How to do fast percentile calculation in C++/Rcpp

Question

I have a large vector containing a bunch of double elements. Given an array of percentile vector, such as percentile_vec = c(0.90, 0.91, 0.92, 0.93, 0.94, 0.95). I am currently using Rcpp sort function to sort the large vector and then find the corresponding percentile value. Here is the main codes:

// [[Rcpp::export]]
NumericVector sort_rcpp(Rcpp::NumericVector& x)
{
  std::vector<double> tmp = Rcpp::as<std::vector<double>> (x);    // or NumericVector tmp = clone(x);
  std::sort(tmp.begin(), tmp.end());
  return wrap(tmp);
}

// [[Rcpp::export]]
NumericVector percentile_rcpp(Rcpp::NumericVector& x, Rcpp::NumericVector& percentile)
{
  NumericVector tmp_sort = sort_rcpp(x);
  int size_per = percentile.size();
  NumericVector percentile_vec = no_init(size_per);
  for (int ii = 0; ii < size_per; ii++)
  {
    double size_per = tmp_sort.size() * percentile[ii];
    double size_per_round;
    if (size_per < 1.0)
    {
      size_per_round = 1.0;
    }
    else
    {
      size_per_round = std::round(size_per);
    }
    percentile_vec[ii] = tmp_sort[size_per_round-1];  // For extreme case such as size_per_round == tmp_sort.size() to avoid overflow
  }
  return percentile_vec;
}

I also try to call R function quantile(x, c(.90, .91, .92, .93, .94, .95)) in Rcpp by using:

sub_percentile <- function (x)
{
  return (quantile(x, c(.90, .91, .92, .93, .94, .95)));
}  

source('C:/Users/~Call_R_function.R')

The test rests for x=runif(1E6) are listed below:

microbenchmark(sub_percentile(x)->aa, percentile_rcpp(x, c(.90, .91, .92, .93, .94, .95))->bb)
#Unit: milliseconds
              expr      min       lq     mean   median       uq       max   neval
  sub_percentile(x) 99.00029 99.24160 99.35339 99.32162 99.41869 100.57160   100
 percentile_rcpp(~) 87.13393 87.30904 87.44847 87.40826 87.51547  88.41893   100

I expect a fast speed percentile calculation, yet I assume std::sort(tmp.begin(), tmp.end()) slows down the speed. Is there any better way to get a fast result using C++, RCpp/RcppAramdillo? Thanks.

Answer 1

Branching in a loop could be surely optimized. Use std::min/max calls with ints.

I would solve percent calculation of array indices this way:

uint PerCentIndex( double pc, uint size )
{
    return 0.5 + ( double ) ( size - 1 ) * pc;
}

Only this line in the middle of the loop above:

percentile_vec[ii] 
 = tmp_sort[ PerCentIndex( percentile[ii], tmp_sort.size() ) ];