Performance of the bit package

A performance example

Before we measure performance of the main functionality of the package, note that something simple as ‘(a:b)[-i]’ can and has been accelerated in this package:

a <- 1L
b <- 1e7L
i <- sample(a:b, 1e3)
x <- c(
  R = median(microbenchmark((a:b)[-i], times=times)$time),
  bit = median(microbenchmark(bit_rangediff(c(a, b), i), times=times)$time),
  merge = median(microbenchmark(merge_rangediff(c(a, b), bit_sort(i)), times=times)$time)
)
knitr::kable(as.data.frame(as.list(x / x["R"] * 100)), caption="% of time relative to R", digits=1)

% of time relative to R
R	bit	merge
100	27.8	28

The vignette is compiled with the following performance settings: 5 replications with domain size small 1000 and big 10^{6}, sample size small 1000 and big 10^{6}.

Boolean data types

“A designer knows he has achieved perfection not when there is nothing left to add, but when there is nothing left to take away.” “Il semble que la perfection soit atteinte non quand il n’y a plus rien à ajouter, mais quand il n’y a plus rien à retrancher” (Antoine de St. Exupery, Terre des Hommes (Gallimard, 1939), p. 60.)

We compare memory consumption (n=1e+06) and runtime (median of 5 replications) of the different booltypes for the following filter scenarios:

knitr::kable(
  data.frame(
    coin="random 50%",
    often="random 99%",
    rare="random 1%",
    chunk="contiguous chunk of 5%"
  ),
  caption="selection characteristic"
)

selection characteristic
coin	often	rare	chunk
random 50%	random 99%	random 1%	contiguous chunk of 5%

# nolint end: strings_as_factors_linter.

There are substantial savings in skewed filter situations:

% size and execution time for bit (b) and bitwhich (w) relative to logical (R) in the ‘rare’ scenario

% size and execution time for bit (b) and bitwhich (w) relative to logical (R) in the ‘often’ scenario

Even in non-skewed situations the new booltypes are competitive:

% size and execution time for bit (b) and bitwhich (w) relative to logical (R) in the ‘coin’ scenario

Detailed tables follow.

% memory consumption of filter

% bytes of logical
	coin	often	rare	chunk
logical	100.0	100.0	100.0	100.0
bit	3.2	3.2	3.2	3.2
bitwhich	50.0	1.0	1.0	5.0
which	50.0	99.0	1.0	5.0
ri	NA	NA	NA	0.0

% time extracting

% time of logical
	coin	often	rare	chunk
logical	22.3	5.9	5.7	NA
bit	18.4	18.5	18.5	NA
bitwhich	24.9	50.9	6.4	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time assigning

% time of logical
	coin	often	rare	chunk
logical	45.7	45.6	45.9	NA
bit	83.9	16.5	11.3	NA
bitwhich	187.0	47.5	41.0	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time subscripting with ‘which’

% time of logical
	coin	often	rare	chunk
logical	25.1	35.4	1.0	NA
bit	23.6	46.2	0.8	NA
bitwhich	32.4	62.9	1.8	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time assigning with ‘which’

% time of logical
	coin	often	rare	chunk
logical	19.9	38.7	0.7	NA
bit	18.2	38.4	0.5	NA
bitwhich	39.4	29.5	2.6	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean NOT

% time for Boolean NOT
	coin	often	rare	chunk
logical	18.5	18.6	18.6	18.4
bit	0.9	1.0	0.9	0.9
bitwhich	8.7	0.9	0.9	1.8
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean AND

% time for Boolean &
	coin	often	rare	chunk
logical	100.0	28.7	27.4	25.9
bit	4.4	4.5	4.6	4.5
bitwhich	18.2	5.4	4.7	5.8
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean OR

% time for Boolean |
	coin	often	rare	chunk
logical	98.4	27.4	25.6	25.1
bit	4.8	4.8	4.8	4.7
bitwhich	38.3	4.8	5.6	7.5
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean EQUALITY

% time for Boolean ==
	coin	often	rare	chunk
logical	26.6	26.5	26.6	26.6
bit	4.5	5.2	4.9	4.7
bitwhich	14.3	4.5	4.4	5.4
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean XOR

% time for Boolean !=
	coin	often	rare	chunk
logical	25.2	25.5	25.3	25.3
bit	4.6	4.4	4.6	4.5
bitwhich	17.5	4.5	4.4	5.4
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean SUMMARY

% time for Boolean summary
	coin	often
logical	88.2	20.9
bit	3.5	3.6

Fast methods for `integer` set operations

“The space-efficient structure of bitmaps dramatically reduced the run time of sorting” (Jon Bently, Programming Pearls, Cracking the oyster, p. 7)

Execution time for R (R) and bit (b)

Execution time for R, bit and merge relative to most expensive R in ‘unsorted bigbig’ scenario

Execution time for R, bit and merge in ‘sorted bigbig’ scenario

% time for sorting

sorted data relative to R’s sort
	small	big
sort	140.6	174.3
sortunique	78.2	37.9

unsorted data relative to R’s sort
	small	big
sort	24.0	32.0
sortunique	18.5	11.6

% time for unique

sorted data relative to R
	small	big
bit	112.7	13.1
merge	24.0	5.4
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	130.8	15.4
merge	108.5	63.5
sort	85.2	56.2

% time for duplicated

sorted data relative to R
	small	big
bit	178.9	16.6
merge	22.0	5.2
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	192.3	16.2
merge	130.7	70.5
sort	106.4	64.2

% time for anyDuplicated

sorted data relative to R
	small	big
bit	156.2	24.0
merge	19.0	3.4
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	127.3	17.8
merge	124.5	76.2
sort	108.1	73.0

% time for sumDuplicated

sorted data relative to R
	small	big
bit	112.2	18.3
merge	12.9	3.9
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	107.9	16.2
merge	104.7	71.4
sort	91.7	67.0

% time for match

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	NA	NA	NA	NA
merge	31.1	0	10.8	4.7
sort	0.0	0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	NA	NA	NA	NA
merge	191.3	79.3	84.2	78.2
sort	161.1	79.2	81.0	73.4

% time for in

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	158.3	5.8	15.1	17.1
merge	25.0	0.0	13.0	4.0
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	148.5	5.0	5.5	12.6
merge	169.6	71.9	77.7	72.8
sort	146.4	71.9	73.0	69.1

% time for notin

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	242.1	4	6.5	13.6
merge	25.0	0	4.1	3.4
sort	0.0	0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	227.0	5.1	4.9	13.3
merge	148.6	71.4	64.7	68.4
sort	126.1	71.4	61.8	64.9

% time for union

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	88.0	21.0	22.4	26.1
merge	52.8	9.5	9.7	19.3
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	80.8	23.3	21.9	10.5
merge	124.1	68.1	64.7	41.4
sort	74.4	56.5	53.9	32.9

% time for intersect

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	56.7	8.4	4.5	9.9
merge	17.1	0.0	0.0	5.7
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	59.0	9.4	4.0	6.2
merge	79.3	69.9	29.6	37.4
sort	60.9	69.9	29.5	32.7

% time for setdiff

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	61.9	5.4	15.3	10.5
merge	19.8	0.0	6.3	7.3
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	55.3	4.8	11.8	6.6
merge	86.6	69.9	33.1	44.4
sort	67.5	69.9	27.6	38.8

% time for symdiff

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	37.3	8.3	11.2	9.8
merge	8.1	2.5	3.5	3.2
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	35.8	7.7	7.7	7.5
merge	39.8	16.9	17.3	24.0
sort	31.5	14.1	14.4	21.2

% time for setequal

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	79.6	78.8	12	14.3
merge	19.9	16.3	5	6.0
sort	0.0	0.0	0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	80.1	79.7	8.0	8.6
merge	97.4	39276.3	23.1	45.6
sort	77.6	39258.7	18.8	41.0

% time for setearly

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	79.0	3.3	18.3	12.6
merge	21.9	0.0	0.1	5.3
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	77.3	2.3	5.3	7.4
merge	94.3	33.6	80.9	38.4
sort	73.4	33.6	80.9	34.5

- A performance example
- Boolean data types