Skill rate formulas for Dwarf Therapist.

#include<stdio.h>

const int max_xp = 29000;

const int xp_levels [] = {0, 500, 1100, 1800, 2600, 3500, 4500, 5600, 6800, 8100, 9500,
        11000, 12600, 14300, 16100, 18000, 20000, 22100, 24300, 26600, 29000};
// xp(lvl) = 500*lvl + 100 * (lvl * (lvl -1)) / 2
// const int lev_size = sizeof(xp_levels) / sizeof(int);   // 21 , unused

int get_level_from_xp(int xp)   // Uses busection method. Assumes xp >= 0.
{ if (xp >= max_xp)
    return 20;

  int min = 0;
  int max = 19;
  int current = 10;

  while (1)
  { if (xp < xp_levels[current])
    { max = current;
      current = (min + max)/2;
    } else if (xp > xp_levels[current+1])
    { min = current;
      current = (min + max)/2;
    } else
      return current;
  }
}

/* Simulation method for judging a dwarf's skill level and rate.
   Simple version of the while loop, without the interpolation.
   Inputs: dwarf's current xp and learning rate for a skill.
   Output: rating based on simulating gaining experience in that skill. In <0, 1>
*/
double simulate_skill_gain(int xp, int rate)
{ if (xp >= max_xp)
    return 20.0 / 20.0;

  if (rate == 0)
    return get_level_from_xp(xp) / 20.0;       // Obviously stays the same.

  int sim_xp = max_xp;          // 29k seems like a good value to me.
  sim_xp = (sim_xp / 100.0) * rate; // This is how much XP will go towards skill learning.
  int total_xp = sim_xp;
  double ret = 0.0;
  int curr_level = get_level_from_xp(xp);
  int curr_xp = xp;

  while ((sim_xp > 0) && (curr_level < 20))
  { int xp_gap = xp_levels[curr_level+1] - curr_xp;         // How much XP till mext level?
    if (xp_gap > sim_xp)
      xp_gap = sim_xp;
    ret += xp_gap * curr_level;
    curr_level++;
    curr_xp = xp_levels[curr_level];
    sim_xp -= xp_gap;
  }

  if (sim_xp > 0)
    ret += 20 * sim_xp;
  ret /= total_xp;
  ret /= 20.0;
  return ret;
}

/* Simulation method for judging a dwarf's skill level and rate.
   This version of the while loop is interpolating the level. It may be smoother.
   Inputs: dwarf's current xp and learning rate for a skill.
   Output: rating based on simulating gaining experience in that skill. in <0, 1>
*/
double simulate_skill_gain_slopes(int xp, int rate)
{ if (xp >= max_xp)
    return 20.0 / 20.0;

  if (rate == 0)
    return get_level_from_xp(xp) / 20.0;       // Obviously stays the same.

  int sim_xp = max_xp;          // 29k seems like a good value to me.
  sim_xp = (sim_xp / 100.0) * rate; // This is how much XP will go towards skill learning.
  int total_xp = sim_xp;
  double ret = 0.0;
  int curr_level = get_level_from_xp(xp);
  int curr_xp = xp;

  while ((sim_xp > 0) && (curr_level < 20))
  { int xp_gap = xp_levels[curr_level+1] - curr_xp;         // How much XP till mext level?
    if (xp_gap > sim_xp)
      xp_gap = sim_xp;
    double low = (0.0 +curr_xp -xp_levels[curr_level]) / (xp_levels[curr_level+1] -xp_levels[curr_level]);
    double high = (0.0 +curr_xp + xp_gap -xp_levels[curr_level]) / (xp_levels[curr_level+1] -xp_levels[curr_level]);
    double avg_level = curr_level + (low + high) / 2.0;   // Average scaled level for this iteration.
    ret += xp_gap * avg_level;
    curr_level++;
    curr_xp = xp_levels[curr_level];
    sim_xp -= xp_gap;
  }

  if (sim_xp > 0)
    ret += 20 * sim_xp;
  ret /= total_xp;
  ret /= 20.0;
  return ret;
}

/* An approximate formula to judge how close a dwarf is to legendary +5
   Inputs: dwarf's current xp and learning rate for a skill.
   Output: rating in <0, 1>
*/
double skill_rate_eval(int xp, int rate)
{ if (xp >= max_xp)
    return 1.0;
  rate = (rate < 1)? 1 : rate;  // 0 or 1 doesn't really matter.
  double jobs_left = (29000.0 - xp) / rate;  // Ignore division by 60.
  double normalised_XP = 0.5 * (1.0 - jobs_left/290.0);    // Scaled to <-49.5, 0.5>
  if (normalised_XP >= 0)
    normalised_XP += 0.5;    // Values <0, 0.5> reserved for those suitable for a task.
  else
    normalised_XP = -0.5 / (normalised_XP - 1.0);
  return normalised_XP;
}

/* I could add fancy options to use this from command line or reading from a file,
   but that's not really necessary. Just use $ rates <file_in.txt >file_out.txt */
int main(void)
{ int xp, rate;
  int ret = 2;

  printf("xp, rate, slill_level, sim1, sim2, interp1\n");
  while ((ret = scanf("%d %d", &xp, &rate)) == 2)
    printf("%d, %d, %d, %f, %f, %f\n", xp, rate, get_level_from_xp(xp), simulate_skill_gain(xp, rate), simulate_skill_gain_slopes(xp, rate), skill_rate_eval(xp, rate));

  return ret;
}