Computing an Inner Product with RcppParallel

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The RcppParallel package includes high level functions for doing parallel programming with Rcpp. For example, the parallelReduce function can be used aggreggate values from a set of inputs in parallel. This article describes using RcppParallel to parallelize the inner-product example previously posted to the Rcpp Gallery.

Serial Version

First the serial version of computing the inner product. For this we use a simple call to the STL std::inner_product function:

#include <Rcpp.h>
using namespace Rcpp;

#include <algorithm>

// [[Rcpp::export]]
double innerProduct(NumericVector x, NumericVector y) {
   return std::inner_product(x.begin(), x.end(), y.begin(), 0.0);

Parallel Version

Now we adapt our code to run in parallel. We’ll use the parallelReduce function to do this. This function requires a “worker” function object (defined below as InnerProduct). For details on worker objects see the parallel-vector-sum article on the Rcpp Gallery.

// [[Rcpp::depends(RcppParallel)]]
#include <RcppParallel.h>
using namespace RcppParallel;

struct InnerProduct : public Worker
   // source vectors
   const RVector<double> x;
   const RVector<double> y;
   // product that I have accumulated
   double product;
   // constructors
   InnerProduct(const NumericVector x, const NumericVector y) 
      : x(x), y(y), product(0) {}
   InnerProduct(const InnerProduct& innerProduct, Split) 
      : x(innerProduct.x), y(innerProduct.y), product(0) {}
   // process just the elements of the range I've been asked to
   void operator()(std::size_t begin, std::size_t end) {
      product += std::inner_product(x.begin() + begin, 
                                    x.begin() + end, 
                                    y.begin() + begin, 
   // join my value with that of another InnerProduct
   void join(const InnerProduct& rhs) { 
     product += rhs.product; 

Note that InnerProduct derives from the RcppParallel::Worker class. This is required for function objects passed to parallelReduce.

Note also that we use the RVector<double> type for accessing the vector. This is because this code will execute on a background thread where it’s not safe to call R or Rcpp APIs. The RVector class is included in the RcppParallel package and provides a lightweight, thread-safe wrapper around R vectors.

Now that we’ve defined the function object, implementing the parallel inner product function is straightforward. Just initialize an instance of InnerProduct with the input vectors and call parallelReduce:

// [[Rcpp::export]]
double parallelInnerProduct(NumericVector x, NumericVector y) {
   // declare the InnerProduct instance that takes a pointer to the vector data
   InnerProduct innerProduct(x, y);
   // call paralleReduce to start the work
   parallelReduce(0, x.length(), innerProduct);
   // return the computed product
   return innerProduct.product;


A comparison of the performance of the two functions shows the parallel version performing about 2.5 times as fast on a machine with 4 cores:

x <- runif(1000000)
y <- runif(1000000)

res <- benchmark(sum(x*y),
                 innerProduct(x, y),
                 parallelInnerProduct(x, y),

                        test replications elapsed relative
3 parallelInnerProduct(x, y)          100   0.035    1.000
2         innerProduct(x, y)          100   0.088    2.514
1                 sum(x * y)          100   0.283    8.086

Note that performance gains will typically be 30-50% less on Windows systems as a result of less sophisticated thread scheduling (RcppParallel does not currently use TBB on Windows whereas it does on the Mac and Linux).

You can learn more about using RcppParallel at

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