Rcpp keeps running for a seemingly simple task - r

Question

I've been thinking about it all day and still cannot figure out why this happens. My objective is simple: STEP1, generate a function S(h,p); STEP2, numerically integrate S(h,p) with respect to p by trapezoidal rule and obtain a new function SS(h). I wrote the code and source it by sourceCpp, and it successfully generated two functions S(h,p) and SS(h) in R. But when I tried to test it by calculating SS(1), R just kept running and never gave the result, which is weird because the calculation amount is not that big. Any idea why this would happen？
My code is here:
#include <Rcpp.h>
using namespace Rcpp;
//generate the first function that gives S(h,p)
// [[Rcpp::export]]
double S(double h, double p){
double out=2*(h+p+h*p);
return out;
}
//generate the second function that gives the numerically integreation of S(h,p) w.r.t p
//[[Rcpp::export]]
double SS(double h){
double out1=0;
double sum=0;
for (int i=0;i<1;i=i+0.01){
sum=sum+S(h,i);
}
out1=0.01/2*(2*sum-S(h,0)-S(h,1));
return out1;
}

Answer 1

The problem is that you are treating i as if it were not an int in this statement:
for (int i=0;i<1;i=i+0.01){
sum=sum+S(h,i);
}
After each iteration you are attempting to add 0.01 to an integer, which is of course immediately truncated towards 0, meaning that i is always equal to zero, and you have an infinite loop. A minimal example highlighting the problem, with a couple of possible solutions:
#include <Rcpp.h>
// [[Rcpp::export]]
void bad_loop() {
for (int i = 0; i < 1; i += 0.01) {
std::printf("i = %d\n", i);
Rcpp::checkUserInterrupt();
}
}
// [[Rcpp::export]]
void good_loop() {
for (int i = 0; i < 100; i++) {
std::printf("i = %d\n", i);
Rcpp::checkUserInterrupt();
}
}
// [[Rcpp::export]]
void good_loop2() {
for (double j = 0.0; j < 1.0; j += 0.01) {
std::printf("j = %.2f\n", j);
Rcpp::checkUserInterrupt();
}
}
The first alternative (good_loop) is to scale your step size appropriately -- looping from 0 through 99 by 1 takes the same number of iterations as looping from 0 to 0.99 by 0.01. Additionally, you could just use a double instead of an int, as in good_loop2. At any rate, the main takeaway here is that you need to be more careful about choosing your variable types in C++. Unlike R, when you declare i to be an int it will be treated like an int, not a floating point number.

Answer 2

As #nrussell pointed out very expertly, there is an issue with treating i as an int when the type held is a double. The goal of posting this answer is to stress the need to avoid using a double or float as a loop incrementer. I've opted to post it as an answer instead of a comment for readability.
Please note, the loop increment should not ever be given as a double or a float due to precision issues. e.g. it is hard to get i = .99 since i = 0.981111111 et cetera...
Instead, I would opt to have the loop be processed as an int and convert it to a double / float as soon as possible, e.g.
for (int i=0; i < 100; i++){
// Make sure to use double division
// (e.g. either numerator or denominator is a floating / double)
sum += S(h, i/100.0);
}
Further notes:
RcppArmadillo and C++ division issue
Using float / double as a loop variable