math/fft/arbitrary-mod-convolution-long.hpp

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• Last update: 2026-08-10 07:26:44+00:00
• Include: #include "math/fft/arbitrary-mod-convolution-long.hpp"

Depends on

• math/fft/fast-fourier-transform.hpp

Code

#pragma once

#include <cstdint>
#include <vector>

#include "fast-fourier-transform.hpp"

template <typename T>
struct ArbitraryModConvolutionLong {
  using real = FastFourierTransform::real;
  using C = FastFourierTransform::C;

  ArbitraryModConvolutionLong() = default;

  std::vector<T> multiply(const std::vector<T>& a, const std::vector<T>& b,
                          int need = -1) {
    if (need == -1) need = a.size() + b.size() - 1;
    int nbase = 0;
    while ((1 << nbase) < need) nbase++;
    FastFourierTransform::ensure_base(nbase);
    int sz = 1 << nbase;
    std::vector<C> fa(sz);
    for (int i = 0; i < a.size(); i++) {
      fa[i] = C(a[i].x & ((1 << 19) - 1), a[i].x >> 19);
    }
    fft(fa, sz);
    std::vector<C> fb(sz);
    if (a == b) {
      fb = fa;
    } else {
      for (int i = 0; i < b.size(); i++) {
        fb[i] = C(b[i].x & ((1 << 19) - 1), b[i].x >> 19);
      }
      fft(fb, sz);
    }
    real ratio = 0.25 / sz;
    C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
    for (int i = 0; i <= (sz >> 1); i++) {
      int j = (sz - i) & (sz - 1);
      C a1 = (fa[i] + fa[j].conj());
      C a2 = (fa[i] - fa[j].conj()) * r2;
      C b1 = (fb[i] + fb[j].conj()) * r3;
      C b2 = (fb[i] - fb[j].conj()) * r4;
      if (i != j) {
        C c1 = (fa[j] + fa[i].conj());
        C c2 = (fa[j] - fa[i].conj()) * r2;
        C d1 = (fb[j] + fb[i].conj()) * r3;
        C d2 = (fb[j] - fb[i].conj()) * r4;
        fa[i] = c1 * d1 + c2 * d2 * r5;
        fb[i] = c1 * d2 + c2 * d1;
      }
      fa[j] = a1 * b1 + a2 * b2 * r5;
      fb[j] = a1 * b2 + a2 * b1;
    }
    fft(fa, sz);
    fft(fb, sz);
    std::vector<T> ret(need);
    auto mul1 = T(2).pow(19);
    auto mul2 = T(2).pow(38);
    for (int i = 0; i < need; i++) {
      std::int64_t aa = std::llround(fa[i].x);
      std::int64_t bb = std::llround(fb[i].x);
      std::int64_t cc = std::llround(fa[i].y);
      aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;
      ret[i] = (mul1 * bb) + (mul2 * cc) + aa;
    }
    return ret;
  }
};

#line 2 "math/fft/arbitrary-mod-convolution-long.hpp"

#include <cstdint>
#include <vector>

#line 2 "math/fft/fast-fourier-transform.hpp"

#include <algorithm>
#include <cassert>
#include <cmath>
#line 8 "math/fft/fast-fourier-transform.hpp"

namespace FastFourierTransform {
using real = double;

struct C {
  real x, y;

  C() : x(0), y(0) {}

  C(real x, real y) : x(x), y(y) {}

  inline C operator+(const C& c) const { return C(x + c.x, y + c.y); }

  inline C operator-(const C& c) const { return C(x - c.x, y - c.y); }

  inline C operator*(const C& c) const {
    return C(x * c.x - y * c.y, x * c.y + y * c.x);
  }

  inline C conj() const { return C(x, -y); }
};

const real PI = std::acos(-1);
int base = 1;
std::vector<C> rts = {{0, 0}, {1, 0}};
std::vector<int> rev = {0, 1};

void ensure_base(int nbase) {
  if (nbase <= base) return;
  rev.resize(1 << nbase);
  rts.resize(1 << nbase);
  for (int i = 0; i < (1 << nbase); i++) {
    rev[i] = (rev[i >> 1] >> 1) + ((i & 1) << (nbase - 1));
  }
  while (base < nbase) {
    real angle = PI * 2.0 / (1 << (base + 1));
    for (int i = 1 << (base - 1); i < (1 << base); i++) {
      rts[i << 1] = rts[i];
      real angle_i = angle * (2 * i + 1 - (1 << base));
      rts[(i << 1) + 1] = C(std::cos(angle_i), std::sin(angle_i));
    }
    ++base;
  }
}

void fft(std::vector<C>& a, int n) {
  assert((n & (n - 1)) == 0);
  int zeros = __builtin_ctz(n);
  ensure_base(zeros);
  int shift = base - zeros;
  for (int i = 0; i < n; i++) {
    if (i < (rev[i] >> shift)) {
      std::swap(a[i], a[rev[i] >> shift]);
    }
  }
  for (int k = 1; k < n; k <<= 1) {
    for (int i = 0; i < n; i += 2 * k) {
      for (int j = 0; j < k; j++) {
        C z = a[i + j + k] * rts[j + k];
        a[i + j + k] = a[i + j] - z;
        a[i + j] = a[i + j] + z;
      }
    }
  }
}

std::vector<std::int64_t> multiply(const std::vector<int>& a,
                                   const std::vector<int>& b) {
  int need = (int)a.size() + (int)b.size() - 1;
  int nbase = 1;
  while ((1 << nbase) < need) nbase++;
  ensure_base(nbase);
  int sz = 1 << nbase;
  std::vector<C> fa(sz);
  for (int i = 0; i < sz; i++) {
    int x = (i < (int)a.size() ? a[i] : 0);
    int y = (i < (int)b.size() ? b[i] : 0);
    fa[i] = C(x, y);
  }
  fft(fa, sz);
  C r(0, -0.25 / (sz >> 1)), s(0, 1), t(0.5, 0);
  for (int i = 0; i <= (sz >> 1); i++) {
    int j = (sz - i) & (sz - 1);
    C z = (fa[j] * fa[j] - (fa[i] * fa[i]).conj()) * r;
    fa[j] = (fa[i] * fa[i] - (fa[j] * fa[j]).conj()) * r;
    fa[i] = z;
  }
  for (int i = 0; i < (sz >> 1); i++) {
    C A0 = (fa[i] + fa[i + (sz >> 1)]) * t;
    C A1 = (fa[i] - fa[i + (sz >> 1)]) * t * rts[(sz >> 1) + i];
    fa[i] = A0 + A1 * s;
  }
  fft(fa, sz >> 1);
  std::vector<std::int64_t> ret(need);
  for (int i = 0; i < need; i++) {
    ret[i] = std::llround(i & 1 ? fa[i >> 1].y : fa[i >> 1].x);
  }
  return ret;
}
};  // namespace FastFourierTransform
#line 7 "math/fft/arbitrary-mod-convolution-long.hpp"

template <typename T>
struct ArbitraryModConvolutionLong {
  using real = FastFourierTransform::real;
  using C = FastFourierTransform::C;

  ArbitraryModConvolutionLong() = default;

  std::vector<T> multiply(const std::vector<T>& a, const std::vector<T>& b,
                          int need = -1) {
    if (need == -1) need = a.size() + b.size() - 1;
    int nbase = 0;
    while ((1 << nbase) < need) nbase++;
    FastFourierTransform::ensure_base(nbase);
    int sz = 1 << nbase;
    std::vector<C> fa(sz);
    for (int i = 0; i < a.size(); i++) {
      fa[i] = C(a[i].x & ((1 << 19) - 1), a[i].x >> 19);
    }
    fft(fa, sz);
    std::vector<C> fb(sz);
    if (a == b) {
      fb = fa;
    } else {
      for (int i = 0; i < b.size(); i++) {
        fb[i] = C(b[i].x & ((1 << 19) - 1), b[i].x >> 19);
      }
      fft(fb, sz);
    }
    real ratio = 0.25 / sz;
    C r2(0, -1), r3(ratio, 0), r4(0, -ratio), r5(0, 1);
    for (int i = 0; i <= (sz >> 1); i++) {
      int j = (sz - i) & (sz - 1);
      C a1 = (fa[i] + fa[j].conj());
      C a2 = (fa[i] - fa[j].conj()) * r2;
      C b1 = (fb[i] + fb[j].conj()) * r3;
      C b2 = (fb[i] - fb[j].conj()) * r4;
      if (i != j) {
        C c1 = (fa[j] + fa[i].conj());
        C c2 = (fa[j] - fa[i].conj()) * r2;
        C d1 = (fb[j] + fb[i].conj()) * r3;
        C d2 = (fb[j] - fb[i].conj()) * r4;
        fa[i] = c1 * d1 + c2 * d2 * r5;
        fb[i] = c1 * d2 + c2 * d1;
      }
      fa[j] = a1 * b1 + a2 * b2 * r5;
      fb[j] = a1 * b2 + a2 * b1;
    }
    fft(fa, sz);
    fft(fb, sz);
    std::vector<T> ret(need);
    auto mul1 = T(2).pow(19);
    auto mul2 = T(2).pow(38);
    for (int i = 0; i < need; i++) {
      std::int64_t aa = std::llround(fa[i].x);
      std::int64_t bb = std::llround(fb[i].x);
      std::int64_t cc = std::llround(fa[i].y);
      aa = T(aa).x, bb = T(bb).x, cc = T(cc).x;
      ret[i] = (mul1 * bb) + (mul2 * cc) + aa;
    }
    return ret;
  }
};

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