/*
  Simple linear congruential random number generator with the
  following parameters
     X(n+1) = (a*X(n) + b) mod m
  where
     a = 11
     b = 23
     mod = 127
     X(1) = 1

  The first entries: 1 34 16 72 53 98 85 69 20 116 29 88
  It has a cycle of 125.

  Can we restore the parameters?

  * With only the specific contants [1,11,23,127] (i.e. cheating)

    gen = 172
    [program = (11 * A + 23) mod (127 * 1),res = 88,count = 1]

  * With constants 0..130 stop_criteria=generations, num_gens=1800
    gen = 700  (time: 10.287s)
    results_best = [[172,(82 * 86 + (A + A)) mod 78]]

    gen = 33  (time: 0.316s)
    results_best = [[21,if_then_else(if_then_else(10 != A == 85,20,A),34 * (A != 10),if_then_else(88,(A == A) mod A != 75 + 86,A * A) mod 87)]]
        
    gen = 990  (time: 14.559s)
    results_best = [[129,(A + A + (A + 35)) mod 111]]

    gen = 487  (time: 7.026s)
    results_best = [[132,56 * 100 div 46 * A mod 111]]


*/
data(linear_congruential_generator,Data,Vars,Unknown,Ops,Constants,MaxSize,Params) :-
  % make_seq([1,34,16,72,53,98,85,69,20,116,29,88],1,Data,Unknown,Vars),
  make_seq([1,34,16,72,53,98,85,69,20,116,29],1,Data,Unknown,Vars),
  % make_seq([1,34,16,72,53],1,Data,Unknown,Vars),  
  println(data=Data),
  % Ops = [+,*,mod], % We know that it's an LCG.  
  Ops = [+,*,-,mod,==,!=],
  % Constants = [1,11,23,127], % OK, but cheating :-)
  % Constants = 0..10,
  Constants = 0..130,
  MaxSize = 21,
  Params = new_map([
                    init_size=500,
                    show_best=1,
                    show_only_improvements=true,
                    stop_criteria=generations,
                    num_gens=1800
                   ]).