FFT最新卡常研究

指针优化并没有什么卵用，反而增大了代码的不可读性。

除了本来的循环顺序优化寻址，在预处理单位复数根时，可以连续存储，以增快寻址速度，细节见代码。

代码给出的是FFT，NTT是一样的。

#include<bits/stdc++.h>
#define fo(i, x, y) for(int i = x, B = y; i <= B; i ++)
#define ff(i, x, y) for(int i = x, B = y; i <  B; i ++)
#define fd(i, x, y) for(int i = x, B = y; i >= B; i --)
#define ll long long
#define db double
#define pp printf
#define hh pp("\n")
using namespace std;

struct P {
    db x, y;
    P(db _x = 0, db _y = 0) { x = _x, y = _y;}
};

P operator + (P a, P b) { return P(a.x + b.x, a.y + b.y);}
P operator - (P a, P b) { return P(a.x - b.x, a.y - b.y);}
P operator * (P a, P b) { return P(a.x * b.x - a.y * b.y, a.x * b.y + a.y * b.x);}

const db pi = acos(-1);

const int nm = 1 << 21;

int r[nm]; P a[nm], b[nm], W[nm];

void dft(P *a, int n, int f) {
    ff(i, 0, n) {
        r[i] = r[i / 2] / 2 + (i & 1) * (n / 2);
        if(i < r[i]) swap(a[i], a[r[i]]);
    } P b;
    for(int i = 1; i < n; i *= 2) for(int j = 0; j < n; j += 2 * i)
        ff(k, 0, i) b = W[i + k] * a[i + j + k], a[i + j + k] = a[j + k] - b, a[j + k] = a[j + k] + b;
    if(f == -1) {
        reverse(a + 1, a + n);
        ff(i, 0, n) a[i].x /= n;
    }
}
void fft(P *a, P *b, int n) {
    dft(a, n, 1); dft(b, n, 1);
    ff(i, 0, n) a[i] = a[i] * b[i];
    dft(a, n, -1);
}

int main() {
    for(int i = 1; i < nm; i *= 2) ff(j, 0, i)
        W[i + j] = P(cos(pi * j / i), sin(pi * j / i));
    ff(i, 0, 1 << 20) a[i].x = b[i].x = i;
    fft(a, b, 1 << 21);
}