Get started with cpp11

Outline

• Section intro teaches you how to write C++ by converting simple R functions to their C++ equivalents. You’ll learn how C++ differs from R, and what the key scalar, vector, and matrix classes are called.

• Section cpp_source shows you how to use cpp11::cpp_source() to load a C++ file from disk in the same way you use source() to load a file of R code.

• Section classes discusses how to modify attributes from cpp11, and mentions some of the other important classes.

• Section na teaches you how to work with R’s missing values in C++.

• Section stl shows you how to use some of the most important data structures and algorithms from the standard template library, or STL, built-in to C++.

• Section case-studies shows two real case studies where cpp11 was used to get considerable performance improvements.

• Section package teaches you how to add C++ code to an R package.

• Section more concludes the vignette with pointers to more resources to help you learn cpp11 and C++.

Prerequisites

We’ll use cpp11 to call C++ from R:

library(cpp11)

You’ll also need a working C++ compiler. To get it:

• On Windows, install Rtools.
• On Mac, install Xcode from the app store.
• On Linux, sudo apt-get install r-base-dev or similar.

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 cpp_function()

cpp_function('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: doubles, integers, strings, and logicals.

• 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 ;.

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:

sign_r <- function(x) {
  if (x > 0) {
    1
  } else if (x == 0) {
    0
  } else {
    -1
  }
}
cpp_function('int sign_cpp(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.

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!

sum_r <- 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 stl, 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.

cpp_function('double sum_cpp(doubles 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, sum_cpp() is competitive with the built-in (and highly optimised) sum(), while sum_r() is several orders of magnitude slower.

x <- runif(1e3)
bench::mark(
  sum(x),
  sum_cpp(x),
  sum_r(x)
)[1:6]

Vector input, vector output

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

pdist_r <- 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:

cpp_function('doubles pdist_cpp(double x, doubles ys) {
  int n = ys.size();
  writable::doubles out(n);
  for(int i = 0; i < n; ++i) {
    out[i] = sqrt(pow(ys[i] - x, 2.0));
  }
  return out;
}')

This function introduces a few new concepts:

• Because we are creating a new vector we need to use writable::doubles rather than the read-only doubles.

• We create a new numeric vector of length n with a constructor: cpp11::writable::doubles out(n). Another useful way of making a vector is to copy an existing one: cpp11::doubles zs(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(
  pdist_r(0.5, y),
  pdist_cpp(0.5, y)
)[1:6]

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.

Using cpp_source

So far, we’ve used inline C++ with cpp_function(). 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 cpp_source(). 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 "cpp11.hpp"
using namespace cpp11;

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

[[cpp11::register]]

If you’re familiar with roxygen2, you might wonder how this relates to @export. cpp11::register registers a C++ function to be called from R. @export controls whether a function is exported from a package and made available to the user.

To compile the C++ code, use cpp_source("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.

This example also illustrates a different kind of a for loop, a for-each loop.

#include "cpp11/doubles.hpp"
using namespace cpp11;

[[cpp11::register]]
double mean_cpp(doubles x) {
  int n = x.size();
  double total = 0;
  for(double value : x) {
    total += value;
  }
  return total / n;
}

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

For the remainder of this vignette C++ code will be presented stand-alone rather than wrapped in a call to cpp_function. 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 by using {cpp11} instead of {r} at the beginning of your code blocks.

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.

#include "cpp11.hpp"

using namespace cpp11;
namespace writable = cpp11::writable;

[[cpp11::register]]
double f1(doubles x) {
  int n = x.size();
  double y = 0;

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

[[cpp11::register]]
doubles f2(doubles x) {
  int n = x.size();
  writable::doubles out(n);

  out[0] = x[0];
  for(int i = 1; i < n; ++i) {
    out[i] = out[i - 1] + x[i];
  }
  return out;
}

[[cpp11::register]]
bool f3(logicals x) {
  int n = x.size();

  for(int i = 0; i < n; ++i) {
    if (x[i]) {
      return true;
    }
  }
  return false;
}

[[cpp11::register]]
int f4(cpp11::function pred, list x) {
  int n = x.size();

  for(int i = 0; i < n; ++i) {
    logicals res(pred(x[i]));
    if (res[0]) {
      return i + 1;
    }
  }
  return 0;
}

1. 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.

Lists and data frames

cpp11 also provides list and data_frame 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_cpp(). 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 Rf_inherits() and the stop() to check that the object really is a linear model.

#include "cpp11.hpp"
using namespace cpp11;

[[cpp11::register]]
double mpe(list mod) {
  if (!Rf_inherits(mod, "lm")) {
    stop("Input must be a linear model");
  }
  doubles resid(mod["residuals"]);
  doubles fitted(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)

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 sexp. This stands for S-Expression and is used as the type of all R Objects in the internal C code.

#include "cpp11.hpp"
using namespace cpp11;
namespace writable = cpp11::writable;

[[cpp11::register]]
sexp call_with_one(function f) {
  return f(1);
}

call_with_one(function(x) x + 1)
call_with_one(paste)

Calling R functions with positional arguments is obvious:

f("y", 1);

But you need a special syntax for named arguments:

using namespace cpp11::literals;

f("x"_nm = "y", "value"_nm = 1);

Attributes

All R objects have attributes, which can be queried and modified with .attr(). cpp11 also provides .names() as an alias for the names attribute. The following code snippet illustrates these methods. Note the use of {} initializer list syntax. This allows you to create an R vector from C++ scalar values:

#include "cpp11.hpp"
using namespace cpp11;
namespace writable = cpp11::writable;

[[cpp11::register]]
doubles attribs() {
  writable::doubles out = {1., 2., 3.};
  out.names() = {"a", "b", "c"};
  out.attr("my-attr") = "my-value";
  out.attr("class") = "my-class";
  return out;
}

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 "cpp11.hpp"
using namespace cpp11;

[[cpp11::register]]
list scalar_missings() {
  int int_s = NA_INTEGER;
  r_string chr_s = NA_STRING;
  bool lgl_s = NA_LOGICAL;
  double num_s = NA_REAL;
  return writable::list({as_sexp(int_s), as_sexp(chr_s), as_sexp(lgl_s), as_sexp(num_s)});
}

str(scalar_missings())

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.

cpp_eval("NAN == 1")
cpp_eval("NAN < 1")
cpp_eval("NAN > 1")
cpp_eval("NAN == NAN")

cpp_eval("NAN && TRUE")
cpp_eval("NAN || FALSE")

cpp_eval("NAN + 1")
cpp_eval("NAN - 1")
cpp_eval("NAN / 1")
cpp_eval("NAN * 1")

Strings

String is a scalar string class introduced by cpp11, so it knows how to deal with missing values.

Boolean

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. One way to fix this is to use int instead, as this can represent TRUE, FALSE, and NA.

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 "cpp11.hpp"
using namespace cpp11;
namespace writable = cpp11::writable;

[[cpp11::register]]
list missing_sampler() {
  return writable::list({
    writable::doubles({NA_REAL}),
    writable::integers({NA_INTEGER}),
    writable::logicals({r_bool(NA_LOGICAL)}),
    writable::strings({NA_STRING})
  });
}

str(missing_sampler())

Exercises

1. Rewrite any of the functions from the first exercise 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.

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 "cpp11.hpp"
using namespace cpp11;

[[cpp11::register]]
double sum2(doubles x) {
  double total = 0;

  for(auto 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 we use auto rather than giving the type of the iterator.

This code can be simplified still further through the use of a C++11 feature: range-based for loops.

#include "cpp11.hpp"
using namespace cpp11;

[[cpp11::register]]
double sum3(doubles xs) {
  double total = 0;

  for(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 "cpp11.hpp"
using namespace cpp11;

[[cpp11::register]]
double sum4(doubles x) {
  return std::accumulate(x.begin(), x.end(), 0.0);
}

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 cpp11 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 "cpp11.hpp"
using namespace cpp11;

[[cpp11::register]] integers findInterval2(doubles x, doubles breaks) {
  writable::integers out(x.size());
  auto out_it = out.begin();

  for (auto&& val : x) {
    auto pos = std::upper_bound(breaks.begin(), breaks.end(), val);
    *out_it = std::distance(breaks.begin(), pos);
    ++out_it;
  }
  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.

When in doubt, it is 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.

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.

cpp11 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.

Vectors

An STL vector is very similar to an R vector, except that it grows efficiently. This makes STL 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 "cpp11.hpp"
#include <vector>
using namespace cpp11;
namespace writable = cpp11::writable;

[[cpp11::register]]
list rle_cpp(doubles 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);

  for(auto 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 writable::list({
    "lengths"_nm = lengths,
    "values"_nm = 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.

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 can somtimes be much faster (because they use a hash table internally rather than a tree). Often even if you need an ordered set, you could consider using an unordered set and then sorting the output. Benchmarking with your expected dataset is the best way to determine which is fastest for your data. 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.

#include <unordered_set>
#include "cpp11.hpp"
using namespace cpp11;
namespace writable = cpp11::writable;

[[cpp11::register]]
logicals duplicated_cpp(integers x) {
  std::unordered_set<int> seen;
  int n = x.size();
  writable::logicals out(n);
  for (int i = 0; i < n; ++i) {
    out[i] = !seen.insert(x[i]).second;
  }
  return out;
}

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.

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 30 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 relatively straightforward to convert to C++. We:

• Add type declarations to all variables.

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

• Include “Rmath.h” and call the functions with Rf_.

#include "cpp11/matrix.hpp"
#include "cpp11/doubles.hpp"
#include "Rmath.h"
using namespace cpp11;
namespace writable = cpp11::writable;

[[cpp11::register]] cpp11::doubles_matrix<> gibbs_cpp(int N, int thin) {
  writable::doubles_matrix<> mat(N, 2);
  double x = 0, y = 0;
  for (int i = 0; i < N; i++) {
    for (int j = 0; j < thin; j++) {
      x = Rf_rgamma(3., 1. / double(y * y + 4));
      y = Rf_rnorm(1. / (x + 1.), 1. / sqrt(2. * (x + 1.)));
    }
    mat(i, 0) = x;
    mat(i, 1) = y;
  }
  return mat;
}

Benchmarking the two implementations yields a significant speedup for running the loops in C++:

bench::mark(
  r = {
    set.seed(42)
    gibbs_r(100, 10)
  },
  cpp = {
    set.seed(42)
    gibbs_cpp(100, 10)
  },
  check = TRUE,
  relative = TRUE
)

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 "cpp11.hpp"
using namespace cpp11;
namespace writable = cpp11::writable;

[[cpp11::register]]
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;
}

[[cpp11::register]]
doubles vacc3(doubles age, logicals female,
                    logicals ily) {
  int n = age.size();
  writable::doubles 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)
)

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.