Inconsistent results between Rcpp and R code - r

Question

UPDATE
Previous example is complicated, hence please allow me to use a simpler example as shown below:
Here is the Rcpp code:
#include <RcppArmadillo.h>
#include <RcppArmadilloExtensions/sample.h>
#include <Rmath.h>
#include <Rcpp.h>
// [[Rcpp::depends(RcppArmadillo)]]
using namespace Rcpp ;
using namespace arma;
using namespace std;
// [[Rcpp::export]]
double chooseC(double n, double k) {
return Rf_choose(n, k);
}
// [[Rcpp::export]]
double function3(double n, double m, double beta) {
double prob;
NumericVector k(m);
NumericVector k_vec(m);
if(n<m){prob=0;}
else{
if(chooseC(n,m)==R_PosInf){
k=seq_len(m)-1;
k_vec= (n-k)/(m-k)*std::pow((1-beta),(n-m)/m)*beta;
prob=std::accumulate(k_vec.begin(),k_vec.end(), 1, std::multiplies<double>())*beta;
}
else{
prob = beta * chooseC(n,m) * std::pow(beta,m) * std::pow((1-beta),(n-m));
}
}
return(prob);
}
Here is the R code:
function4 <- function ( n , m , beta )
{
if ( n < m )
{
prob <- 0.0
}
else
{
if (is.infinite(choose(n,m))){
k<-0:(m-1)
prob <- beta *prod((n-k)/(m-k)*(1-beta)^((n-m)/m)*beta)
}
else{
prob <- beta * choose(n,m) * beta^m * (1-beta)^(n-m)
}
}
prob
}
Comparison:
input<-619
beta<-0.09187495
x<-seq(0, (input+1)/beta*3)
yy<-sapply(x,function(n)function3(n,input, beta=beta))
yy2<-sapply(x,function(n)function4(n,input, beta=beta))
sum(yy)=0
sum(yy2)=1
However， with other input:
input<-1
beta<-0.08214248
Both results are the same, sum(yy)=sum(yy2)=0.9865887.
I used double in Rcpp code, I don't know what else could cause the inconsistent precision between Rcpp and R code.
Thanks a lot!

Answer 1

I think I fix the Rcpp code, so right now both Rcpp and R code produce the same results when the results are very small values. The solution is shown as below:
#include <RcppArmadillo.h>
#include <RcppArmadilloExtensions/sample.h>
#include <Rmath.h>
#include <Rcpp.h>
// [[Rcpp::depends(RcppArmadillo)]]
using namespace Rcpp ;
using namespace arma;
using namespace std;
// [[Rcpp::export]]
double chooseC(double n, double k) {
return Rf_choose(n, k);
}
// [[Rcpp::export]]
double function3(double n, double m, double beta) {
double prob;
arma::vec k = arma::linspace<vec>(0, m-1, m);
arma::vec k_vec;
if(n<m){prob=0;}
else{
if(chooseC(n,m)==R_PosInf){
k_vec= (n-k)/(m-k)*pow((1-beta),(n-m)/m)*beta;
prob=arma::prod(k_vec)*beta;
}
else{
prob = beta * chooseC(n,m) * pow(beta,m) * pow((1-beta),(n-m));
}
}
return(prob);
}
However, I still do not understand why by writing code in this way will fix the precision inconsistent. Rcpp and RcppArmadillo still look like black boxes to me.