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	25.5	25.3

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	20.4	6.7	6.7	NA
bit	18.3	18.4	19.0	NA
bitwhich	26.8	55.1	6.7	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time assigning

% time of logical
	coin	often	rare	chunk
logical	40.3	40.2	40.6	NA
bit	80.0	13.9	13.3	NA
bitwhich	183.0	43.5	43.3	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time subscripting with ‘which’

% time of logical
	coin	often	rare	chunk
logical	22.1	35.1	1.1	NA
bit	22.2	43.7	0.9	NA
bitwhich	31.7	62.1	1.9	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	40.2	0.7	NA
bit	16.0	38.0	0.5	NA
bitwhich	36.7	28.9	2.3	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean NOT

% time for Boolean NOT
	coin	often	rare	chunk
logical	18.3	19.5	18.2	18.3
bit	0.7	0.7	0.8	0.8
bitwhich	10.4	0.8	0.8	1.8
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean AND

% time for Boolean &
	coin	often	rare	chunk
logical	97.4	28.9	27.1	25.5
bit	4.5	4.8	4.7	4.7
bitwhich	18.1	5.6	4.9	5.9
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	25.1	24.9
bit	4.6	4.6	4.6	4.4
bitwhich	38.4	4.7	5.5	7.6
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean EQUALITY

% time for Boolean ==
	coin	often	rare	chunk
logical	26.1	26.2	26.1	26.0
bit	4.7	4.8	4.5	4.6
bitwhich	14.8	4.7	4.8	5.7
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean XOR

% time for Boolean !=
	coin	often	rare	chunk
logical	24.8	24.8	24.8	24.8
bit	4.6	4.6	4.5	4.7
bitwhich	15.7	4.8	4.8	5.4
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean SUMMARY

% time for Boolean summary
	coin	often
logical	84.6	17.9
bit	3.8	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	126.4	173.9
sortunique	76.3	39.5

unsorted data relative to R’s sort
	small	big
sort	26.8	36.2
sortunique	16.6	12.5

% time for unique

sorted data relative to R
	small	big
bit	127.2	23.5
merge	24.4	9.7
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	106.0	16.7
merge	123.0	72.7
sort	100.7	64.5

% time for duplicated

sorted data relative to R
	small	big
bit	261.4	26.9
merge	28.9	10.2
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	213.9	11.7
merge	147.7	53.1
sort	120.8	47.7

% time for anyDuplicated

sorted data relative to R
	small	big
bit	150.2	25.7
merge	18.5	4.0
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	155.9	19.3
merge	161.1	84.9
sort	142.6	81.0

% time for sumDuplicated

sorted data relative to R
	small	big
bit	121.6	19.2
merge	20.7	7.9
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	118.7	17.9
merge	123.7	84.2
sort	104.5	74.7

% time for match

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	NA	NA	NA	NA
merge	26.2	0	10.1	4.5
sort	0.0	0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	NA	NA	NA	NA
merge	217.7	82.7	84.6	81.4
sort	192.6	82.7	81.5	77.4

% time for in

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	173.2	6.2	19.8	18.4
merge	22.8	0.0	7.9	4.5
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	155.6	5.6	7.7	14.3
merge	195.3	80.6	76.6	74.0
sort	173.3	80.6	73.5	70.2

% time for notin

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	255.4	4.1	14.3	19
merge	21.1	0.0	9.5	4
sort	0.0	0.0	0.0	0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	379.1	5.7	6.8	13.3
merge	191.9	79.6	67.0	69.2
sort	167.9	79.6	62.5	66.0

% time for union

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	34.5	14.8	13.9	11.0
merge	23.9	6.3	6.0	7.9
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	30.8	12.0	13.9	13.3
merge	61.0	37.5	42.5	43.7
sort	38.8	31.7	35.9	35.5

% time for intersect

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	31.3	4.3	4.9	7.8
merge	10.0	0.0	0.0	4.0
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	27.9	4.8	4.5	6.3
merge	51.4	36.8	34.1	38.4
sort	41.6	36.8	34.0	34.0

% time for setdiff

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	28.4	2.2	14.7	7.7
merge	9.4	0.0	5.8	4.1
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	25.3	2.6	13.1	5.9
merge	52.2	36.0	39.1	39.3
sort	43.1	36.0	33.1	35.3

% time for symdiff

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	19.7	7.8	6.9	7.4
merge	4.0	2.2	1.9	2.4
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	20.8	6.5	6.9	6.0
merge	24.5	15.0	15.0	20.0
sort	20.2	12.7	12.7	17.7

% time for setequal

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	54.0	54.2	9.1	10.2
merge	12.4	12.1	4.4	4.9
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	61.3	52.2	8.6	9.1
merge	78.0	26089.7	25.8	48.8
sort	64.3	26077.4	20.6	43.2

% time for setearly

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	65.2	3.5	16.3	12.0
merge	14.1	0.0	0.1	5.8
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	61.9	2.4	5.2	8.6
merge	75.8	36.9	80.6	46.1
sort	61.6	36.9	80.5	40.9

- A performance example
- Boolean data types