bit64-package: A S3 class for vectors of 64bit integers

Description Usage Arguments Details Value Design considerations Arithmetic precision and coercion Creating and testing S3 class 'integer64' Index of implemented methods Limitations inherited from implementing 64 bit integers via an external package Limitations inherited from Base R, Core team, can you change this? further limitations Note Author(s) See Also Examples

Description

Package 'bit64' provides fast serializable S3 atomic 64bit (signed) integers that can be used in vectors, matrices, arrays and data.frames. Methods are available for coercion from and to logicals, integers, doubles, characters and factors as well as many elementwise and summary functions.
Version 0.8 With 'integer64' vectors you can store very large integers at the expense of 64 bits, which is by factor 7 better than 'int64' from package 'int64'. Due to the smaller memory footprint, the atomic vector architecture and using only S3 instead of S4 classes, most operations are one to three orders of magnitude faster: Example speedups are 4x for serialization, 250x for adding, 900x for coercion and 2000x for object creation. Also 'integer64' avoids an ongoing (potentially infinite) penalty for garbage collection observed during existence of 'int64' objects (see code in example section).
Version 0.9 Package 'bit64' - which extends R with fast 64-bit integers - now has fast (single-threaded) implementations the most important univariate algorithmic operations (those based on hashing and sorting). We now have methods for 'match', ' 'quantile', 'median' and 'summary'. Regarding data management we also have novel generics 'unipos' (positions of the unique values), 'tiepos' ( positions of ties), 'keypos' (positions of foreign keys in a sorted dimension table) and derived methods 'as.factor' and 'as.ordered'. This 64- bit functionality is implemented carefully to be not slower than the respective 32-bit operations in Base R and also to avoid outlying waiting times observed with 'order', 'rank' and 'table' (speedup factors 20/16/200 respective). This increases the dataset size with wich we can work truly interactive. The speed is achieved by simple heuristic optimizers in high- level functions choosing the best from multiple low-level algorithms and further taking advantage of a novel caching if activated. In an example R session using a couple of these operations the 64-bit integers performed 22x faster than base 32-bit integers, hash-caching improved this to 24x, sortorder-caching was most efficient with 38x (caching hashing and sorting is not worth it with 32x at duplicated RAM consumption).

Usage

1
2
3
4
5
6
7
8
9
 integer64(length)
 ## S3 method for class 'integer64'
is(x)
 ## S3 replacement method for class 'integer64'
length(x) <- value
 ## S3 method for class 'integer64'
print(x, quote=FALSE, ...)
 ## S3 method for class 'integer64'
str(object, vec.len  = strO$vec.len, give.head = TRUE, give.length = give.head, ...)

Arguments

length

length of vector using integer

x

an integer64 vector

object

an integer64 vector

value

an integer64 vector of values to be assigned

quote

logical, indicating whether or not strings should be printed with surrounding quotes.

vec.len

see str

give.head

see str

give.length

see str

...

further arguments to the NextMethod

Details

Package: bit64
Type: Package
Version: 0.5.0
Date: 2011-12-12
License: GPL-2
LazyLoad: yes
Encoding: latin1

Value

integer64 returns a vector of 'integer64', i.e. a vector of double decorated with class 'integer64'.

Design considerations

64 bit integers are related to big data: we need them to overcome address space limitations. Therefore performance of the 64 bit integer type is critical. In the S language – designed in 1975 – atomic objects were defined to be vectors for a couple of good reasons: simplicity, option for implicit parallelization, good cache locality. In recent years many analytical databases have learnt that lesson: column based data bases provide superior performance for many applications, the result are products such as MonetDB, Sybase IQ, Vertica, Exasol, Ingres Vectorwise. If we introduce 64 bit integers not natively in Base R but as an external package, we should at least strive to make them as 'basic' as possible. Therefore the design choice of bit64 not only differs from int64, it is obvious: Like the other atomic types in Base R, we model data type 'integer64' as a contiguous atomic vector in memory, and we use the more basic S3 class system, not S4. Like package int64 we want our 'integer64' to be serializeable, therefore we also use an existing data type as the basis. Again the choice is obvious: R has only one 64 bit data type: doubles. By using doubles, integer64 inherits some functionality such as is.atomic, length, length<-, names, names<-, dim, dim<-, dimnames, dimnames.
Our R level functions strictly follow the functional programming paragdim: no modification of arguments or other sideffects. Before version 0.93 we internally deviated from the strict paradigm in order to boost performance. Our C functions do not create new return values, instead we pass-in the memory to be returned as an argument. This gives us the freedom to apply the C-function to new or old vectors, which helps to avoid unnecessary memory allocation, unnecessary copying and unnessary garbage collection. Prior to 0.93 within our R functions we also deviated from conventional R programming by not using attr<- and attributes<- because they always did new memory allocation and copying in older R versions. If we wanted to set attributes of return values that we have freshly created, we instead used functions setattr and setattributes from package bit. From version 0.93 setattr is only used for manipulating cache objects, in ramsort.integer64 and sort.integer64 and in as.data.frame.integer64.

Arithmetic precision and coercion

The fact that we introduce 64 bit long long integers – without introducing 128-bit long doubles – creates some subtle challenges: Unlike 32 bit integers, the integer64 are no longer a proper subset of double. If a binary arithmetic operation does involve a double and a integer, it is a no-brainer to return double without loss of information. If an integer64 meets a double, it is not trivial what type to return. Switching to integer64 limits our ability to represent very large numbers, switching to double limits our ability to distinguish x from x+1. Since the latter is the purpose of introducing 64 bit integers, we usually return integer64 from functions involving integer64, for example in c, cbind and rbind.
Different from Base R, our operators +, -, %/% and %% coerce their arguments to integer64 and always return integer64.
The multiplication operator * coerces its first argument to integer64 but allows its second argument to be also double: the second argument is internaly coerced to 'long double' and the result of the multiplication is returned as integer64.
The division / and power ^ operators also coerce their first argument to integer64 and coerce internally their second argument to 'long double', they return as double, like sqrt, log, log2 and log10 do.

argument1 op argument2 -> coerced1 op coerced2 -> result
integer64 + double -> integer64 + integer64 -> integer64
double + integer64 -> integer64 + integer64 -> integer64
integer64 - double -> integer64 - integer64 -> integer64
double - integer64 -> integer64 - integer64 -> integer64
integer64 %/% double -> integer64 %/% integer64 -> integer64
double %/% integer64 -> integer64 %/% integer64 -> integer64
integer64 %% double -> integer64 %% integer64 -> integer64
double %% integer64 -> integer64 %% integer64 -> integer64
integer64 * double -> integer64 * long double -> integer64
double * integer64 -> integer64 * integer64 -> integer64
integer64 / double -> integer64 / long double -> double
double / integer64 -> integer64 / long double -> double
integer64 ^ double -> integer64 / long double -> double
double ^ integer64 -> integer64 / long double -> double

Creating and testing S3 class 'integer64'

Our creator function integer64 takes an argument length, creates an atomic double vector of this length, attaches an S3 class attribute 'integer64' to it, and that's it. We simply rely on S3 method dispatch and interpret those 64bit elements as 'long long int'.
is.double currently returns TRUE for integer64 and might return FALSE in a later release. Consider is.double to have undefined behaviour and do query is.integer64 before querying is.double. The methods is.integer64 and is.vector both return TRUE for integer64. Note that we did not patch storage.mode and typeof, which both continue returning 'double' Like for 32 bit integer, mode returns 'numeric' and as.double) tries coercing to double). It is likely that 'integer64' becomes a vmode in package ff.
Further methods for creating integer64 are range which returns the range of the data type if calles without arguments, rep, seq.
For all available methods on integer64 vectors see the index below and the examples.

Index of implemented methods

creating,testing,printing see also description
NA_integer64_ NA_integer_ NA constant
integer64 integer create zero atomic vector
rep.integer64 rep
seq.integer64 seq
is.integer64 is
is.integer inherited from Base R
is.vector.integer64 is.vector
identical.integer64 identical
length<-.integer64 length<-
length inherited from Base R
names<- inherited from Base R
names inherited from Base R
dim<- inherited from Base R
dim inherited from Base R
dimnames<- inherited from Base R
dimnames inherited from Base R
str inherited from Base R, does not print values correctly
print.integer64 print
str.integer64 str
coercing to integer64 see also description
as.integer64 generic
as.integer64.character character
as.integer64.double double
as.integer64.integer integer
as.integer64.integer64 integer64
as.integer64.logical logical
as.integer64.NULL NULL
coercing from integer64 see also description
as.bitstring as.bitstring generic
as.bitstring.integer64
as.character.integer64 as.character
as.double.integer64 as.double
as.integer.integer64 as.integer
as.logical.integer64 as.logical
data structures see also description
c.integer64 c vector concatenate
cbind.integer64 cbind column bind
rbind.integer64 rbind row bind
as.data.frame.integer64 as.data.frame coerce atomic object to data.frame
data.frame inherited from Base R since we have coercion
subscripting see also description
[.integer64 [ vector and array extract
[<-.integer64 [<- vector and array assign
[[.integer64 [[ scalar extract
[[<-.integer64 [[<- scalar assign
binary operators see also description
+.integer64 + returns integer64
-.integer64 - returns integer64
*.integer64 * returns integer64
^.integer64 ^ returns double
/.integer64 / returns double
%/%.integer64 %/% returns integer64
%%.integer64 %% returns integer64
comparison operators see also description
==.integer64 ==
!=.integer64 !=
<.integer64 <
<=.integer64 <=
>.integer64 >
>=.integer64 >=
logical operators see also description
!.integer64 !
&.integer64 &
|.integer64 |
xor.integer64 xor
math functions see also description
is.na.integer64 is.na returns logical
format.integer64 format returns character
abs.integer64 abs returns integer64
sign.integer64 sign returns integer64
log.integer64 log returns double
log10.integer64 log10 returns double
log2.integer64 log2 returns double
sqrt.integer64 sqrt returns double
ceiling.integer64 ceiling dummy returning its argument
floor.integer64 floor dummy returning its argument
trunc.integer64 trunc dummy returning its argument
round.integer64 round dummy returning its argument
signif.integer64 signif dummy returning its argument
cumulative functions see also description
cummin.integer64 cummin
cummax.integer64 cummax
cumsum.integer64 cumsum
cumprod.integer64 cumprod
diff.integer64 diff
summary functions see also description
range.integer64 range
min.integer64 min
max.integer64 max
sum.integer64 sum
mean.integer64 mean
prod.integer64 prod
all.integer64 all
any.integer64 any
algorithmically complex functions see also description (caching)
match.integer64 match position of x in table (h//o/so)
%in%.integer64 %in% is x in table? (h//o/so)
duplicated.integer64 duplicated is current element duplicate of previous one? (h//o/so)
unique.integer64 unique (shorter) vector of unique values only (h/s/o/so)
unipos.integer64 unipos positions corresponding to unique values (h/s/o/so)
tiepos.integer64 tiepos positions of values that are tied (//o/so)
keypos.integer64 keypos position of current value in sorted list of unique values (//o/so)
as.factor.integer64 as.factor convert to (unordered) factor with sorted levels of previous values (//o/so)
as.ordered.integer64 as.ordered convert to ordered factor with sorted levels of previous values (//o/so)
table.integer64 table unique values and their frequencies (h/s/o/so)
sort.integer64 sort sorted vector (/s/o/so)
order.integer64 order positions of elements that would create sorted vector (//o/so)
rank.integer64 rank (average) ranks of non-NAs, NAs kept in place (/s/o/so)
quantile.integer64 quantile (existing) values at specified percentiles (/s/o/so)
median.integer64 median (existing) value at percentile 0.5 (/s/o/so)
summary.integer64 summary (/s/o/so)
helper functions see also description
minusclass minusclass removing class attritbute
plusclass plusclass inserting class attribute
binattr binattr define binary op behaviour
tested I/O functions see also description
read.table inherited from Base R
write.table inherited from Base R
serialize inherited from Base R
unserialize inherited from Base R
save inherited from Base R
load inherited from Base R
dput inherited from Base R
dget inherited from Base R

Limitations inherited from implementing 64 bit integers via an external package

Limitations inherited from Base R, Core team, can you change this?

further limitations

Note

integer64 are useful for handling database keys and exact counting in +-2^63. Do not use them as replacement for 32bit integers, integer64 are not supported for subscripting by R-core and they have different semantics when combined with double. Do understand that integer64 can only be useful over double if we do not coerce it to double.

While
integer + double -> double + double -> double
or
1L + 0.5 -> 1.5
for additive operations we coerce to integer64
integer64 + double -> integer64 + integer64 -> integer64
hence
as.integer64(1) + 0.5 -> 1LL + 0LL -> 1LL

see section "Arithmetic precision and coercion" above

Author(s)

Jens Oehlschl<c3><a4>gel <[email protected]> Maintainer: Jens Oehlschl<c3><a4>gel <[email protected]>

See Also

integer in base R

Examples

  1
  2
  3
  4
  5
  6
  7
  8
  9
 10
 11
 12
 13
 14
 15
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
message("Using integer64 in vector")
x <- integer64(8)    # create 64 bit vector
x
is.atomic(x)         # TRUE
is.integer64(x)      # TRUE
is.numeric(x)        # TRUE
is.integer(x)        # FALSE - debatable
is.double(x)         # FALSE - might change
x[] <- 1:2           # assigned value is recycled as usual
x[1:6]               # subscripting as usual
length(x) <- 13      # changing length as usual
x
rep(x, 2)            # replicate as usual
seq(as.integer64(1), 10)     # seq.integer64 is dispatched on first given argument
seq(to=as.integer64(10), 1)  # seq.integer64 is dispatched on first given argument
seq.integer64(along.with=x)  # or call seq.integer64 directly
# c.integer64 is dispatched only if *first* argument is integer64 ...
x <- c(x,runif(length(x), max=100)) 
# ... and coerces everything to integer64 - including double
x                                   
names(x) <- letters  # use names as usual
x

message("Using integer64 in array - note that 'matrix' currently does not work")
message("as.vector.integer64 removed as requested by the CRAN maintainer")
message("as consequence 'array' also does not work anymore")

message("we still can create a matrix or array by assigning 'dim'")
y <- rep(as.integer64(NA), 12)
dim(y) <- c(3,4)
dimnames(y) <- list(letters[1:3], LETTERS[1:4])
y["a",] <- 1:2       # assigning as usual
y
y[1:2,-4]            # subscripting as usual
# cbind.integer64 dispatched on any argument and coerces everything to integer64
cbind(E=1:3, F=runif(3, 0, 100), G=c("-1","0","1"), y)

message("Using integer64 in data.frame")
str(as.data.frame(x))
str(as.data.frame(y))
str(data.frame(y))
str(data.frame(I(y)))
d <- data.frame(x=x, y=runif(length(x), 0, 100))
d
d$x

message("Using integer64 with csv files")
fi64 <- tempfile()
write.csv(d, file=fi64, row.names=FALSE)
e <- read.csv(fi64, colClasses=c("integer64", NA))
unlink(fi64)
str(e)
identical.integer64(d$x,e$x)

message("Serializing and unserializing integer64")
dput(d, fi64)
e <- dget(fi64)
identical.integer64(d$x,e$x)
e <- d[,]
save(e, file=fi64)
rm(e)
load(file=fi64)
identical.integer64(d,e)

### A couple of unit tests follow hidden in a dontshow{} directive ###
  

  ## Not run: 
message("== Differences between integer64 and int64 ==")
require(bit64)
require(int64)

message("-- integer64 is atomic --")
is.atomic(integer64())
#is.atomic(int64())
str(integer64(3))
#str(int64(3))

message("-- The following performance numbers are measured under RWin64  --")
message("-- under RWin32 the advantage of integer64 over int64 is smaller --")

message("-- integer64 needs 7x/5x less RAM than int64 under 64/32 bit OS 
(and twice the RAM of integer as it should be) --")
#as.vector(object.size(int64(1e6))/object.size(integer64(1e6)))
as.vector(object.size(integer64(1e6))/object.size(integer(1e6)))

message("-- integer64 creates 2000x/1300x faster than int64 under 64/32 bit OS
(and 3x the time of integer) --")
t32 <- system.time(integer(1e8))
t64 <- system.time(integer64(1e8))
#T64 <- system.time(int64(1e7))*10  # using 1e8 as above stalls our R on an i7 8 GB RAM Thinkpad
#T64/t64
t64/t32

i32 <- sample(1e6)
d64 <- as.double(i32)

message("-- the following timings are rather conservative since timings
 of integer64 include garbage collection -- due to looped calls")
message("-- integer64 coerces 900x/100x faster than int64 
 under 64/32 bit OS (and 2x the time of coercing to integer) --")
t32 <- system.time(for(i in 1:1000)as.integer(d64))
t64 <- system.time(for(i in 1:1000)as.integer64(d64))
#T64 <- system.time(as.int64(d64))*1000
#T64/t64
t64/t32
td64 <- system.time(for(i in 1:1000)as.double(i32))
t64 <- system.time(for(i in 1:1000)as.integer64(i32))
#T64 <- system.time(for(i in 1:10)as.int64(i32))*100
#T64/t64
t64/td64

message("-- integer64 serializes 4x/0.8x faster than int64 
 under 64/32 bit OS (and less than 2x/6x the time of integer or double) --")
t32 <- system.time(for(i in 1:10)serialize(i32, NULL))
td64 <- system.time(for(i in 1:10)serialize(d64, NULL))
i64 <- as.integer64(i32); 
t64 <- system.time(for(i in 1:10)serialize(i64, NULL))
rm(i64); gc()
#I64 <- as.int64(i32); 
#T64 <- system.time(for(i in 1:10)serialize(I64, NULL))
#rm(I64); gc()
#T64/t64
t64/t32
t64/td64


message("-- integer64 adds 250x/60x faster than int64
 under 64/32 bit OS (and less than 6x the time of integer or double) --")
td64 <- system.time(for(i in 1:100)d64+d64)
t32 <- system.time(for(i in 1:100)i32+i32)
i64 <- as.integer64(i32); 
t64 <- system.time(for(i in 1:100)i64+i64)
rm(i64); gc()
#I64 <- as.int64(i32); 
#T64 <- system.time(for(i in 1:10)I64+I64)*10
#rm(I64); gc()
#T64/t64
t64/t32
t64/td64

message("-- integer64 sums 3x/0.2x faster than int64 
(and at about 5x/60X the time of integer and double) --")
td64 <- system.time(for(i in 1:100)sum(d64))
t32 <- system.time(for(i in 1:100)sum(i32))
i64 <- as.integer64(i32); 
t64 <- system.time(for(i in 1:100)sum(i64))
rm(i64); gc()
#I64 <- as.int64(i32); 
#T64 <- system.time(for(i in 1:100)sum(I64))
#rm(I64); gc()
#T64/t64
t64/t32
t64/td64

message("-- integer64 diffs 5x/0.85x faster than integer and double
(int64 version 1.0 does not support diff) --")
td64 <- system.time(for(i in 1:10)diff(d64, lag=2L, differences=2L))
t32 <- system.time(for(i in 1:10)diff(i32, lag=2L, differences=2L))
i64 <- as.integer64(i32); 
t64 <- system.time(for(i in 1:10)diff(i64, lag=2L, differences=2L))
rm(i64); gc()
t64/t32
t64/td64


message("-- integer64 subscripts 1000x/340x faster than int64
(and at the same speed / 10x slower as integer) --")
ts32 <- system.time(for(i in 1:1000)sample(1e6, 1e3))
t32<- system.time(for(i in 1:1000)i32[sample(1e6, 1e3)])
i64 <- as.integer64(i32); 
t64 <- system.time(for(i in 1:1000)i64[sample(1e6, 1e3)])
rm(i64); gc()
#I64 <- as.int64(i32); 
#T64 <- system.time(for(i in 1:100)I64[sample(1e6, 1e3)])*10
#rm(I64); gc()
#(T64-ts32)/(t64-ts32)
(t64-ts32)/(t32-ts32)

message("-- integer64 assigns 200x/90x faster than int64
(and 50x/160x slower than integer) --")
ts32 <- system.time(for(i in 1:100)sample(1e6, 1e3))
t32 <- system.time(for(i in 1:100)i32[sample(1e6, 1e3)] <- 1:1e3)
i64 <- as.integer64(i32); 
i64 <- system.time(for(i in 1:100)i64[sample(1e6, 1e3)] <- 1:1e3)
rm(i64); gc()
#I64 <- as.int64(i32); 
#I64 <- system.time(for(i in 1:10)I64[sample(1e6, 1e3)] <- 1:1e3)*10
#rm(I64); gc()
#(T64-ts32)/(t64-ts32)
(t64-ts32)/(t32-ts32)


tdfi32 <- system.time(dfi32 <- data.frame(a=i32, b=i32, c=i32))
tdfsi32 <- system.time(dfi32[1e6:1,])
fi32 <- tempfile()
tdfwi32 <- system.time(write.csv(dfi32, file=fi32, row.names=FALSE))
tdfri32 <- system.time(read.csv(fi32, colClasses=rep("integer", 3)))
unlink(fi32)
rm(dfi32); gc()

i64 <- as.integer64(i32); 
tdfi64 <- system.time(dfi64 <- data.frame(a=i64, b=i64, c=i64))
tdfsi64 <- system.time(dfi64[1e6:1,])
fi64 <- tempfile()
tdfwi64 <- system.time(write.csv(dfi64, file=fi64, row.names=FALSE))
tdfri64 <- system.time(read.csv(fi64, colClasses=rep("integer64", 3)))
unlink(fi64)
rm(i64, dfi64); gc()

#I64 <- as.int64(i32); 
#tdfI64 <- system.time(dfI64<-data.frame(a=I64, b=I64, c=I64))
#tdfsI64 <- system.time(dfI64[1e6:1,])
#fI64 <- tempfile()
#tdfwI64 <- system.time(write.csv(dfI64, file=fI64, row.names=FALSE))
#tdfrI64 <- system.time(read.csv(fI64, colClasses=rep("int64", 3)))
#unlink(fI64)
#rm(I64, dfI64); gc()

message("-- integer64 coerces 40x/6x faster to data.frame than int64
(and factor 1/9 slower than integer) --")
#tdfI64/tdfi64
tdfi64/tdfi32
message("-- integer64 subscripts from data.frame 20x/2.5x faster than int64
 (and 3x/13x slower than integer) --")
#tdfsI64/tdfsi64
tdfsi64/tdfsi32
message("-- integer64 csv writes about 2x/0.5x faster than int64
(and about 1.5x/5x slower than integer) --")
#tdfwI64/tdfwi64
tdfwi64/tdfwi32
message("-- integer64 csv reads about 3x/1.5 faster than int64
(and about 2x slower than integer) --")
#tdfrI64/tdfri64
tdfri64/tdfri32

rm(i32, d64); gc()


message("-- investigating the impact on garbage collection: --")
message("-- the fragmented structure of int64 messes up R's RAM --")
message("-- and slows down R's gargbage collection just by existing --")

td32 <- double(21)
td32[1] <- system.time(d64 <- double(1e7))[3]
for (i in 2:11)td32[i] <- system.time(gc(), gcFirst=FALSE)[3]
rm(d64)
for (i in 12:21)td32[i] <- system.time(gc(), gcFirst=FALSE)[3]

t64 <- double(21)
t64[1] <- system.time(i64 <- integer64(1e7))[3]
for (i in 2:11)t64[i] <- system.time(gc(), gcFirst=FALSE)[3]
rm(i64)
for (i in 12:21)t64[i] <- system.time(gc(), gcFirst=FALSE)[3]

#T64 <- double(21)
#T64[1] <- system.time(I64 <- int64(1e7))[3]
#for (i in 2:11)T64[i] <- system.time(gc(), gcFirst=FALSE)[3]
#rm(I64)
#for (i in 12:21)T64[i] <- system.time(gc(), gcFirst=FALSE)[3]

#matplot(1:21, cbind(td32, t64, T64), pch=c("d","i","I"), log="y")
matplot(1:21, cbind(td32, t64), pch=c("d","i"), log="y")
  
## End(Not run)

bit64 documentation built on May 2, 2019, 5:08 a.m.