---
title: "High Performance Benchmarks"
author: "Joseph Wood"
date: "2026-03-04"
output:
  prettydoc::html_pretty:
    theme: architect
    toc: true
    number_sections: false
vignette: >
  %\VignetteIndexEntry{High Performance Benchmarks}
  %\VignetteEngine{knitr::rmarkdown}
  %\VignetteEncoding{UTF-8}
---

This document serves as an overview for measuring the performance of `RcppAlgos` against other tools for generating combinations, permutations, and partitions. This stackoverflow post: [How to generate permutations or combinations of object in R?](<https://stackoverflow.com/a/47983855/4408538>) has some benchmarks. You will note that the examples in that post are relatively small. The benchmarks below will focus on larger examples where performance really matters and for this reason we only consider the packages [arrangements](<https://cran.r-project.org/package=arrangements>), [partitions](<https://cran.r-project.org/package=partitions>), and [RcppAlgos](<https://cran.r-project.org/package=RcppAlgos>).

## Setup Information

For the benchmarks below, we used a `2025 Macbook Air Apple M4 24 GB` machine.

``` r
library(RcppAlgos)
library(partitions)
library(arrangements)
#> 
#> Attaching package: 'arrangements'
#> The following object is masked from 'package:partitions':
#> 
#>     compositions
library(microbenchmark)

options(digits = 4)
options(width = 90)

pertinent_output <- capture.output(sessionInfo())
cat(paste(pertinent_output[1:3], collapse = "\n"))
#> R version 4.5.2 (2025-10-31)
#> Platform: aarch64-apple-darwin20
#> Running under: macOS Sequoia 15.7.4

pkgs <- c("RcppAlgos", "arrangements", "partitions", "microbenchmark")
sapply(pkgs, packageVersion, simplify = FALSE)
#> $RcppAlgos
#> [1] '2.10.0'
#> 
#> $arrangements
#> [1] '1.1.9'
#> 
#> $partitions
#> [1] '1.10.9'
#> 
#> $microbenchmark
#> [1] '1.5.0'

numThreads <- min(as.integer(RcppAlgos::stdThreadMax() / 2), 6)
numThreads
#> [1] 5
```

## Combinations

### Combinations - Distinct

``` r
set.seed(13)
v1 <- sort(sample(100, 30))
m <- 21
t1 <- comboGeneral(v1, m, Parallel = T)
t2 <- combinations(v1, m)
stopifnot(identical(t1, t2))
dim(t1)
#> [1] 14307150       21
rm(t1, t2)
invisible(gc())
microbenchmark(cbRcppAlgosPar = comboGeneral(v1, m, nThreads = numThreads),
               cbRcppAlgosSer = comboGeneral(v1, m),
               cbArrangements = combinations(v1, m),
               times = 15, unit = "relative")
#> Warning in microbenchmark(cbRcppAlgosPar = comboGeneral(v1, m, nThreads = numThreads), :
#> less accurate nanosecond times to avoid potential integer overflows
#> Unit: relative
#>            expr   min    lq  mean median    uq   max neval
#>  cbRcppAlgosPar 1.000 1.000 1.000  1.000 1.000 1.000    15
#>  cbRcppAlgosSer 3.360 3.111 3.024  3.055 3.027 2.695    15
#>  cbArrangements 3.371 3.150 3.053  3.092 3.062 2.708    15
```

### Combinations - Repetition

``` r
v2 <- v1[1:10]
m <- 20
t1 <- comboGeneral(v2, m, repetition = TRUE, nThreads = numThreads)
t2 <- combinations(v2, m, replace = TRUE)
stopifnot(identical(t1, t2))
dim(t1)
#> [1] 10015005       20
rm(t1, t2)
invisible(gc())
microbenchmark(cbRcppAlgosPar = comboGeneral(v2, m, TRUE, nThreads = numThreads),
               cbRcppAlgosSer = comboGeneral(v2, m, TRUE),
               cbArrangements = combinations(v2, m, replace = TRUE),
               times = 15, unit = "relative")
#> Unit: relative
#>            expr   min    lq  mean median    uq   max neval
#>  cbRcppAlgosPar 1.000 1.000 1.000  1.000 1.000 1.000    15
#>  cbRcppAlgosSer 3.119 2.993 2.956  2.986 2.940 2.689    15
#>  cbArrangements 2.963 2.895 2.857  2.882 2.829 2.722    15
```

### Combinations - Multisets

``` r
myFreqs <- c(2, 4, 4, 5, 3, 2, 2, 2, 3, 4, 1, 4, 2, 5)
v3 <- as.integer(c(1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610))
t1 <- comboGeneral(v3, 20, freqs = myFreqs, nThreads = numThreads)
t2 <- combinations(freq = myFreqs, k = 20, x = v3)
stopifnot(identical(t1, t2))
dim(t1)
#> [1] 14594082       20
rm(t1, t2)
invisible(gc())
microbenchmark(cbRcppAlgosPar = comboGeneral(v3, 20, freqs = myFreqs, nThreads = numThreads),
               cbRcppAlgosSer = comboGeneral(v3, 20, freqs = myFreqs),
               cbArrangements = combinations(freq = myFreqs, k = 20, x = v3),
               times = 10, unit = "relative")
#> Unit: relative
#>            expr   min    lq  mean median    uq   max neval
#>  cbRcppAlgosPar 1.000 1.000 1.000  1.000 1.000 1.000    10
#>  cbRcppAlgosSer 3.293 3.164 3.073  3.096 3.016 2.757    10
#>  cbArrangements 6.804 6.579 6.332  6.421 6.241 5.418    10
```

## Permutations

### Permutations - Distinct

``` r
v4 <- as.integer(c(2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59))
t1 <- permuteGeneral(v4, 6, nThreads = numThreads)
t2 <- permutations(v4, 6)
stopifnot(identical(t1, t2))
dim(t1)
#> [1] 8910720       6
rm(t1, t2)
invisible(gc())
microbenchmark(cbRcppAlgosPar = permuteGeneral(v4, 6, nThreads = numThreads),
               cbRcppAlgosSer = permuteGeneral(v4, 6),
               cbArrangements = permutations(v4, 6),
               times = 15, unit = "relative")
#> Unit: relative
#>            expr   min    lq  mean median    uq   max neval
#>  cbRcppAlgosPar 1.000 1.000 1.000  1.000 1.000 1.000    15
#>  cbRcppAlgosSer 1.494 1.446 1.352  1.421 1.364 1.283    15
#>  cbArrangements 2.177 2.110 2.032  2.081 2.135 1.793    15


## Indexing permutation example with the partitions package
t1 <- permuteGeneral(11, nThreads = 4)
t2 <- permutations(11)
t3 <- perms(11)

dim(t1)
#> [1] 39916800       11

stopifnot(identical(t1, t2), identical(t1, t(as.matrix(t3))))
rm(t1, t2, t3)
invisible(gc())

microbenchmark(cbRcppAlgosPar = permuteGeneral(11, nThreads = 4),
               cbRcppAlgosSer = permuteGeneral(11),
               cbArrangements = permutations(11),
               cbPartitions   = perms(11),
               times = 5, unit = "relative")
#> Unit: relative
#>            expr   min    lq  mean median    uq   max neval
#>  cbRcppAlgosPar 1.000 1.000 1.000  1.000 1.000 1.000     5
#>  cbRcppAlgosSer 2.223 2.538 2.263  2.528 1.879 2.312     5
#>  cbArrangements 3.537 3.568 3.267  3.432 2.610 3.430     5
#>    cbPartitions 9.250 9.446 7.978  9.493 6.656 6.588     5
```

### Permutations - Repetition

``` r
v5 <- v3[1:5]
t1 <- permuteGeneral(v5, 10, repetition = TRUE, nThreads = numThreads)
t2 <- permutations(v5, 10, replace = TRUE)
stopifnot(identical(t1, t2))
dim(t1)
#> [1] 9765625      10
rm(t1, t2)
invisible(gc())
microbenchmark(cbRcppAlgosPar = permuteGeneral(v5, 10, TRUE, nThreads = numThreads),
               cbRcppAlgosSer = permuteGeneral(v5, 10, TRUE),
               cbArrangements = permutations(x = v5, k = 10, replace = TRUE),
               times = 10, unit = "relative")
#> Unit: relative
#>            expr   min    lq  mean median    uq    max neval
#>  cbRcppAlgosPar 1.000 1.000 1.000  1.000 1.000 1.0000    10
#>  cbRcppAlgosSer 2.423 2.355 1.997  2.327 2.159 0.9621    10
#>  cbArrangements 2.822 2.768 2.494  2.712 2.521 1.8244    10
```

### Permutations - Multisets

``` r
v6 <- sort(runif(12))
t1 <- permuteGeneral(v6, 7, freqs = rep(1:3, 4), nThreads = numThreads)
t2 <- permutations(freq = rep(1:3, 4), k = 7, x = v6)
stopifnot(identical(t1, t2))
dim(t1)
#> [1] 19520760        7
rm(t1, t2)
invisible(gc())
microbenchmark(cbRcppAlgosPar = permuteGeneral(v6, 7, freqs = rep(1:3, 4), nThreads = numThreads),
               cbRcppAlgosSer = permuteGeneral(v6, 7, freqs = rep(1:3, 4)),
               cbArrangements = permutations(freq = rep(1:3, 4), k = 7, x = v6),
               times = 10, unit = "relative")
#> Unit: relative
#>            expr   min    lq  mean median    uq   max neval
#>  cbRcppAlgosPar 1.000 1.000 1.000  1.000 1.000 1.000    10
#>  cbRcppAlgosSer 3.473 3.511 3.153  3.367 2.552 2.731    10
#>  cbArrangements 3.937 3.985 3.658  3.874 3.138 3.117    10
```

## Partitions

### Partitions - Distinct

#### All Distinct Partitions

``` r
t1 <- comboGeneral(0:140, freqs=c(140, rep(1, 140)),
                   constraintFun = "sum", comparisonFun = "==",
                   limitConstraints = 140)
t2 <- partitions(140, distinct = TRUE)
t3 <- diffparts(140)

# Each package has different output formats... we only examine dimensions
# and that each result is a partition of 140
stopifnot(identical(dim(t1), dim(t2)), identical(dim(t1), dim(t(t3))),
                    all(rowSums(t1) == 140), all(rowSums(t2) == 140),
                    all(colSums(t3) == 140))
dim(t1)
#> [1] 9617150      16
rm(t1, t2, t3)
invisible(gc())
microbenchmark(cbRcppAlgosPar = partitionsGeneral(0:140, freqs=c(140, rep(1, 140)), nThreads = numThreads),
               cbRcppAlgosSer = partitionsGeneral(0:140, freqs=c(140, rep(1, 140))),
               cbArrangements = partitions(140, distinct = TRUE),
               cbPartitions   = diffparts(140),
               times = 10, unit = "relative")
#> Unit: relative
#>            expr    min     lq   mean median     uq    max neval
#>  cbRcppAlgosPar  1.000  1.000  1.000  1.000  1.000  1.000    10
#>  cbRcppAlgosSer  3.252  3.133  2.911  2.982  2.739  2.709    10
#>  cbArrangements  2.492  2.431  2.256  2.292  2.168  2.146    10
#>    cbPartitions 17.359 17.199 15.909 17.115 14.684 13.572    10
```

#### Restricted Distinct Partitions

``` r
t1 <- comboGeneral(160, 10,
                   constraintFun = "sum", comparisonFun = "==",
                   limitConstraints = 160)
t2 <- partitions(160, 10, distinct = TRUE)
stopifnot(identical(t1, t2))
dim(t1)
#> [1] 8942920      10
rm(t1, t2)
invisible(gc())
microbenchmark(cbRcppAlgosPar = partitionsGeneral(160, 10, nThreads = numThreads),
               cbRcppAlgosSer = partitionsGeneral(160, 10),
               cbArrangements = partitions(160, 10, distinct = TRUE),
               times = 10, unit = "relative")
#> Unit: relative
#>            expr   min    lq  mean median    uq   max neval
#>  cbRcppAlgosPar 1.000 1.000 1.000  1.000 1.000 1.000    10
#>  cbRcppAlgosSer 3.153 3.082 2.713  3.017 2.973 1.902    10
#>  cbArrangements 4.490 4.400 3.700  4.303 4.192 2.230    10
```

### Partitions - Repetition

#### All Partitions

``` r
t1 <- comboGeneral(0:65, repetition = TRUE, constraintFun = "sum",
                   comparisonFun = "==", limitConstraints = 65)
t2 <- partitions(65)
t3 <- parts(65)

# Each package has different output formats... we only examine dimensions
# and that each result is a partition of 65
stopifnot(identical(dim(t1), dim(t2)), identical(dim(t1), dim(t(t3))),
          all(rowSums(t1) == 65), all(rowSums(t2) == 65),
          all(colSums(t3) == 65))
dim(t1)
#> [1] 2012558      65
rm(t1, t2, t3)
invisible(gc())
microbenchmark(cbRcppAlgosPar = partitionsGeneral(0:65, repetition = TRUE,
                                                  nThreads = numThreads),
               cbRcppAlgosSer = partitionsGeneral(0:65, repetition = TRUE),
               cbArrangements = partitions(65),
               cbPartitions   = parts(65),
               times = 20, unit = "relative")
#> Unit: relative
#>            expr   min    lq  mean median    uq   max neval
#>  cbRcppAlgosPar 1.000 1.000 1.000  1.000 1.000 1.000    20
#>  cbRcppAlgosSer 2.793 2.749 2.276  2.415 2.182 1.776    20
#>  cbArrangements 2.011 1.961 1.628  1.746 1.644 1.076    20
#>    cbPartitions 9.885 9.768 7.711  8.600 7.274 4.866    20
```

#### Restricted Partitions

``` r
t1 <- comboGeneral(100, 15, TRUE, constraintFun = "sum",
                   comparisonFun = "==", limitConstraints = 100)
t2 <- partitions(100, 15)
stopifnot(identical(t1, t2))
dim(t1)
#> [1] 9921212      15
rm(t1, t2)

# This takes a really long time... not because of restrictedparts,
# but because apply is not that fast. This transformation is
# needed for proper comparisons. As a result, we will compare
# a smaller example
# t3 <- t(apply(as.matrix(restrictedparts(100, 15, include.zero = F)), 2, sort))
t3 <- t(apply(as.matrix(restrictedparts(50, 15, include.zero = F)), 2, sort))
stopifnot(identical(partitions(50, 15), t3))
rm(t3)
invisible(gc())
microbenchmark(cbRcppAlgosPar = partitionsGeneral(100, 15, TRUE,
                                                  nThreads = numThreads),
               cbRcppAlgosSer = partitionsGeneral(100, 15, TRUE),
               cbArrangements = partitions(100, 15),
               cbPartitions   = restrictedparts(100, 15,
                                                include.zero = FALSE),
               times = 10, unit = "relative")
#> Unit: relative
#>            expr    min    lq   mean median     uq    max neval
#>  cbRcppAlgosPar  1.000  1.00  1.000  1.000  1.000  1.000    10
#>  cbRcppAlgosSer  3.378  3.31  2.974  2.952  2.735  2.638    10
#>  cbArrangements  4.484  4.44  4.079  4.091  3.653  4.024    10
#>    cbPartitions 15.181 15.09 13.452 13.576 12.017 11.979    10
```

### Partitions - Multisets

Currently, `RcppAlgos` is the only package capable of efficiently generating partitions of multisets. Therefore, we will only time `RcppAlgos` and use this as a reference for future improvements.

``` r
t1 <- comboGeneral(120, 10, freqs = rep(1:8, 15),
                   constraintFun = "sum", comparisonFun = "==",
                   limitConstraints = 120)
dim(t1)
#> [1] 7340225      10
stopifnot(all(rowSums(t1) == 120))
microbenchmark(cbRcppAlgos = partitionsGeneral(120, 10, freqs = rep(1:8, 15)),
               times = 10)
#> Unit: milliseconds
#>         expr min    lq  mean median    uq   max neval
#>  cbRcppAlgos 178 180.3 182.4  181.4 182.9 189.6    10
```

## Compositions

### Compositions - Repetition

#### All Compositions (Small case)

``` r
t1 <- compositionsGeneral(0:15, repetition = TRUE)
t2 <- arrangements::compositions(15)
t3 <- partitions::compositions(15)

# Each package has different output formats... we only examine dimensions
# and that each result is a partition of 15
stopifnot(identical(dim(t1), dim(t2)), identical(dim(t1), dim(t(t3))),
          all(rowSums(t1) == 15), all(rowSums(t2) == 15),
          all(colSums(t3) == 15))
dim(t1)
#> [1] 16384    15
rm(t1, t2, t3)
invisible(gc())
microbenchmark(cbRcppAlgosSer = compositionsGeneral(0:15, repetition = TRUE),
               cbArrangements = arrangements::compositions(15),
               cbPartitions   = partitions::compositions(15),
               times = 20, unit = "relative")
#> Unit: relative
#>            expr     min      lq    mean  median      uq     max neval
#>  cbRcppAlgosSer   1.107   1.101   1.098   1.096   1.094   1.053    20
#>  cbArrangements   1.000   1.000   1.000   1.000   1.000   1.000    20
#>    cbPartitions 110.419 117.834 145.577 145.641 165.113 191.249    20
```

For the next two examples, we will exclude the `partitions` package for efficiency reasons.

#### All Compositions (Larger case)

``` r
t1 <- compositionsGeneral(0:23, repetition = TRUE)
t2 <- arrangements::compositions(23)

# Each package has different output formats... we only examine dimensions
# and that each result is a partition of 23
stopifnot(identical(dim(t1), dim(t2)), all(rowSums(t1) == 23),
          all(rowSums(t2) == 23))
dim(t1)
#> [1] 4194304      23
rm(t1, t2)
invisible(gc())
microbenchmark(cbRcppAlgosPar = compositionsGeneral(0:23, repetition = TRUE,
                                                    nThreads = numThreads),
               cbRcppAlgosSer = compositionsGeneral(0:23, repetition = TRUE),
               cbArrangements = arrangements::compositions(23),
               times = 20, unit = "relative")
#> Unit: relative
#>            expr   min    lq  mean median    uq   max neval
#>  cbRcppAlgosPar 1.000 1.000 1.000  1.000 1.000 1.000    20
#>  cbRcppAlgosSer 3.833 3.639 3.562  3.580 3.526 3.051    20
#>  cbArrangements 4.138 3.921 3.831  3.853 3.783 3.250    20
```

#### Compositions of Specific Length

``` r
t1 <- compositionsGeneral(30, 10, repetition = TRUE)
t2 <- arrangements::compositions(30, 10)

stopifnot(identical(t1, t2), all(rowSums(t1) == 30))
dim(t1)
#> [1] 10015005       10
rm(t1, t2)
invisible(gc())
microbenchmark(cbRcppAlgosPar = compositionsGeneral(30, 10, repetition = TRUE,
                                                    nThreads = numThreads),
               cbRcppAlgosSer = compositionsGeneral(30, 10, repetition = TRUE),
               cbArrangements = arrangements::compositions(30, 10),
               times = 20, unit = "relative")
#> Unit: relative
#>            expr   min    lq  mean median    uq   max neval
#>  cbRcppAlgosPar 1.000 1.000 1.000  1.000 1.000 1.000    20
#>  cbRcppAlgosSer 3.075 2.986 2.908  2.874 2.845 2.780    20
#>  cbArrangements 3.133 2.992 2.945  2.891 2.861 3.108    20
```

### Specialized Composition Benchmarks

Similar to partitions of multisets, several composition variants supported in `RcppAlgos` (e.g., distinct parts, capped cases, etc.) are not currently available in other R packages or combinatorics libraries. In such cases, benchmarks will only report timings for `RcppAlgos`, which can serve as a reference point for future implementations and improvements.

#### Compositions with Specific `target`

``` r
t1 <- compositionsGeneral(10, 10, repetition = TRUE, target = 30)
dim(t1)
#> [1] 9091270      10

stopifnot(all(rowSums(t1) == 30))
microbenchmark(
    cbRcppAlgosSer = compositionsGeneral(10, 10, repetition = TRUE, target = 30),
    cbRcppAlgosPar = compositionsGeneral(10, 10, repetition = TRUE,
                                         target = 30, nThreads = numThreads),
    times = 10,
    check = "identical"
)
#> Unit: milliseconds
#>            expr   min    lq  mean median    uq   max neval
#>  cbRcppAlgosSer 57.44 57.49 59.77  59.17 61.68 63.69    10
#>  cbRcppAlgosPar 17.49 17.90 23.16  21.83 25.34 39.69    10
```

#### Compositions with Distinct Parts

``` r
t1 <- compositionsGeneral(50, 8)
dim(t1)
#> [1] 4677120       8

stopifnot(all(rowSums(t1) == 50))
microbenchmark(
    cbRcppAlgosSer = compositionsGeneral(50, 8),
    cbRcppAlgosPar = compositionsGeneral(50, 8, nThreads = numThreads),
    times = 10,
    check = "identical"
)
#> Unit: milliseconds
#>            expr    min     lq   mean median     uq    max neval
#>  cbRcppAlgosSer 214.49 215.25 216.22 215.53 215.99 221.19    10
#>  cbRcppAlgosPar  52.13  53.51  55.81  55.12  56.63  64.84    10
```

#### Compositions with Distinct Parts & Specific `target`

``` r
t1 <- compositionsGeneral(30, 7, target = 60)
dim(t1)
#> [1] 11773440        7

stopifnot(all(rowSums(t1) == 60))
microbenchmark(
    cbRcppAlgosSer = compositionsGeneral(30, 7, target = 60),
    cbRcppAlgosPar = compositionsGeneral(30, 7, target = 60, nThreads = numThreads),
    times = 10,
    check = "identical"
)
#> Unit: milliseconds
#>            expr   min     lq   mean median     uq   max neval
#>  cbRcppAlgosSer 359.1 359.62 363.92 361.99 364.36 380.2    10
#>  cbRcppAlgosPar  92.9  94.45  96.98  96.17  97.18 105.7    10
```

## Iterators

We will show one example from each category to demonstrate the efficiency of the iterators in `RcppAlgos`. The results are similar for the rest of the cases not shown.

### Combinations

``` r
pkg_arrangements <- function(n, total) {
    a <- icombinations(n, as.integer(n / 2))
    for (i in 1:total) a$getnext()
}

pkg_RcppAlgos <- function(n, total) {
    a <- comboIter(n, as.integer(n / 2))
    for (i in 1:total) a@nextIter()
}

total <- comboCount(18, 9)
total
#> [1] 48620

microbenchmark(cbRcppAlgos    = pkg_RcppAlgos(18, total),
               cbArrangements = pkg_arrangements(18, total),
               times = 15, unit = "relative")
#> Unit: relative
#>            expr   min   lq  mean median    uq   max neval
#>     cbRcppAlgos  1.00  1.0  1.00   1.00  1.00  1.00    15
#>  cbArrangements 19.78 19.5 19.13  19.27 18.76 18.57    15
```

### Permutations

``` r
pkg_arrangements <- function(n, total) {
    a <- ipermutations(n)
    for (i in 1:total) a$getnext()
}

pkg_RcppAlgos <- function(n, total) {
    a <- permuteIter(n)
    for (i in 1:total) a@nextIter()
}

total <- permuteCount(8)
total
#> [1] 40320

microbenchmark(cbRcppAlgos    = pkg_RcppAlgos(8, total),
               cbArrangements = pkg_arrangements(8, total),
               times = 15, unit = "relative")
#> Unit: relative
#>            expr   min    lq  mean median    uq   max neval
#>     cbRcppAlgos  1.00  1.00  1.00   1.00  1.00  1.00    15
#>  cbArrangements 19.42 19.19 18.87  18.76 18.38 19.43    15
```

### Partitions

``` r
pkg_partitions <- function(n, total) {
    a <- firstpart(n)
    for (i in 1:(total - 1)) a <- nextpart(a)
}

pkg_arrangements <- function(n, total) {
    a <- ipartitions(n)
    for (i in 1:total) a$getnext()
}

pkg_RcppAlgos <- function(n, total) {
    a <- partitionsIter(0:n, repetition = TRUE)
    for (i in 1:total) a@nextIter()
}

total <- partitionsCount(0:40, repetition = TRUE)
total
#> [1] 37338

microbenchmark(cbRcppAlgos    = pkg_RcppAlgos(40, total),
               cbArrangements = pkg_arrangements(40, total),
               cbPartitions   = pkg_partitions(40, total),
               times = 15, unit = "relative")
#> Unit: relative
#>            expr   min    lq  mean median    uq   max neval
#>     cbRcppAlgos  1.00  1.00  1.00   1.00  1.00  1.00    15
#>  cbArrangements 15.38 15.19 14.39  15.04 13.39 13.75    15
#>    cbPartitions 24.48 24.25 22.94  23.91 21.30 21.55    15
```

### Compositions

``` r
pkg_partitions <- function(n, total) {
    a <- firstcomposition(n)
    for (i in 1:(total - 1)) a <- nextcomposition(a, FALSE)
}

pkg_arrangements <- function(n, total) {
    a <- icompositions(n)
    for (i in 1:total) a$getnext()
}

pkg_RcppAlgos <- function(n, total) {
    a <- compositionsIter(0:n, repetition = TRUE)
    for (i in 1:total) a@nextIter()
}

total <- compositionsCount(0:15, repetition = TRUE)
total
#> [1] 16384

microbenchmark(cbRcppAlgos    = pkg_RcppAlgos(15, total),
               cbArrangements = pkg_arrangements(15, total),
               cbPartitions   = pkg_partitions(15, total),
               times = 15, unit = "relative")
#> Unit: relative
#>            expr   min    lq mean median    uq   max neval
#>     cbRcppAlgos  1.00  1.00  1.0   1.00  1.00  1.00    15
#>  cbArrangements 14.35 14.16 13.8  14.01 13.81 12.46    15
#>    cbPartitions 44.92 44.54 43.8  44.08 43.62 41.54    15
```
