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double distance;
float unit_scaling_factor;
float logarithmized_distance;
float adjusted_unit_scaling_factor;

/*
  we want the z-buffer to stay linear at close range to avoid artifacts,
  but we could live perhaps with a logarithmic linearity at long range,
  so assume we decide on a crossover range, below which we move
  more towards linearly, and above which we turn more logarithmic..
*/
const double logarithmic_distance_threshold = blablabla.5; //~777km?
const double logarithmized_raw_threshold = log(logarithmic_distance_threshold;
const double multiplying_factor = logarithmic_distance_threshold/logarithmized_raw_threshold;

double raw_log_distance()
{
    return multiplying_factor * log( distance + 1.0 );
}

/*
   we want our final distance to be the lesser of the two, so that it
   is logarithmic at long range and linear at close range; BUT, we
   want the transition between them to be rounded and smooth, so...
*/

void compute_logarithmized_distance()
{
    double RLD = raw_log_distance();
    double product = RLD * distance;
    double sum = RLD + distance;
    logarithmized_distance = float( product / sum );
}

/*
   now we need to adjust our scaling accordingly...
*/

void compute_adjusted_scaling()
{
    float factor = float( logarithmized_distance / distance );
    adjusted_unit_scaling_factor = unit_scaling_factor * factor;
}