R Language Speeding up tough-to-vectorize code Speeding tough-to-vectorize for loops by byte compiling
Example
Following the Rcpp example in this documentation entry, consider the following tough-to-vectorize function, which creates a vector of length len where the first element is specified (first) and each element x_i is equal to cos(x_{i-1} + 1):
repeatedCosPlusOne <- function(first, len) {
x <- numeric(len)
x[1] <- first
for (i in 2:len) {
x[i] <- cos(x[i-1] + 1)
}
return(x)
}
One simple approach to speeding up such a function without rewriting a single line of code is byte compiling the code using the R compile package:
library(compiler)
repeatedCosPlusOneCompiled <- cmpfun(repeatedCosPlusOne)
The resulting function will often be significantly faster while still returning the same results:
all.equal(repeatedCosPlusOne(1, 1e6), repeatedCosPlusOneCompiled(1, 1e6))
# [1] TRUE
system.time(repeatedCosPlusOne(1, 1e6))
# user system elapsed
# 1.175 0.014 1.201
system.time(repeatedCosPlusOneCompiled(1, 1e6))
# user system elapsed
# 0.339 0.002 0.341
In this case, byte compiling sped up the tough-to-vectorize operation on a vector of length 1 million from 1.20 seconds to 0.34 seconds.
Remark
The essence of repeatedCosPlusOne, as the cumulative application of a single function, can be expressed more transparently with Reduce:
iterFunc <- function(init, n, func) {
funcs <- replicate(n, func)
Reduce(function(., f) f(.), funcs, init = init, accumulate = TRUE)
}
repeatedCosPlusOne_vec <- function(first, len) {
iterFunc(first, len - 1, function(.) cos(. + 1))
}
repeatedCosPlusOne_vec may be regarded as a "vectorization" of repeatedCosPlusOne. However, it can be expected to be slower by a factor of 2:
library(microbenchmark)
microbenchmark(
repeatedCosPlusOne(1, 1e4),
repeatedCosPlusOne_vec(1, 1e4)
)
#> Unit: milliseconds
#> expr min lq mean median uq max neval cld
#> repeatedCosPlusOne(1, 10000) 8.349261 9.216724 10.22715 10.23095 11.10817 14.33763 100 a
#> repeatedCosPlusOne_vec(1, 10000) 14.406291 16.236153 17.55571 17.22295 18.59085 24.37059 100 b
