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	25.6	25.5

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	21.2	5.7	6.5	NA
bit	18.9	19.1	21.3	NA
bitwhich	25.7	51.5	6.8	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time assigning

% time of logical
	coin	often	rare	chunk
logical	39.4	39.7	39.8	NA
bit	84.3	16.9	11.4	NA
bitwhich	193.0	51.3	45.4	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time subscripting with ‘which’

% time of logical
	coin	often	rare	chunk
logical	27.1	35.1	1.2	NA
bit	22.2	44.0	0.8	NA
bitwhich	31.0	66.8	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	19.7	38.5	0.8	NA
bit	16.4	39.4	0.6	NA
bitwhich	38.6	22.5	2.7	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean NOT

% time for Boolean NOT
	coin	often	rare	chunk
logical	18.9	19.5	18.6	18.6
bit	1.0	0.9	1.0	0.9
bitwhich	11.5	0.9	0.9	2.3
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean AND

% time for Boolean &
	coin	often	rare	chunk
logical	100.0	27.7	27.4	25.7
bit	4.9	5.0	5.0	4.9
bitwhich	18.8	5.6	5.1	6.6
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean OR

% time for Boolean |
	coin	often	rare	chunk
logical	98.1	27.5	25.3	24.9
bit	4.8	4.9	4.8	5.0
bitwhich	40.4	4.9	5.5	8.2
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean EQUALITY

% time for Boolean ==
	coin	often	rare	chunk
logical	26.6	26.7	26.4	26.6
bit	4.7	4.6	4.8	4.8
bitwhich	18.0	4.9	4.9	6.4
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean XOR

% time for Boolean !=
	coin	often	rare	chunk
logical	25.1	25.1	25.0	25.2
bit	5.2	5.0	5.1	5.0
bitwhich	15.1	4.9	4.8	5.7
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean SUMMARY

% time for Boolean summary
	coin	often
logical	89.1	21.8
bit	5.3	5.5

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	149	126.7
sortunique	78	38.7

unsorted data relative to R’s sort
	small	big
sort	27.3	32.0
sortunique	21.6	13.1

% time for unique

sorted data relative to R
	small	big
bit	111.1	20.7
merge	21.9	8.3
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	126.9	16.1
merge	107.1	70.0
sort	87.7	62.2

% time for duplicated

sorted data relative to R
	small	big
bit	198.0	22.9
merge	22.2	8.4
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	198.3	17.0
merge	141.0	77.3
sort	118.5	69.6

% time for anyDuplicated

sorted data relative to R
	small	big
bit	125.9	26.8
merge	21.0	4.2
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	119.3	18.7
merge	142.7	82.1
sort	120.8	78.5

% time for sumDuplicated

sorted data relative to R
	small	big
bit	100.1	20.8
merge	17.0	6.6
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	105.8	16.6
merge	127.5	77.0
sort	108.1	70.4

% time for match

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	NA	NA	NA	NA
merge	25.4	0	23.6	5.8
sort	0.0	0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	NA	NA	NA	NA
merge	184.3	74.7	82.6	78.8
sort	162.0	74.7	73.9	74.6

% time for in

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	152.3	6.1	14.3	17.7
merge	20.1	0.0	16.3	4.2
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	141.1	4.7	6.5	13.2
merge	179.5	69.2	71.3	77.6
sort	160.2	69.1	63.9	73.7

% time for notin

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	209.9	6.4	13.0	15.9
merge	20.0	0.0	4.9	4.7
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	226.4	4.9	6.1	12.0
merge	173.6	69.3	59.8	67.2
sort	153.3	69.2	57.6	63.1

% time for union

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	33.8	17.0	20.9	14.3
merge	24.3	13.9	12.3	10.0
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	34.3	14.3	20.2	12.9
merge	62.9	34.0	48.6	42.9
sort	39.2	25.0	35.7	33.3

% time for intersect

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	28.7	5.1	8.1	7.2
merge	8.6	0.0	0.0	3.7
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	26.7	4.6	5.3	7.3
merge	46.0	35.6	32.8	36.5
sort	37.4	35.6	32.8	32.4

% time for setdiff

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	26.4	2.6	18.3	7.2
merge	9.7	0.0	15.0	5.0
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	23.3	2.3	12.8	6.0
merge	50.6	34.9	42.2	40.9
sort	41.3	34.8	30.9	35.9

% time for symdiff

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	19.2	10.4	11	6.5
merge	4.2	4.7	5	2.4
sort	0.0	0.0	0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	21.3	8.5	8.1	5.7
merge	24.9	17.0	16.0	19.8
sort	20.0	12.5	11.7	17.4

% time for setequal

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	48.9	50.7	13.1	9.2
merge	12.0	11.6	7.0	4.9
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	50.6	48.3	8.0	9.2
merge	68.8	24105.7	24.9	51.4
sort	55.5	24094.2	19.5	45.1

% time for setearly

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	49.9	3.8	14.5	14.2
merge	12.4	0.0	0.1	7.6
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	58.0	2.4	5.0	8.1
merge	75.1	37.2	78.1	44.9
sort	61.0	37.1	78.0	39.4

- A performance example
- Boolean data types