import math


def _compute_softmax(scores):
  """Computes softmax probability over raw logits."""
  if not scores:
    return []

  max_score = None
  for score in scores:
    if max_score is None or score > max_score:
      max_score = score

  exp_scores = []
  total_sum = 0.0
  for score in scores:
    x = math.exp(score - max_score)
    exp_scores.append(x)
    total_sum += x

  probs = []
  for score in exp_scores:
    probs.append(score / total_sum)
  return probs