Faster version of 1-(prod(1-x))

or.cpp

#include <vector>
// [[Rcpp::export]]
double or_cpp(std::vector<double> x) {
  double tot = 1.0;
  for ( size_t i = 0; i < x.size(); i++ )
    tot *= (1 - x[i]);
  return 1 - tot;
}

/*
  ## Benchmarking:
  library(Rcpp)
  library(rbenchmark)
  sourceCpp("or.cpp")

  f <- function(n) {
    set.seed(1)
    x <- runif(n, 0, .1)
    or <- function(x) 1-(prod(1-x))
    gc()
    res <- benchmark(or(x), or_cpp(x), replications=500, order=NULL)
    res$relative[[2]] / res$relative[[1]]
  }

  ## Surprising behaviour -- R is about the same as C++ until very
  ## large sample sizes, where R starts killing C++; probably switching
  ## to a different algorithm?
  n <- round(10^(seq(1, 5, length=21)))
  r <- sapply(n, f)
  plot(r ~ n, log="x")
  abline(h=1, lty=3)
*/