In part 2 of this series on benchmarking R, we’ll explore sorting. This has been a topic on numerous blogs, discussions and posts around the internet, including here: r-blogger post. Similarly, julialang.org showed that sorting was particularly bad in R. We, again, felt that this was a case of poor R coding, or more accurately, missing the point of whether R was capable or not. Another example here compares R sorting with standard library of C++, called from R.

In all cases, we felt that one of the points of using R is that there are concise ways of doing things because the open source community has brought them to R. So lets take advantage of that! We will cover both real number sorting and integer sorting.

### Sorting

This was in part inspired from a blog post by Wingfeet at http://www.r-bloggers.com/quicksort-speed-just-in-time-compiling-and-vectorizing/ which drew on benchmark tests here: http://julialang.org/ Essentially, that julia test was a benchmark to test the speed of Julia. It showed for the Quicksort, that R is 524x slower than C. Below is that version. But, there was no explicit comparison of how the base R sort would match with C, nor how any of the more recent packages with sorting capability fare against these procedural versions of low level languages.

#### Real number sorting

x = runif(1e5)
xtbl <- tbl_df(data.frame(x=x))
(mbReal <- benchmark(
a <- qsort(x),
d <- sort(x),
e <- sort(x, method="quick"),
f <- .Internal(sort(x,decreasing = FALSE)),
g <- data.table(x=x,key="x"),
h <- arrange(xtbl,x),
i <- stl_sort(x),
replications=25L, columns=c("test", "elapsed", "relative"),
order="relative"))

##                                          test elapsed relative
## 7                            i <- stl_sort(x)    0.19    1.000
## 5           g <- data.table(x = x, key = "x")    0.21    1.105
## 3              e <- sort(x, method = "quick")    0.22    1.158
## 4 f <- .Internal(sort(x, decreasing = FALSE))    0.26    1.368
## 2                                d <- sort(x)    0.28    1.474
## 6                       h <- arrange(xtbl, x)    1.48    7.789
## 1                               a <- qsort(x)   86.58  455.684

all.equalV(a, d, e, f, g$x, h$x, i)

## [1] TRUE


#### Integer sorting

x = sample(1e6,size = 1e5)
xtbl <- tbl_df(data.frame(x=x))
(mbInteger <- benchmark(
a <- qsort(x),
d <- sort(x),
e <- sort(x, method="quick"),
f <- .Internal(sort(x,decreasing = FALSE)),
g <- data.table(x=x,key="x"), h<-arrange(xtbl,x),
i <- stl_sort(x),
replications=25L, columns=c("test", "elapsed", "relative"),
order="relative"))

##                                          test elapsed relative
## 5           g <- data.table(x = x, key = "x")    0.13    1.000
## 3              e <- sort(x, method = "quick")    0.17    1.308
## 7                            i <- stl_sort(x)    0.19    1.462
## 4 f <- .Internal(sort(x, decreasing = FALSE))    0.23    1.769
## 2                                d <- sort(x)    0.25    1.923
## 6                       h <- arrange(xtbl, x)    0.67    5.154
## 1                               a <- qsort(x)   89.28  686.769

all.equalV(a, d, e, f, g$x, h$x, i)

## [1] TRUE


Both real numbers and integers can be sorted quickly with R. The slowest function is indeed the procedural qsort written in native R without any optimization. This was also the qsort that the Julia testers used. Our numbers match almost exactly those from the the table in julialang.org; however, here we also test the real world R usage that a normal R user would face (i.e., we can all use sort()). We show that R competes quite favourably and regularly outperforms standard library of C++ (and Julia!, though that is not tested here explicitly).

#### Take home points:

1. the basic R sorting functions are fast. The sort(method="quick") is about as fast as the standard C++ library sort (11% faster).
2. using data.table on integers is 32% faster than the C++ standard library sort.

In real world situations, where we want to use the easiest, shortest code to produce fast, accurate results, R certainly holds its own compared to the standard C++ library. But of course, there are many ways to do things in R. Some are much faster than others.

#### Conclusion

Using the sort(method="quick") and data.table sorting, we were able to sort a vector of real numbers 412x faster than a naive procedural coding (qsort) and 687x faster on a vector of integers. These put the data.table sort as fast as or substantially faster than C or Fortran or Julia’s version of quicksort (based on timings on julialang.org).

YES! R is more than fast enough.

#### Next time (really! I promised it last time…)

We will redo the Fibonacci series, a common low level benchmarking test that shows R to be slow. But it turns out to be a case of bad coding…

#### Functions used

The C++ functions that were used are:

cppFunction('NumericVector stl_sort(NumericVector x) {
NumericVector y = clone(x);
std::sort(y.begin(), y.end());
return y;
}')
qsort = function(a) {
qsort_kernel = function(lo, hi) {
i = lo
j = hi
while (i < hi) {
pivot = a[floor((lo+hi)/2)]
while (i <= j) {
while (a[i] < pivot) i = i + 1
while (a[j] > pivot) j = j - 1
if (i <= j) {
t = a[i]
a[i] <<- a[j]
a[j] <<- t
i = i + 1;
j = j - 1;
}
}
if (lo < j) qsort_kernel(lo, j)
lo = i
j = hi
}
}
qsort_kernel(1, length(a))
return(a)
}

all.equalV = function(...) {
vals <- list(...)
all(sapply(vals[-1], function(x) all.equal(vals[[1]], x)))
}


#### System used:

Tests were done on an HP Z400, Xeon 3.33 GHz processor, running Windows 7 Enterprise, using:

## R version 3.2.0 (2015-04-16)
## Platform: x86_64-w64-mingw32/x64 (64-bit)
## Running under: Windows 7 x64 (build 7601) Service Pack 1
##
## locale:
##
## attached base packages:
## [1] stats     graphics  grDevices utils     datasets  methods   base
##
## other attached packages:
## [1] data.table_1.9.4 Rcpp_0.11.5      dplyr_0.4.1      rbenchmark_1.0.0
##
## loaded via a namespace (and not attached):
##  [1] digest_0.6.8    assertthat_0.1  chron_2.3-45    plyr_1.8.1
##  [5] DBI_0.3.1       formatR_1.0     magrittr_1.5    evaluate_0.5.5
##  [9] lazyeval_0.1.10 reshape2_1.4.1  rmarkdown_0.5.1 tools_3.2.0
## [13] stringr_0.6.2   yaml_2.1.13     parallel_3.2.0  htmltools_0.2.6
## [17] knitr_1.9