#ifndef COMPLEX_H
#define COMPLEX_H

#include <math.h>

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_smul (complex_t a, double s)
{
    a.re *= s;
    a.im *= s;

    return a;
}

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 fmod (atan2 (a.im, a.re) + 2 * M_PI, 2 * M_PI);
}

static inline complex_t
complex_from_mag_arg (double mag, double arg)
{
    complex_t r;

    r.re = mag * cos (arg);
    r.im = mag * sin (arg);

    return r;
}

#endif