High Performance Benchmarks

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? 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, partitions, and RcppAlgos.

Setup Information

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

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

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

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

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

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

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

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

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

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

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

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.

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)

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)

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

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`

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

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`

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

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

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

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

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

High Performance Benchmarks

Joseph Wood

2026-03-04

Setup Information

Combinations

Combinations - Distinct

Combinations - Repetition

Combinations - Multisets

Permutations

Permutations - Distinct

Permutations - Repetition

Permutations - Multisets

Partitions

Partitions - Distinct

All Distinct Partitions

Restricted Distinct Partitions

Partitions - Repetition

All Partitions

Restricted Partitions

Partitions - Multisets

Compositions

Compositions - Repetition

All Compositions (Small case)

All Compositions (Larger case)

Compositions of Specific Length

Specialized Composition Benchmarks

Compositions with Specific `target`

Compositions with Distinct Parts

Compositions with Distinct Parts & Specific `target`

Iterators

Combinations

Permutations

Partitions

Compositions

Setup Information

Combinations

Combinations - Distinct

Combinations - Repetition

Combinations - Multisets

Permutations

Permutations - Distinct

Permutations - Repetition

Permutations - Multisets

Partitions

Partitions - Distinct

All Distinct Partitions

Restricted Distinct Partitions

Partitions - Repetition

All Partitions

Restricted Partitions

Partitions - Multisets

Compositions

Compositions - Repetition

All Compositions (Small case)

All Compositions (Larger case)

Compositions of Specific Length

Specialized Composition Benchmarks

Compositions with Specific target

Compositions with Distinct Parts

Compositions with Distinct Parts & Specific target

Iterators

Combinations

Permutations

Partitions

Compositions

Compositions with Specific `target`

Compositions with Distinct Parts & Specific `target`