Factorial table !20

uint64_t fact_u64_tabular(uint64_t val, bool * oflow) {

  static
  uint64_t const factorials[] = {
    /* 0!*/                   0ULL, /* TODO: Added to make picking factorials intuitive */
    /* 1!*/                   1ULL,
    /* 2!*/                   2ULL,
    /* 3!*/                   6ULL,
    /* 4!*/                  24ULL,
    /* 5!*/                 120ULL,
    /* 6!*/                 720ULL,
    /* 7!*/                5040ULL,
    /* 8!*/               40320ULL,
    /* 9!*/              362880ULL,
    /*10!*/             3628800ULL,
    /*11!*/            39916800ULL,
    /*12!*/           479001600ULL, /* TODO: max factorial for 32-bit integers */
    /*13!*/          6227020800ULL,
    /*14!*/         87178291200ULL,
    /*15!*/       1307674368000ULL,
    /*16!*/      20922789888000ULL,
    /*17!*/     355687428096000ULL,
    /*18!*/    6402373705728000ULL,
    /*19!*/  121645100408832000ULL,
    /*20!*/ 2432902008176640000ULL, /* TODO: max factorial for 64-bit integers */
  };
  size_t factorials_c = sizeof(factorials) / sizeof(*factorials);
  uint64_t fv = 0;

  if (val > 0 && val < factorials_c) {
    fv = factorials[val];
    *oflow = false;
  }
  else {
    fv = 0;
    *oflow = true;
  }

  return fv;
}