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typedef struct
{
    double re;
    double im;
} complex_t;

static inline complex_t
complex_mul (complex_t a, complex_t b)
{
    complex_t r;

    r.re = a.re * b.re - a.im * b.im;
    r.im = a.re * b.im + a.im * b.re;

    return r;
}

static inline complex_t
complex_add (complex_t a, complex_t b)
{
    complex_t r;

    r.re = a.re + b.re;
    r.im = a.im + b.im;

    return r;
}

static inline complex_t
complex_sub (complex_t a, complex_t b)
{
    complex_t r;

    r.re = a.re - b.re;
    r.im = a.im - b.im;

    return r;
}

static inline double
complex_mag (complex_t a)
{
    return sqrt (a.re * a.re + a.im * a.im);
}
static inline double
complex_arg (complex_t a)
{
    return atan2 (a.im, a.re) + M_PI;
}

static inline double
rad_to_degree (double theta)
{
    return theta * (360.0 / (2 * M_PI));
}

void
fft (complex_t *buffer, int n);