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	29.9	30

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	6.4	4.1	6.2	NA
bit	13.6	12.9	13.3	NA
bitwhich	215.7	51.3	3.9	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time assigning

% time of logical
	coin	often	rare	chunk
logical	36.9	37.0	36.8	NA
bit	80.1	12.0	10.5	NA
bitwhich	184.0	43.3	40.8	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time subscripting with ‘which’

% time of logical
	coin	often	rare	chunk
logical	34.3	34.5	0.4	NA
bit	20.9	42.7	0.7	NA
bitwhich	32.8	60.1	1.4	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time assigning with ‘which’

% time of logical
	coin	often	rare	chunk
logical	20.1	39.0	0.4	NA
bit	20.0	29.6	0.5	NA
bitwhich	151.9	28.4	1.8	NA
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean NOT

% time for Boolean NOT
	coin	often	rare	chunk
logical	16.7	16.7	16.8	16.8
bit	0.6	0.6	0.6	0.6
bitwhich	7.3	0.7	0.8	1.4
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean AND

% time for Boolean &
	coin	often	rare	chunk
logical	97.5	29.0	21.1	20.0
bit	3.7	3.7	3.8	4.2
bitwhich	29.2	4.2	3.7	5.3
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean OR

% time for Boolean |
	coin	often	rare	chunk
logical	100.0	27.2	25.9	24.8
bit	3.7	3.7	4.0	3.8
bitwhich	17.1	3.7	4.2	6.5
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean EQUALITY

% time for Boolean ==
	coin	often	rare	chunk
logical	26.4	73.2	26.5	26.4
bit	4.0	3.7	3.8	3.7
bitwhich	13.8	3.5	3.7	4.8
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean XOR

% time for Boolean !=
	coin	often	rare	chunk
logical	26.7	25.3	25.4	25.4
bit	3.6	3.6	3.7	3.9
bitwhich	14.5	3.5	3.8	4.4
which	NA	NA	NA	NA
ri	NA	NA	NA	NA

% time Boolean SUMMARY

% time for Boolean summary
	coin	often
logical	87.4	15.9
bit	3.5	3.4

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	175.4	191.9
sortunique	82.7	34.5

unsorted data relative to R’s sort
	small	big
sort	27.2	35.9
sortunique	36.1	15.4

% time for unique

sorted data relative to R
	small	big
bit	125.9	12.5
merge	24.6	5.1
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	110.6	11.1
merge	121.3	40.3
sort	97.8	35.1

% time for duplicated

sorted data relative to R
	small	big
bit	190.7	14.6
merge	30.7	5.9
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	178.6	9.0
merge	138.1	34.8
sort	108.2	30.8

% time for anyDuplicated

sorted data relative to R
	small	big
bit	134.8	13.8
merge	20.5	1.6
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	128.9	11.7
merge	142.5	43.0
sort	122.3	41.4

% time for sumDuplicated

sorted data relative to R
	small	big
bit	107.6	12.7
merge	21.4	5.7
sort	0.0	0.0

unsorted data relative to R
	small	big
bit	99.2	9.5
merge	113.7	37.9
sort	93.4	33.1

% time for match

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	NA	NA	NA	NA
merge	83.8	0	9.9	2.7
sort	0.0	0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	NA	NA	NA	NA
merge	261.9	68.1	72.9	42.1
sort	181.7	68.1	70.3	39.9

% time for in

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	157.7	3.3	21.4	10.0
merge	24.9	0.0	6.9	2.6
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	193.5	5.8	7.3	7.0
merge	209.1	74.0	66.1	38.5
sort	181.1	74.0	63.8	36.5

% time for notin

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	225.8	3.9	11.7	10.3
merge	22.2	0.0	3.7	2.8
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	207.0	5.7	5.8	6.1
merge	166.6	71.2	51.1	32.8
sort	144.2	71.2	49.2	31.0

% time for union

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	33.6	14.1	10.3	8.3
merge	21.0	5.5	4.1	6.8
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	34.4	11.4	8.4	6.9
merge	60.7	32.7	23.5	20.9
sort	39.4	27.8	19.9	16.3

% time for intersect

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	29.7	3.5	4.8	4.1
merge	8.9	0.0	0.0	2.4
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	32.5	4.4	3.9	3.5
merge	48.4	29.7	26.4	18.7
sort	39.5	29.7	26.4	16.3

% time for setdiff

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	24.9	1.7	15.7	5.1
merge	8.5	0.0	5.5	3.2
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	25.5	1.8	12.0	3.8
merge	50.6	23.9	30.3	22.3
sort	42.3	23.9	25.8	19.7

% time for symdiff

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	21.1	7.1	6.1	5.0
merge	4.8	1.9	1.6	1.7
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	18.6	5.8	5.3	3.8
merge	21.9	11.5	10.2	10.9
sort	17.4	9.8	8.7	9.5

% time for setequal

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	55.4	53.1	5.8	6.8
merge	13.9	16.0	3.1	3.6
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	60.8	53.3	6.7	5.9
merge	71.4	25279.4	17.5	27.6
sort	57.5	25263.0	13.6	24.1

% time for setearly

sorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	56.6	3.1	18.8	7.2
merge	14.1	0.0	0.1	3.8
sort	0.0	0.0	0.0	0.0

unsorted data relative to R
	smallsmall	smallbig	bigsmall	bigbig
bit	59.2	1.9	5.2	5.8
merge	71.6	26.1	70.4	27.0
sort	57.7	26.1	70.3	23.5

- A performance example
- Boolean data types