/* Convert the fps base to an integer. Simply shift the decimal places until we get an integer
 * (within a floating point error range). */
unsigned int den = rd->frs_sec;
double num = rd->frs_sec_base;
float eps = FLT_EPSILON;
unsigned int DENUM_MAX = (codec_id == AV_CODEC_ID_MPEG4) ? (1UL << 16) - 1 : (1UL << 31) - 1;

/* Calculate the precision of the initial floating point number. */
if (num > 1.0) {
  unsigned int integer_bits = log2_floor_u((unsigned int)num);

  /* Formula for calculating the epsilon value: (power of two range) / (pow mantissa bits)
   * For example, a float has 23 manitissa bits and 3.5f as a pow2 range of (4-2):
   * (4-2) / pow2(23) = floating point precision
   */
  eps = (float)(1 << integer_bits) * FLT_EPSILON;
}

/* Calculate how many decimal shifts we can do until we run out of precision. */
int max_num_shift = fabsf(log10f(eps));
/* Calculate how many times we can shift the denominator. */
int max_den_shift = log10f(DENUM_MAX) - log10f(den);
int max_iter = min_ii(max_num_shift, max_den_shift);

for (int i = 0; i < max_iter && fabs(num - round(num)) > eps; i++) {
  /* Increase the number and denominator until both are integers. */
  num *= 10;
  den *= 10;
  eps *= 10;
}