多项式对数函数 | 指数函数

constexpr int maxn = 262144;
constexpr int mod = 998244353;

using i64 = long long;
using poly_t = int[maxn];
using poly = int *const;

inline void derivative(const poly &h, const int n, poly &f) {
  for (int i = 1; i != n; ++i) f[i - 1] = (i64)h[i] * i % mod;
  f[n - 1] = 0;
}

inline void integrate(const poly &h, const int n, poly &f) {
  for (int i = n - 1; i; --i) f[i] = (i64)h[i - 1] * inv[i] % mod;
  f[0] = 0; /* C */
}

void polyln(const poly &h, const int n, poly &f) {
  /* f = ln h = ∫ h' / h dx */
  assert(h[0] == 1);
  static poly_t ln_t;
  const int t = n << 1;

  derivative(h, n, ln_t);
  std::fill(ln_t + n, ln_t + t, 0);
  polyinv(h, n, f);

  DFT(ln_t, t);
  DFT(f, t);
  for (int i = 0; i != t; ++i) ln_t[i] = (i64)ln_t[i] * f[i] % mod;
  IDFT(ln_t, t);

  integrate(ln_t, n, f);
}

void polyexp(const poly &h, const int n, poly &f) {
  /* f = exp(h) = f_0 (1 - ln f_0 + h) */
  assert(h[0] == 0);
  static poly_t exp_t;
  std::fill(f, f + n + n, 0);
  f[0] = 1;
  for (int t = 2; t <= n; t <<= 1) {
    const int t2 = t << 1;

    polyln(f, t, exp_t);
    exp_t[0] = sub(pls(h[0], 1), exp_t[0]);
    for (int i = 1; i != t; ++i) exp_t[i] = sub(h[i], exp_t[i]);
    std::fill(exp_t + t, exp_t + t2, 0);

    DFT(f, t2);
    DFT(exp_t, t2);
    for (int i = 0; i != t2; ++i) f[i] = (i64)f[i] * exp_t[i] % mod;
    IDFT(f, t2);

    std::fill(f + t, f + t2, 0);
  }
}