25.2.1 No inputs, scalar output

Let’s start with a very simple function. It has no arguments and always returns the integer 1:

one <- function() 1L

The equivalent C++ function is:

int one() {
  return 1;
}

We can compile and use this from R with cppFunction()

cppFunction('int one() {
  return 1;
}')

This small function illustrates a number of important differences between R and C++:

• The syntax to create a function looks like the syntax to call a function; you don’t use assignment to create functions as you do in R.

• You must declare the type of output the function returns. This function returns an int (a scalar integer). The classes for the most common types of R vectors are: NumericVector, IntegerVector, CharacterVector, and LogicalVector.

• Scalars and vectors are different. The scalar equivalents of numeric, integer, character, and logical vectors are: double, int, String, and bool.

• You must use an explicit return statement to return a value from a function.

• Every statement is terminated by a ;.

25.2.2 Scalar input, scalar output

The next example function implements a scalar version of the sign() function which returns 1 if the input is positive, and -1 if it’s negative:

signR <- function(x) {
  if (x > 0) {
    1
  } else if (x == 0) {
    0
  } else {
    -1
  }
}

cppFunction('int signC(int x) {
  if (x > 0) {
    return 1;
  } else if (x == 0) {
    return 0;
  } else {
    return -1;
  }
}')

In the C++ version:

• We declare the type of each input in the same way we declare the type of the output. While this makes the code a little more verbose, it also makes clear the type of input the function needs.

• The if syntax is identical — while there are some big differences between R and C++, there are also lots of similarities! C++ also has a while statement that works the same way as R’s. As in R you can use break to exit the loop, but to skip one iteration you need to use continue instead of next.

25.2.3 Vector input, scalar output

One big difference between R and C++ is that the cost of loops is much lower in C++. For example, we could implement the sum function in R using a loop. If you’ve been programming in R a while, you’ll probably have a visceral reaction to this function!

sumR <- function(x) {
  total <- 0
  for (i in seq_along(x)) {
    total <- total + x[i]
  }
  total
}

In C++, loops have very little overhead, so it’s fine to use them. In Section 25.5, you’ll see alternatives to for loops that more clearly express your intent; they’re not faster, but they can make your code easier to understand.

cppFunction('double sumC(NumericVector x) {
  int n = x.size();
  double total = 0;
  for(int i = 0; i < n; ++i) {
    total += x[i];
  }
  return total;
}')

The C++ version is similar, but:

• To find the length of the vector, we use the .size() method, which returns an integer. C++ methods are called with . (i.e., a full stop).

• The for statement has a different syntax: for(init; check; increment). This loop is initialised by creating a new variable called i with value 0. Before each iteration we check that i < n, and terminate the loop if it’s not. After each iteration, we increment the value of i by one, using the special prefix operator ++ which increases the value of i by 1.

• In C++, vector indices start at 0, which means that the last element is at position n - 1. I’ll say this again because it’s so important: IN C++, VECTOR INDICES START AT 0! This is a very common source of bugs when converting R functions to C++.

• Use = for assignment, not <-.

• C++ provides operators that modify in-place: total += x[i] is equivalent to total = total + x[i]. Similar in-place operators are -=, *=, and /=.

This is a good example of where C++ is much more efficient than R. As shown by the following microbenchmark, sumC() is competitive with the built-in (and highly optimised) sum(), while sumR() is several orders of magnitude slower.

x <- runif(1e3)
bench::mark(
  sum(x),
  sumC(x),
  sumR(x)
)[1:6]
#> # A tibble: 3 x 6
#>   expression      min   median `itr/sec` mem_alloc `gc/sec`
#>   <bch:expr> <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
#> 1 sum(x)       2.51µs   2.81µs   336848.        0B      0  
#> 2 sumC(x)      3.59µs   5.24µs   177706.    2.49KB     17.8
#> 3 sumR(x)     27.14µs  29.11µs    32752.  182.59KB      0

25.2.4 Vector input, vector output

Next we’ll create a function that computes the Euclidean distance between a value and a vector of values:

pdistR <- function(x, ys) {
  sqrt((x - ys) ^ 2)
}

In R, it’s not obvious that we want x to be a scalar from the function definition, and we’d need to make that clear in the documentation. That’s not a problem in the C++ version because we have to be explicit about types:

cppFunction('NumericVector pdistC(double x, NumericVector ys) {
  int n = ys.size();
  NumericVector out(n);

  for(int i = 0; i < n; ++i) {
    out[i] = sqrt(pow(ys[i] - x, 2.0));
  }
  return out;
}')

This function introduces only a few new concepts:

• We create a new numeric vector of length n with a constructor: NumericVector out(n). Another useful way of making a vector is to copy an existing one: NumericVector zs = clone(ys).

• C++ uses pow(), not ^, for exponentiation.

Note that because the R version is fully vectorised, it’s already going to be fast.

y <- runif(1e6)
bench::mark(
  pdistR(0.5, y),
  pdistC(0.5, y)
)[1:6]
#> # A tibble: 2 x 6
#>   expression          min   median `itr/sec` mem_alloc `gc/sec`
#>   <bch:expr>     <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
#> 1 pdistR(0.5, y)   6.31ms   6.75ms      145.    7.63MB     72.4
#> 2 pdistC(0.5, y)   2.31ms   2.77ms      380.    7.63MB    192.

On my computer, it takes around 5 ms with a 1 million element y vector. The C++ function is about 2.5 times faster, ~2 ms, but assuming it took you 10 minutes to write the C++ function, you’d need to run it ~200,000 times to make rewriting worthwhile. The reason why the C++ function is faster is subtle, and relates to memory management. The R version needs to create an intermediate vector the same length as y (x - ys), and allocating memory is an expensive operation. The C++ function avoids this overhead because it uses an intermediate scalar.

25.2.5 Using sourceCpp

So far, we’ve used inline C++ with cppFunction(). This makes presentation simpler, but for real problems, it’s usually easier to use stand-alone C++ files and then source them into R using sourceCpp(). This lets you take advantage of text editor support for C++ files (e.g., syntax highlighting) as well as making it easier to identify the line numbers in compilation errors.

Your stand-alone C++ file should have extension .cpp, and needs to start with:

#include <Rcpp.h>
using namespace Rcpp;

And for each function that you want available within R, you need to prefix it with:

// [[Rcpp::export]]

You can embed R code in special C++ comment blocks. This is really convenient if you want to run some test code:

/*** R
# This is R code
*/

The R code is run with source(echo = TRUE) so you don’t need to explicitly print output.

To compile the C++ code, use sourceCpp("path/to/file.cpp"). This will create the matching R functions and add them to your current session. Note that these functions can not be saved in a .Rdata file and reloaded in a later session; they must be recreated each time you restart R.

For example, running sourceCpp() on the following file implements mean in C++ and then compares it to the built-in mean():

#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
double meanC(NumericVector x) {
  int n = x.size();
  double total = 0;

  for(int i = 0; i < n; ++i) {
    total += x[i];
  }
  return total / n;
}

/*** R
x <- runif(1e5)
bench::mark(
  mean(x),
  meanC(x)
)
*/

NB: If you run this code, you’ll notice that meanC() is much faster than the built-in mean(). This is because it trades numerical accuracy for speed.

For the remainder of this chapter C++ code will be presented stand-alone rather than wrapped in a call to cppFunction. If you want to try compiling and/or modifying the examples you should paste them into a C++ source file that includes the elements described above. This is easy to do in RMarkdown: all you need to do is specify engine = "Rcpp".

25.2.6 Exercises

1. With the basics of C++ in hand, it’s now a great time to practice by reading and writing some simple C++ functions. For each of the following functions, read the code and figure out what the corresponding base R function is. You might not understand every part of the code yet, but you should be able to figure out the basics of what the function does.

   double f1(NumericVector x) {
     int n = x.size();
     double y = 0;
   
     for(int i = 0; i < n; ++i) {
       y += x[i] / n;
     }
     return y;
   }
   
   NumericVector f2(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;
   }
   
   bool f3(LogicalVector x) {
     int n = x.size();
   
     for(int i = 0; i < n; ++i) {
       if (x[i]) return true;
     }
     return false;
   }
   
   int f4(Function pred, List x) {
     int n = x.size();
   
     for(int i = 0; i < n; ++i) {
       LogicalVector res = pred(x[i]);
       if (res[0]) return i + 1;
     }
     return 0;
   }
   
   NumericVector f5(NumericVector x, NumericVector y) {
     int n = std::max(x.size(), y.size());
     NumericVector x1 = rep_len(x, n);
     NumericVector y1 = rep_len(y, n);
   
     NumericVector out(n);
   
     for (int i = 0; i < n; ++i) {
       out[i] = std::min(x1[i], y1[i]);
     }
   
     return out;
   }

2. To practice your function writing skills, convert the following functions into C++. For now, assume the inputs have no missing values.

   1. all().

   2. cumprod(), cummin(), cummax().

   3. diff(). Start by assuming lag 1, and then generalise for lag n.

   4. range().

   5. var(). Read about the approaches you can take on Wikipedia. Whenever implementing a numerical algorithm, it’s always good to check what is already known about the problem.

25.3.1 Lists and data frames

Rcpp also provides List and DataFrame classes, but they are more useful for output than input. This is because lists and data frames can contain arbitrary classes but C++ needs to know their classes in advance. If the list has known structure (e.g., it’s an S3 object), you can extract the components and manually convert them to their C++ equivalents with as(). For example, the object created by lm(), the function that fits a linear model, is a list whose components are always of the same type. The following code illustrates how you might extract the mean percentage error (mpe()) of a linear model. This isn’t a good example of when to use C++, because it’s so easily implemented in R, but it shows how to work with an important S3 class. Note the use of .inherits() and the stop() to check that the object really is a linear model.

#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
double mpe(List mod) {
  if (!mod.inherits("lm")) stop("Input must be a linear model");

  NumericVector resid = as<NumericVector>(mod["residuals"]);
  NumericVector fitted = as<NumericVector>(mod["fitted.values"]);

  int n = resid.size();
  double err = 0;
  for(int i = 0; i < n; ++i) {
    err += resid[i] / (fitted[i] + resid[i]);
  }
  return err / n;
}

mod <- lm(mpg ~ wt, data = mtcars)
mpe(mod)
#> [1] -0.0154

25.3.2 Functions

You can put R functions in an object of type Function. This makes calling an R function from C++ straightforward. The only challenge is that we don’t know what type of output the function will return, so we use the catchall type RObject.

#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
RObject callWithOne(Function f) {
  return f(1);
}

callWithOne(function(x) x + 1)
#> [1] 2
callWithOne(paste)
#> [1] "1"

Calling R functions with positional arguments is obvious:

f("y", 1);

But you need a special syntax for named arguments:

f(_["x"] = "y", _["value"] = 1);

25.3.3 Attributes

All R objects have attributes, which can be queried and modified with .attr(). Rcpp also provides .names() as an alias for the name attribute. The following code snippet illustrates these methods. Note the use of ::create(), a class method. This allows you to create an R vector from C++ scalar values:

#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
NumericVector attribs() {
  NumericVector out = NumericVector::create(1, 2, 3);

  out.names() = CharacterVector::create("a", "b", "c");
  out.attr("my-attr") = "my-value";
  out.attr("class") = "my-class";

  return out;
}

For S4 objects, .slot() plays a similar role to .attr().

25.4.1 Scalars

The following code explores what happens when you take one of R’s missing values, coerce it into a scalar, and then coerce back to an R vector. Note that this kind of experimentation is a useful way to figure out what any operation does.

#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
List scalar_missings() {
  int int_s = NA_INTEGER;
  String chr_s = NA_STRING;
  bool lgl_s = NA_LOGICAL;
  double num_s = NA_REAL;

  return List::create(int_s, chr_s, lgl_s, num_s);
}

str(scalar_missings())
#> List of 4
#>  $ : int NA
#>  $ : chr NA
#>  $ : logi TRUE
#>  $ : num NA

With the exception of bool, things look pretty good here: all of the missing values have been preserved. However, as we’ll see in the following sections, things are not quite as straightforward as they seem.

evalCpp("NAN == 1")
#> [1] FALSE
evalCpp("NAN < 1")
#> [1] FALSE
evalCpp("NAN > 1")
#> [1] FALSE
evalCpp("NAN == NAN")
#> [1] FALSE

evalCpp("NAN && TRUE")
#> [1] TRUE
evalCpp("NAN || FALSE")
#> [1] TRUE

evalCpp("NAN + 1")
#> [1] NaN
evalCpp("NAN - 1")
#> [1] NaN
evalCpp("NAN / 1")
#> [1] NaN
evalCpp("NAN * 1")
#> [1] NaN

25.4.2 Strings

String is a scalar string class introduced by Rcpp, so it knows how to deal with missing values.

25.4.3 Boolean

While C++’s bool has two possible values (true or false), a logical vector in R has three (TRUE, FALSE, and NA). If you coerce a length 1 logical vector, make sure it doesn’t contain any missing values; otherwise they will be converted to TRUE. An easy fix is to use int instead, as this can represent TRUE, FALSE, and NA.

25.4.4 Vectors

With vectors, you need to use a missing value specific to the type of vector, NA_REAL, NA_INTEGER, NA_LOGICAL, NA_STRING:

#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
List missing_sampler() {
  return List::create(
    NumericVector::create(NA_REAL),
    IntegerVector::create(NA_INTEGER),
    LogicalVector::create(NA_LOGICAL),
    CharacterVector::create(NA_STRING)
  );
}

str(missing_sampler())
#> List of 4
#>  $ : num NA
#>  $ : int NA
#>  $ : logi NA
#>  $ : chr NA

25.4.5 Exercises

1. Rewrite any of the functions from the first exercise of Section 25.2.6 to deal with missing values. If na.rm is true, ignore the missing values. If na.rm is false, return a missing value if the input contains any missing values. Some good functions to practice with are min(), max(), range(), mean(), and var().

2. Rewrite cumsum() and diff() so they can handle missing values. Note that these functions have slightly more complicated behaviour.

25.5.1 Using iterators

Iterators are used extensively in the STL: many functions either accept or return iterators. They are the next step up from basic loops, abstracting away the details of the underlying data structure. Iterators have three main operators:

1. Advance with ++.
2. Get the value they refer to, or dereference, with *.
3. Compare with ==.

For example we could re-write our sum function using iterators:

#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
double sum3(NumericVector x) {
  double total = 0;
  
  NumericVector::iterator it;
  for(it = x.begin(); it != x.end(); ++it) {
    total += *it;
  }
  return total;
}

The main changes are in the for loop:

• We start at x.begin() and loop until we get to x.end(). A small optimization is to store the value of the end iterator so we don’t need to look it up each time. This only saves about 2 ns per iteration, so it’s only important when the calculations in the loop are very simple.

• Instead of indexing into x, we use the dereference operator to get its current value: *it.

• Notice the type of the iterator: NumericVector::iterator. Each vector type has its own iterator type: LogicalVector::iterator, CharacterVector::iterator, etc.

This code can be simplified still further through the use of a C++11 feature: range-based for loops. C++11 is widely available, and can easily be activated for use with Rcpp by adding [[Rcpp::plugins(cpp11)]].

// [[Rcpp::plugins(cpp11)]]
#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
double sum4(NumericVector xs) {
  double total = 0;
  
  for(const auto &x : xs) {
    total += x;
  }
  return total;
}

Iterators also allow us to use the C++ equivalents of the apply family of functions. For example, we could again rewrite sum() to use the accumulate() function, which takes a starting and an ending iterator, and adds up all the values in the vector. The third argument to accumulate gives the initial value: it’s particularly important because this also determines the data type that accumulate uses (so we use 0.0 and not 0 so that accumulate uses a double, not an int.). To use accumulate() we need to include the <numeric> header.

#include <numeric>
#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
double sum5(NumericVector x) {
  return std::accumulate(x.begin(), x.end(), 0.0);
}

25.5.2 Algorithms

The <algorithm> header provides a large number of algorithms that work with iterators. A good reference is available at https://en.cppreference.com/w/cpp/algorithm. For example, we could write a basic Rcpp version of findInterval() that takes two arguments a vector of values and a vector of breaks, and locates the bin that each x falls into. This shows off a few more advanced iterator features. Read the code below and see if you can figure out how it works.

#include <algorithm>
#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
IntegerVector findInterval2(NumericVector x, NumericVector breaks) {
  IntegerVector out(x.size());

  NumericVector::iterator it, pos;
  IntegerVector::iterator out_it;

  for(it = x.begin(), out_it = out.begin(); it != x.end(); 
      ++it, ++out_it) {
    pos = std::upper_bound(breaks.begin(), breaks.end(), *it);
    *out_it = std::distance(breaks.begin(), pos);
  }

  return out;
}

The key points are:

• We step through two iterators (input and output) simultaneously.

• We can assign into an dereferenced iterator (out_it) to change the values in out.

• upper_bound() returns an iterator. If we wanted the value of the upper_bound() we could dereference it; to figure out its location, we use the distance() function.

• Small note: if we want this function to be as fast as findInterval() in R (which uses handwritten C code), we need to compute the calls to .begin() and .end() once and save the results. This is easy, but it distracts from this example so it has been omitted. Making this change yields a function that’s slightly faster than R’s findInterval() function, but is about 1/10 of the code.

It’s generally better to use algorithms from the STL than hand rolled loops. In Effective STL, Scott Meyers gives three reasons: efficiency, correctness, and maintainability. Algorithms from the STL are written by C++ experts to be extremely efficient, and they have been around for a long time so they are well tested. Using standard algorithms also makes the intent of your code more clear, helping to make it more readable and more maintainable.

25.5.3 Data structures

The STL provides a large set of data structures: array, bitset, list, forward_list, map, multimap, multiset, priority_queue, queue, deque, set, stack, unordered_map, unordered_set, unordered_multimap, unordered_multiset, and vector. The most important of these data structures are the vector, the unordered_set, and the unordered_map. We’ll focus on these three in this section, but using the others is similar: they just have different performance trade-offs. For example, the deque (pronounced “deck”) has a very similar interface to vectors but a different underlying implementation that has different performance trade-offs. You may want to try it for your problem. A good reference for STL data structures is https://en.cppreference.com/w/cpp/container — I recommend you keep it open while working with the STL.

Rcpp knows how to convert from many STL data structures to their R equivalents, so you can return them from your functions without explicitly converting to R data structures.

25.5.4 Vectors

An STL vector is very similar to an R vector, except that it grows efficiently. This makes vectors appropriate to use when you don’t know in advance how big the output will be. Vectors are templated, which means that you need to specify the type of object the vector will contain when you create it: vector<int>, vector<bool>, vector<double>, vector<String>. You can access individual elements of a vector using the standard [] notation, and you can add a new element to the end of the vector using .push_back(). If you have some idea in advance how big the vector will be, you can use .reserve() to allocate sufficient storage.

The following code implements run length encoding (rle()). It produces two vectors of output: a vector of values, and a vector lengths giving how many times each element is repeated. It works by looping through the input vector x comparing each value to the previous: if it’s the same, then it increments the last value in lengths; if it’s different, it adds the value to the end of values, and sets the corresponding length to 1.

#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
List rleC(NumericVector x) {
  std::vector<int> lengths;
  std::vector<double> values;

  // Initialise first value
  int i = 0;
  double prev = x[0];
  values.push_back(prev);
  lengths.push_back(1);

  NumericVector::iterator it;
  for(it = x.begin() + 1; it != x.end(); ++it) {
    if (prev == *it) {
      lengths[i]++;
    } else {
      values.push_back(*it);
      lengths.push_back(1);

      i++;
      prev = *it;
    }
  }

  return List::create(
    _["lengths"] = lengths, 
    _["values"] = values
  );
}

(An alternative implementation would be to replace i with the iterator lengths.rbegin() which always points to the last element of the vector. You might want to try implementing that.)

Other methods of a vector are described at https://en.cppreference.com/w/cpp/container/vector.

25.5.5 Sets

Sets maintain a unique set of values, and can efficiently tell if you’ve seen a value before. They are useful for problems that involve duplicates or unique values (like unique, duplicated, or in). C++ provides both ordered (std::set) and unordered sets (std::unordered_set), depending on whether or not order matters for you. Unordered sets tend to be much faster (because they use a hash table internally rather than a tree), so even if you need an ordered set, you should consider using an unordered set and then sorting the output. Like vectors, sets are templated, so you need to request the appropriate type of set for your purpose: unordered_set<int>, unordered_set<bool>, etc. More details are available at https://en.cppreference.com/w/cpp/container/set and https://en.cppreference.com/w/cpp/container/unordered_set.

The following function uses an unordered set to implement an equivalent to duplicated() for integer vectors. Note the use of seen.insert(x[i]).second. insert() returns a pair, the .first value is an iterator that points to element and the .second value is a Boolean that’s true if the value was a new addition to the set.

// [[Rcpp::plugins(cpp11)]]
#include <Rcpp.h>
#include <unordered_set>
using namespace Rcpp;

// [[Rcpp::export]]
LogicalVector duplicatedC(IntegerVector x) {
  std::unordered_set<int> seen;
  int n = x.size();
  LogicalVector out(n);

  for (int i = 0; i < n; ++i) {
    out[i] = !seen.insert(x[i]).second;
  }

  return out;
}

25.5.6 Map

A map is similar to a set, but instead of storing presence or absence, it can store additional data. It’s useful for functions like table() or match() that need to look up a value. As with sets, there are ordered (std::map) and unordered (std::unordered_map) versions. Since maps have a value and a key, you need to specify both types when initialising a map: map<double, int>, unordered_map<int, double>, and so on. The following example shows how you could use a map to implement table() for numeric vectors:

#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
std::map<double, int> tableC(NumericVector x) {
  std::map<double, int> counts;

  int n = x.size();
  for (int i = 0; i < n; i++) {
    counts[x[i]]++;
  }

  return counts;
}

25.5.7 Exercises

To practice using the STL algorithms and data structures, implement the following using R functions in C++, using the hints provided:

1. median.default() using partial_sort.

2. %in% using unordered_set and the find() or count() methods.

3. unique() using an unordered_set (challenge: do it in one line!).

4. min() using std::min(), or max() using std::max().

5. which.min() using min_element, or which.max() using max_element.

6. setdiff(), union(), and intersect() for integers using sorted ranges and set_union, set_intersection and set_difference.

25.6.1 Gibbs sampler

The following case study updates an example blogged about by Dirk Eddelbuettel, illustrating the conversion of a Gibbs sampler in R to C++. The R and C++ code shown below is very similar (it only took a few minutes to convert the R version to the C++ version), but runs about 20 times faster on my computer. Dirk’s blog post also shows another way to make it even faster: using the faster random number generator functions in GSL (easily accessible from R through the RcppGSL package) can make it another two to three times faster.

The R code is as follows:

gibbs_r <- function(N, thin) {
  mat <- matrix(nrow = N, ncol = 2)
  x <- y <- 0

  for (i in 1:N) {
    for (j in 1:thin) {
      x <- rgamma(1, 3, y * y + 4)
      y <- rnorm(1, 1 / (x + 1), 1 / sqrt(2 * (x + 1)))
    }
    mat[i, ] <- c(x, y)
  }
  mat
}

This is straightforward to convert to C++. We:

• Add type declarations to all variables.

• Use ( instead of [ to index into the matrix.

• Subscript the results of rgamma and rnorm to convert from a vector into a scalar.

#include <Rcpp.h>
using namespace Rcpp;

// [[Rcpp::export]]
NumericMatrix gibbs_cpp(int N, int thin) {
  NumericMatrix mat(N, 2);
  double x = 0, y = 0;

  for(int i = 0; i < N; i++) {
    for(int j = 0; j < thin; j++) {
      x = rgamma(1, 3, 1 / (y * y + 4))[0];
      y = rnorm(1, 1 / (x + 1), 1 / sqrt(2 * (x + 1)))[0];
    }
    mat(i, 0) = x;
    mat(i, 1) = y;
  }

  return(mat);
}

Benchmarking the two implementations yields:

bench::mark(
  gibbs_r(100, 10),
  gibbs_cpp(100, 10),
  check = FALSE
)
#> # A tibble: 2 x 6
#>   expression              min   median `itr/sec` mem_alloc `gc/sec`
#>   <bch:expr>         <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
#> 1 gibbs_r(100, 10)     5.61ms   5.94ms      162.    4.97MB     34.8
#> 2 gibbs_cpp(100, 10)  225.9µs 256.23µs     3765.     4.1KB     30.0

25.6.2 R vectorisation versus C++ vectorisation

This example is adapted from “Rcpp is smoking fast for agent-based models in data frames”. The challenge is to predict a model response from three inputs. The basic R version of the predictor looks like:

vacc1a <- function(age, female, ily) {
  p <- 0.25 + 0.3 * 1 / (1 - exp(0.04 * age)) + 0.1 * ily
  p <- p * if (female) 1.25 else 0.75
  p <- max(0, p)
  p <- min(1, p)
  p
}

We want to be able to apply this function to many inputs, so we might write a vector-input version using a for loop.

vacc1 <- function(age, female, ily) {
  n <- length(age)
  out <- numeric(n)
  for (i in seq_len(n)) {
    out[i] <- vacc1a(age[i], female[i], ily[i])
  }
  out
}

If you’re familiar with R, you’ll have a gut feeling that this will be slow, and indeed it is. There are two ways we could attack this problem. If you have a good R vocabulary, you might immediately see how to vectorise the function (using ifelse(), pmin(), and pmax()). Alternatively, we could rewrite vacc1a() and vacc1() in C++, using our knowledge that loops and function calls have much lower overhead in C++.

Either approach is fairly straightforward. In R:

vacc2 <- function(age, female, ily) {
  p <- 0.25 + 0.3 * 1 / (1 - exp(0.04 * age)) + 0.1 * ily
  p <- p * ifelse(female, 1.25, 0.75)
  p <- pmax(0, p)
  p <- pmin(1, p)
  p
}

(If you’ve worked R a lot you might recognise some potential bottlenecks in this code: ifelse, pmin, and pmax are known to be slow, and could be replaced with p * 0.75 + p * 0.5 * female, p[p < 0] <- 0, p[p > 1] <- 1. You might want to try timing those variations.)

Or in C++:

#include <Rcpp.h>
using namespace Rcpp;

double vacc3a(double age, bool female, bool ily){
  double p = 0.25 + 0.3 * 1 / (1 - exp(0.04 * age)) + 0.1 * ily;
  p = p * (female ? 1.25 : 0.75);
  p = std::max(p, 0.0);
  p = std::min(p, 1.0);
  return p;
}

// [[Rcpp::export]]
NumericVector vacc3(NumericVector age, LogicalVector female, 
                    LogicalVector ily) {
  int n = age.size();
  NumericVector out(n);

  for(int i = 0; i < n; ++i) {
    out[i] = vacc3a(age[i], female[i], ily[i]);
  }

  return out;
}

We next generate some sample data, and check that all three versions return the same values:

n <- 1000
age <- rnorm(n, mean = 50, sd = 10)
female <- sample(c(T, F), n, rep = TRUE)
ily <- sample(c(T, F), n, prob = c(0.8, 0.2), rep = TRUE)

stopifnot(
  all.equal(vacc1(age, female, ily), vacc2(age, female, ily)),
  all.equal(vacc1(age, female, ily), vacc3(age, female, ily))
)

The original blog post forgot to do this, and introduced a bug in the C++ version: it used 0.004 instead of 0.04. Finally, we can benchmark our three approaches:

bench::mark(
  vacc1 = vacc1(age, female, ily),
  vacc2 = vacc2(age, female, ily),
  vacc3 = vacc3(age, female, ily)
)
#> # A tibble: 3 x 6
#>   expression      min   median `itr/sec` mem_alloc `gc/sec`
#>   <bch:expr> <bch:tm> <bch:tm>     <dbl> <bch:byt>    <dbl>
#> 1 vacc1         2.5ms   2.62ms      368.    7.86KB     25.0
#> 2 vacc2        73.3µs   83.7µs    10944.  148.85KB     18.0
#> 3 vacc3          14µs  15.63µs    62306.   14.48KB     18.7

Not surprisingly, our original approach with loops is very slow. Vectorising in R gives a huge speedup, and we can eke out even more performance (about ten times) with the C++ loop. I was a little surprised that the C++ was so much faster, but it is because the R version has to create 11 vectors to store intermediate results, where the C++ code only needs to create 1.