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	26.3

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	19.2	6.2	6.0	NA
bit	18.1	18.2	18.0	NA
bitwhich	26.8	53.5	6.2	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time assigning

% time of logical
	coin	often	rare	chunk
logical	39.7	40.2	40.8	NA
bit	80.1	12.8	12.9	NA
bitwhich	182.6	42.6	42.4	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time subscripting with ‘which’

% time of logical
	coin	often	rare	chunk
logical	21.4	35.0	0.9	NA
bit	22.2	43.2	0.7	NA
bitwhich	31.0	60.9	1.7	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time assigning with ‘which’

% time of logical
	coin	often	rare	chunk
logical	20.8	40.5	0.7	NA
bit	15.8	38.1	0.5	NA
bitwhich	36.0	28.7	2.4	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean NOT

% time for Boolean NOT
	coin	often	rare	chunk
logical	18.4	18.6	18.4	18.6
bit	0.8	0.7	0.7	0.7
bitwhich	12.8	0.8	0.8	1.9
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean AND

% time for Boolean &
	coin	often	rare	chunk
logical	97.2	28.7	26.9	25.5
bit	4.7	4.3	4.7	4.6
bitwhich	17.9	5.2	4.9	6.1
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean OR

% time for Boolean |
	coin	often	rare	chunk
logical	100.0	33.3	24.9	25.2
bit	4.7	4.5	4.6	4.2
bitwhich	38.5	4.7	5.0	7.2
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean EQUALITY

% time for Boolean ==
	coin	often	rare	chunk
logical	26.0	26.1	26.2	26.2
bit	4.7	4.5	4.4	4.3
bitwhich	15.2	4.5	4.4	5.2
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean XOR

% time for Boolean !=
	coin	often	rare	chunk
logical	24.7	24.8	24.7	24.8
bit	4.8	4.6	4.9	4.3
bitwhich	14.3	4.5	4.5	5.4
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean SUMMARY

% time for Boolean summary
	coin	often
logical	85.3	16.9
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	148.1	191.3
sortunique	87.7	37.2

unsorted data relative to R’s sort
	small	big
sort	19.0	31.4
sortunique	16.1	13.1

% time for unique

sorted data relative to R
	small	big
bit	128.1	22.0
merge	24.7	10.9
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	120.2	17.3
merge	133.9	75.2
sort	108.7	65.1

% time for duplicated

sorted data relative to R
	small	big
bit	236.6	26.4
merge	31.6	10.0
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	212.2	18.7
merge	148.1	85.2
sort	119.1	76.4

% time for anyDuplicated

sorted data relative to R
	small	big
bit	163.3	31.8
merge	20.6	4.3
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	155.7	18.8
merge	164.9	81.1
sort	144.0	77.8

% time for sumDuplicated

sorted data relative to R
	small	big
bit	123.9	24.9
merge	21.1	10.6
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	113.3	17.5
merge	120.7	81.3
sort	100.7	72.0

% time for match

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	NA	NA	NA	NA
merge	22.7	0	22.1	5.5
sort	0.0	0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	NA	NA	NA	NA
merge	206.2	75.3	79.7	79.6
sort	181.9	75.3	71.3	75.9

% time for in

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	165.8	7	14.0	23
merge	21.2	0	15.9	5
sort	0.0	0	0.0	0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	166.0	5.4	6.5	15.2
merge	186.8	76.8	68.8	77.6
sort	165.8	76.8	61.5	74.0

% time for notin

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	213.2	6.7	12.1	21.4
merge	18.8	0.0	4.3	4.6
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	265.7	5.1	6.4	13.0
merge	178.9	70.5	58.0	66.4
sort	157.7	70.5	55.8	63.3

% time for union

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	33.6	23.9	22.4	17.1
merge	23.1	14.3	13.6	11.8
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	46.4	13.8	21.2	12.0
merge	65.8	33.2	50.8	43.1
sort	41.0	24.5	37.4	34.1

% time for intersect

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	29.3	5.4	6	9.8
merge	8.6	0.0	0	5.0
sort	0.0	0.0	0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	28.5	4.8	4.4	7.8
merge	47.7	35.4	33.1	38.0
sort	38.8	35.3	33.1	33.7

% time for setdiff

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	28.4	2.8	19.4	9.3
merge	9.0	0.0	15.6	5.1
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	25.9	2.8	12.2	6.3
merge	51.8	39.2	41.6	41.8
sort	42.9	39.2	30.7	37.5

% time for symdiff

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	22.1	11.2	12.6	8.9
merge	3.9	4.9	5.5	2.9
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	16.7	8.8	9.5	6.3
merge	18.5	16.9	18.2	20.5
sort	15.2	12.5	13.4	18.2

% time for setequal

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	66.8	65.0	14.1	15.9
merge	14.4	13.7	6.7	7.7
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	56.2	53.7	8.4	9.8
merge	71.0	26591.2	24.7	51.6
sort	56.4	26579.2	19.6	45.7

% time for setearly

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	59.5	4	12.6	15.6
merge	14.2	0	0.1	7.5
sort	0.0	0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	39.1	2.4	4.7	9.0
merge	47.5	35.7	71.7	47.4
sort	38.0	35.6	71.6	42.0

- A performance example
- Boolean data types