Learn to write cpp in R. [High performance functions with Rcpp](http://adv-r.had.co.nz/Rcpp.html)

learnRcpp.cpp

#include <Rcpp.h>
using namespace Rcpp;

//[[Rcpp::export]]
bool allC(LogicalVector x){
	int n = x.size();
	for (int i = 0; i < n; i++){
		if (x[i] == false){
			return false;
		}
	}
	return true;
}

/***
library(microbenchmark)
x = 1:1000 < 800
microbenchmark(all(x), allC(x)) # slower
all(all(x) == allC(x)) # TRUE
*/

//[[Rcpp::export]]
NumericVector cumprodC(NumericVector x){
	int n = x.size();
	NumericVector out(n);
	out[0] = x[0];
	for (int i = 1; i < n; i++){
		out[i] = out[i - 1] * x[i];
	}
	return out;
}
/***
x = 1:5
microbenchmark(cumprod(x), cumprodC(x)) # slower
all(cumprod(x) == cumprodC(x)) # TRUE
*/

//[[Rcpp::export]]
NumericVector cumminC(NumericVector x){
	int n = x.size();
	NumericVector out(n);
	out[0] = x[0];
	for (int i = 1; i < n; i++){
		if (x[i] < out[i - 1]){
			out[i] = x[i];
		}else{
			out[i] = out[i-1];
		}
	}
	return out;
}

/***
x = c(4, 5, 3, 6, 1)
microbenchmark(cumminC(x), cummin(x)) # slower
all(cumminC(x) == cummin(x)) # TRUE
*/

//[[Rcpp::export]]
NumericVector cummaxC(NumericVector x){
	int n = x.size();
	NumericVector out(n);
	out[0] = x[0];
	for (int i = 1; i < n; i++){
		if (x[i] > out[i - 1]){
			out[i] = x[i];
		}else{
			out[i] = out[i-1];
		}
	}
	return out;
}

/***
x = c(4, 5, 3, 6, 1)
microbenchmark(cummaxC(x), cummax(x)) # slower
all(cummaxC(x) == cummax(x)) # TRUE
*/

//[[Rcpp::export]]
NumericVector diffC(NumericVector x, int lag=1){
	int n = x.size() - lag;
	NumericVector out(n);
	for (int i = 0; i < n; i++){
		out[i] = x[i + lag] - x[i];
	}
	return out;
}
/***
x = c(4, 5, 3, 6, 1)
microbenchmark(diffC(x), diff(x))
all(diffC(x, lag=1) == diff(x)) # TRUE

microbenchmark(diffC(x), diff(x, 2))
all(diffC(x, lag=2) == diff(x, 2)) # TRUE
*/


//[[Rcpp::export]]
NumericVector rangeC(NumericVector x){
	int n = x.size();
	NumericVector out(2);
	out[0] = out[1] = x[0];
	for (int i=0; i < n; i++){
		if (x[i] < out[0]){
			out[0] = x[i];
		}
		if (x[i] > out[1]){
			out[1] = x[i];
		}
	}
	return out;
}
/***
x = c(4, 5, 3, 6, 1)
microbenchmark(rangeC(x), range(x)) # faster
all(rangeC(x) == range(x)) # TRUE
*/

//[[Rcpp::export]]
NumericVector varC(NumericVector x){
	int n = x.size();
	double out = 0, total = 0;
	for (int i=0; i < n; i++){
		out += pow(x[i], 2);
		total += x[i];
	}
	double res = (out - pow(total, 2) / n) / (n - 1);
	return res;
}
/***
x = c(4, 5, 3, 6, 1)
microbenchmark(varC(x), var(x)) # faster
all(varC(x) - var(x) < 1e-9) # TRUE
*/