#! /usr/bin/python3
# Last edited on 2026-02-15 13:07:58 by stolfi

def log_tot_prob_from_plogs(QL):
  # Given a list {QL} of negative numbers,
  # returns {log(sum{ exp(p) : p in QL})}
  
  debug = False
  
  np = len(QL)
  if np == 0: return 0.0
  
  # Sort the list in increasing order:
  QL = sorted(QL)
  
  # Compute the result by factoring the largest factor:
  max_log = QL[-1]
  if debug: err.write(f"    {max_log = :12.6f}")
  tot_prob = 0;
  for p in QL:
    tot_prob += exp(p - max_log)
  if debug: err.write(f" {tot_prob = :12.6e}\n")
  return max_log + log(tot_prob)
  # ----------------------------------------------------------------------

def test_log_tot_prob_from_plogs(QL, plog_exp):
  err.write(f"!! with {QL = } {plog_exp = :12.6f}")
  plog_cmp = log_tot_prob_from_plogs(QL)
  err.write(f" {plog_cmp = :12.6f}\n")
  den = max(abs(plog_exp), 1.0e-200)
  assert abs(plog_cmp - plog_exp)/den < 1.0e-8
  return
  # ----------------------------------------------------------------------
  
def test_log_tot_prob_from_plogs_all():
  err.write("testing {log_tot_prob_from_plogs}\n")
  test_log_tot_prob_from_plogs([], 0.0)
  test_log_tot_prob_from_plogs([-6.57], -6.57)
  test_log_tot_prob_from_plogs([-3.14, -6.57], log(exp(-3.14) + exp(-6.57)))
  return
  # ----------------------------------------------------------------------

test_log_tot_prob_from_plogs_all()