Two apparently similar functions give a different result. Why? - c++

Question

I am using Rcpp to integrate a piece of C++ code in R. I am implementing a function in C++ in two ways:
// [[Rcpp::export]]
double rhobiweight(double x,double k = 2.0){
double rho = 1.0;
if(abs(x)<k){
rho = 1.0-pow((1.0-pow(x/k,2)),3);
}
return rho/Erho(k) ;
}
// [[Rcpp::export]]
double rhobiweight2(double x,double k = 2.0){
double rho = 1.0-pow((1.0-pow(x/k,2)),3);
if(abs(x)>k){
rho = 1.0;
}
return rho/Erho(k) ;
}
If the x-value is between 2 and 3, I get different results of these functions. I can't figure out why.
> set.seed(1)
> x = 3*rnorm(10^5)
> c = x
> c2 = x
> for(i in 1:length(x)){
+ c[i] = rhobiweight(x[i])
+ c2[i] = rhobiweight2(x[i])
+ }
> print(sum(c-c2))
[1] -18564.31

Answer 1

The problem comes from your if statement inside the function. The negative of < is >=. so you should either replace < with <= in one function or > with >= in the other, depending on the expected behaviour.
Your problem happens for value between 2.0 and 2.9 inclusive because the abs(int) will always return 2 for this range.
abs(x) takes an int an return an int. Your double x is implicitly conversion to an int in your case.