pbnbinom and pgpois are slow for some combinations of parameters

[twolodzko]

pbnbinom and pgpois (and potentially bbbinom) are slow for some combinations of parameters. This is caused by the fact that they are computed as F(x) = sum(f(1:x)) and it is inefficient (no matter of optimizations) for large x or for some combinations of parameters (e.g. for beta negative binomial small alpha and large beta).

[twolodzko]

One solution would be to use different mx values for different combinations of x's and parameters, e.g.

  double mx;
  std::map<std::tuple<int, int, int>, double> maxx;
  
  for (int i = 0; i < Nmax; i++) {
    
    mx = std::min(GETV(x, i), GETV(size, i));
    
    if ( // if not exists
        (maxx.find(std::make_tuple(
            static_cast<int>(i % size.length()),
            static_cast<int>(i % alpha.length()),
            static_cast<int>(i % beta.length()))) == maxx.end())
      || // or is smaller than current max
        (maxx[std::make_tuple(
            static_cast<int>(i % size.length()),
            static_cast<int>(i % alpha.length()),
            static_cast<int>(i % beta.length()))] < mx)
    ) {
      
      maxx[std::make_tuple(
          static_cast<int>(i % size.length()),
          static_cast<int>(i % alpha.length()),
          static_cast<int>(i % beta.length()))] = mx;
      
    }
    
  }

and then

   if (!tmp.size()) {
        mx = maxx.at(std::make_tuple(
          static_cast<int>(i % size.length()),
          static_cast<int>(i % alpha.length()),
          static_cast<int>(i % beta.length())
        ));
        tmp = cdf_bbinom_table(mx, GETV(size, i), GETV(alpha, i), GETV(beta, i));
      }

But on benchmarks this makes the code approx 1.35x slower unless when using vectorization heavily (many different combinations of parameters relatively to sample size).