(* Common mathematical functions and data *)
unit cmath;

interface

  const
    factorial: array[1..20] of uint64 = (
      1,
      2,
      6,
      24,
      120,
      720,
      5040,
      40320,
      362880,
      3628800,
      39916800,
      479001600,
      6227020800,
      87178291200,
      1307674368000,
      20922789888000,
      355687428096000,
      6402373705728000,
      121645100408832000,
      2432902008176640000
    );
    fibonacci: array[1..93] of uint64 = (
      1,
      1,
      2,
      3,
      5,
      8,
      13,
      21,
      34,
      55,
      89,
      144,
      233,
      377,
      610,
      987,
      1597,
      2584,
      4181,
      6765,
      10946,
      17711,
      28657,
      46368,
      75025,
      121393,
      196418,
      317811,
      514229,
      832040,
      1346269,
      2178309,
      3524578,
      5702887,
      9227465,
      14930352,
      24157817,
      39088169,
      63245986,
      102334155,
      165580141,
      267914296,
      433494437,
      701408733,
      1134903170,
      1836311903,
      2971215073,
      4807526976,
      7778742049,
      12586269025,
      20365011074,
      32951280099,
      53316291173,
      86267571272,
      139583862445,
      225851433717,
      365435296162,
      591286729879,
      956722026041,
      1548008755920,
      2504730781961,
      4052739537881,
      6557470319842,
      10610209857723,
      17167680177565,
      27777890035288,
      44945570212853,
      72723460248141,
      117669030460994,
      190392490709135,
      308061521170129,
      498454011879264,
      806515533049393,
      1304969544928657,
      2111485077978050,
      3416454622906707,
      5527939700884757,
      8944394323791464,
      14472334024676221,
      23416728348467685,
      37889062373143906,
      61305790721611591,
      99194853094755497,
      160500643816367088,
      259695496911122585,
      420196140727489673,
      679891637638612258,
      1100087778366101931,
      1779979416004714189,
      2880067194370816120,
      4660046610375530309,
      7540113804746346429,
      12200160415121876738
    );

  function gcd(x, y: int64): int64;
  function isprime(x: int64): boolean;
  function issquare(x: int64): boolean;

implementation

  function gcd(x, y: int64): int64;
    var z: int64;
    begin
      while y > 0 do
        begin
          z := y;
          y := x mod y;
          x := z
        end;
      gcd := x
    end;

  function isprime(x: int64): boolean;
    var i: int32;
    begin
      if x < 2 then
        exit(false);
      for i := 2 to trunc(sqrt(x)) do
        if x mod i = 0 then
          exit(false);
      isprime := true
    end;

  function issquare(x: int64): boolean;
    begin
      issquare := (x >= 0) and (sqr(trunc(sqrt(x))) = x)
    end;

end.