A try to implement Fourier Transform in C programming language

fourier.c

#define float_t _std__float_t
#include <stddef.h>
#include <math.h>
#include <stdio.h>
#undef float_t

#define PI trig(atan2)(0, -1)

#define trig(f) f // Uses trigonometric function for float precision of float_t
#define fm "%f" // Format for type float_t (printf)
typedef double float_t; // Defines float precision

typedef struct complex {
  float_t real, imag;
} complex_t; // Definition of complex number

// buf - buffer with samples
// size - count of samples in the buffer
// rate - samples per time unit
// freq - transform frequency
complex_t fourier_transform(float_t *buf, size_t size, size_t rate, float_t freq) {
  complex_t result, tmp;
  size_t i;
  float_t x;
  const float_t dx = 1.0 / rate;
  result.real = 0;
  result.imag = 0;
  for (i = 0; i < size; i++) {
    x = (float_t)i / rate;
    // tmp = dx*sample*e^(-2*pi*x*f*i)
    //     = dx*sample*cos(tau*x*f) - i*dx*sample*sin(tau*x*f)
    // sin(-x) = -sin(x); cos(-x) = cos(x)
    tmp.real = dx*buf[i]*trig(cos)(2 * PI * x * freq);
    tmp.imag = -dx*buf[i]*trig(sin)(2 * PI * x * freq);
    result.real += tmp.real;
    result.imag += tmp.imag;
  }
  return result;
}

int main(void) {
  float_t buf[1000];
  size_t i;
  complex_t c;
  for (i = 0; i < 1000; i++) {
    // Fill in buffer with 3 Hz + 5 Hz wave
    buf[i] = 100*trig(sin)(3 * (float_t)i / 100)
           + 100*trig(sin)(5 * (float_t)i / 100);
  }
  for (i = 0; i < 20; i++) {
    c = fourier_transform(buf, 1000, 100, (float_t)i/2);
    printf("Fourier transform (freq = "fm"): mod="fm" real="fm" imag="fm"\n",
      (float_t)i/2, trig(sqrt)(c.real*c.real + c.imag*c.imag), c.real, c.imag);
  }
  return 0;
}