写一个FFT算法的C语言实现，输入数组是x,输出数组为y，点数为N

以下为C语言实现FFT算法的代码，代码中实现了输入实数数组x，输出实数数组y，点数为N。

#include <stdio.h>
#include <math.h>

// 定义复数结构体
typedef struct {
    double re;
    double im;
} Complex;

// 定义π常量
const double PI = acos(-1.0);

// 计算FFT算法中旋转因子
void calc_w(int k, int n, Complex *w) {
    for (int i = 0; i < n; i++) {
        double angle = 2 * PI * k * i / n;
        w[i].re = cos(angle);
        w[i].im = sin(angle);
    }
}

// 执行递归FFT算法
void fft_recursive(Complex *x, Complex *y, int n, int step) {
    if (n == 1) {
        y[0] = x[0];
        return;
    }
    Complex *x0 = new Complex[n / 2];
    Complex *x1 = new Complex[n / 2];
    Complex *y0 = new Complex[n / 2];
    Complex *y1 = new Complex[n / 2];
    Complex w[n];
    calc_w(step, n, w);
    for (int i = 0; i < n / 2; i++) {
        x0[i] = x[2 * i];
        x1[i] = x[2 * i + 1];
    }
    fft_recursive(x0, y0, n / 2, step * 2);
    fft_recursive(x1, y1, n / 2, step * 2);
    for (int i = 0; i < n / 2; i++) {
        y[i].re = y0[i].re + w[i].re * y1[i].re - w[i].im * y1[i].im;
        y[i].im = y0[i].im + w[i].re * y1[i].im + w[i].im * y1[i].re;
        y[i + n / 2].re = y0[i].re - w[i].re * y1[i].re + w[i].im * y1[i].im;
        y[i + n / 2].im = y0[i].im - w[i].re * y1[i].im - w[i].im * y1[i].re;
    }
    delete[] x0;
    delete[] x1;
    delete[] y0;
    delete[] y1;
}

// 执行FFT算法
void fft(double *x, double *y, int n) {
    Complex *cx = new Complex[n];
    Complex *cy = new Complex[n];
    for (int i = 0; i < n; i++) {
        cx[i].re = x[i];
        cx[i].im = 0;
    }
    fft_recursive(cx, cy, n, 1);
    for (int i = 0; i < n; i++) {
        y[i] = cy[i].re;
    }
    delete[] cx;
    delete[] cy;
}

// 测试程序
int main() {
    // 输入数据
    int N = 8;
    double x[8] = {1, 2, 3, 4, 4, 3, 2, 1};
    double y[N];

    // 执行FFT算法
    fft(x, y, N);

    // 输出结果
    for (int i = 0; i < N; i++) {
        printf("%.2lf + %.2lfi\n", y[i], 0.0);
    }
    return 0;
}