen, std::bit_ceil(n + m - 1) / 2);
dft64 A(a, N), B(b, N);
A.dot(B);
a.resize(n + m - 1);
A.recover_mod(a, n + m - 1);
}
}