A S3 class for vectors of 64bit integers

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', '%in%', 'duplicated', 'unique', 'table', 'sort', 'order', 'rank', '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

integer64(length = 0L)

is.integer64(x)

# S3 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
value: an integer64 vector of values to be assigned
quote: logical, indicating whether or not strings should be printed with surrounding quotes.
...: further arguments to the NextMethod()
object: an integer64 vector
vec.len, give.head, give.length: see utils::str()

Value

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

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

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

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 package 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 paradigm: no modification of arguments or other side-effects. 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 unnecessary 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 bit::setattr() and bit::setattributes(). From version 0.93 bit::setattr() is only used for manipulating cache objects, in ramsort.integer64(), sort.integer64(), and 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 64-bit 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 behavior 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 possible 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
`runif64()`	`runif()`	create random 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.bitstring()`	`as.bitstring()`
`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.list.integer64()`	`as.list()`	generic
`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)
`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)
`all.equal.integer64()`	`all.equal()`	test if two objects are (nearly) equal (/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

vector size of atomic vectors is still limited to .Machine$integer.max. However, external memory extending packages such as ff or bigmemory can extend their address space now with integer64. Having 64 bit integers also help with those not so obvious address issues that arise once we exchange data with SQL databases and datawarehouses, which use big integers as surrogate keys, e.g. on indexed primary key columns. This puts R into a relatively strong position compared to certain commercial statistical softwares, which sell database connectivity but neither have the range of 64 bit integers, nor have integers at all, nor have a single numeric data type in their macro-glue-language.
literals such as 123LL would require changes to Base R, up to then we need to write (and call) as.integer64(123L) or as.integer64(123) or as.integer64('123'). Only the latter allows to specify numbers beyond Base R's numeric data types and therefore is the recommended way to use – using only one way may facilitate migrating code to literals at a later stage.

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

identical() with default parameters does not distinguish all bit-patterns of doubles. For testing purposes we provide a wrapper identical.integer64() that will distinguish all bit-patterns. It would be desireable to have a single call of identical() handle both, double and integer64.
the colon operator : officially does not dispatch S3 methods, however, we have made it generic:
```
from <- lim.integer64()[1]
to <- from+99
from:to
```
As a limitation remains: it will only dispatch at its first argument from but not at its second to.
is.double() does not dispatch S3 methods, However, we have made it generic and it will return FALSE on integer64.
c() only dispatches c.integer64() if the first argument is integer64 and it does not recursively dispatch the proper method when called with argument recursive=TRUE. Therefore c(list(integer64, integer64)) does not work and for now you can only call c.integer64(list(x, x)).
generic binary operators fail to dispatch any user-defined S3 method if the two arguments have two different S3 classes. For example we have two classes bit::bit and bit::bitwhich sparsely representing boolean vectors and we have methods &.bit and &.bitwhich. For an expression involving both as in bit & bitwhich, none of the two methods is dispatched. Instead a standard method is dispatched, which neither handles bit nor bitwhich. Although it lacks symmetry, the better choice would be to dispatch simply the method of the class of the first argument in case of class conflict. This choice would allow authors of extension packages providing coherent behaviour at least within their contributed classes. But as long as none of the package author's methods is dispatched, they cannot handle the conflicting classes at all.
unlist() is not generic and if it were, we would face similar problems as with c()
vector() with argument mode='integer64' cannot work without adjustment of Base R
as.vector() with argument mode='integer64' cannot work without adjustment of Base R
is.vector() does not dispatch its method is.vector.integer64()
mode<-() drops the class 'integer64' which is returned from as.integer64(). Also it does not remove an existing class 'integer64' when assigning mode 'integer'.
storage.mode<-() does not support external data types such as integer64
matrix() does drop the 'integer64' class attribute.
array() does drop the 'integer64' class attribute.
- In current R versions (1.15.1) this can be circumvented by activating the function as.vector.integer64(). However, the CRAN maintainer has requested to remove as.vector.integer64(), even at the price of breaking previously working functionality of the package.
str() does not print the values of integer64 correctly

Further limitations

subscripting non-existing elements and subscripting with NAs is currently not supported. Such subscripting currently returns 9218868437227407266 instead of NA (the NA value of the underlying double code). Following the full R behaviour here would either destroy performance or require extensive C-coding.

Author

Maintainer: Michael Chirico michaelchirico4@gmail.com

Authors:

Jens Oehlschlägel

Other contributors:

Leonardo Silvestri [contributor]
Ofek Shilon [contributor]

Examples

message("Using integer64 in vector")
#> Using integer64 in vector
x <- integer64(8)    # create 64 bit vector
x
#> integer64
#> [1] 0 0 0 0 0 0 0 0
is.atomic(x)         # TRUE
#> [1] TRUE
is.integer64(x)      # TRUE
#> [1] TRUE
is.numeric(x)        # TRUE
#> [1] TRUE
is.integer(x)        # FALSE - debatable
#> [1] FALSE
is.double(x)         # FALSE - might change
#> [1] FALSE
x[] <- 1:2           # assigned value is recycled as usual
x[1:6]               # subscripting as usual
#> integer64
#> [1] 1 2 1 2 1 2
length(x) <- 13      # changing length as usual
x
#> integer64
#>  [1] 1 2 1 2 1 2 1 2 0 0 0 0 0
rep(x, 2)            # replicate as usual
#> integer64
#>  [1] 1 2 1 2 1 2 1 2 0 0 0 0 0 1 2 1 2 1 2 1 2 0 0 0 0 0
seq(as.integer64(1), 10)     # seq.integer64 is dispatched on first given argument
#> integer64
#>  [1] 1  2  3  4  5  6  7  8  9  10
seq(to=as.integer64(10), 1)  # seq.integer64 is dispatched on first given argument
#> integer64
#>  [1] 1  2  3  4  5  6  7  8  9  10
seq.integer64(along.with=x)  # or call seq.integer64 directly
#> integer64
#>  [1] 1  2  3  4  5  6  7  8  9  10 11 12 13
# 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
#> integer64
#>  [1] 1  2  1  2  1  2  1  2  0  0  0  0  0  76 91 70 58 13 8  76 40 15 9 
#> [24] 2  8  28
names(x) <- letters  # use names as usual
x
#> integer64
#>  a  b  c  d  e  f  g  h  i  j  k  l  m  n  o  p  q  r  s  t  u  v  w  x 
#>  1  2  1  2  1  2  1  2  0  0  0  0  0 76 91 70 58 13  8 76 40 15  9  2 
#>  y  z 
#>  8 28 

message("Using integer64 in array - note that 'matrix' currently does not work")
#> Using integer64 in array - note that 'matrix' currently does not work
message("as.vector.integer64 removed as requested by the CRAN maintainer")
#> as.vector.integer64 removed as requested by the CRAN maintainer
message("as consequence 'array' also does not work anymore")
#> as consequence 'array' also does not work anymore
message("we still can create a matrix or array by assigning 'dim'")
#> 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
#> integer64
#>   A    B    C    D   
#> a 1    2    1    2   
#> b <NA> <NA> <NA> <NA>
#> c <NA> <NA> <NA> <NA>
y[1:2,-4]            # subscripting as usual
#> integer64
#>   A    B    C   
#> a 1    2    1   
#> b <NA> <NA> <NA>
# 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)
#> integer64
#>   E F  G  A    B    C    D   
#> a 1 58 -1 1    2    1    2   
#> b 2 71 0  <NA> <NA> <NA> <NA>
#> c 3 96 1  <NA> <NA> <NA> <NA>

message("Using integer64 in data.frame")
#> Using integer64 in data.frame
str(as.data.frame(x))
#> 'data.frame':	26 obs. of  1 variable:
#>  $ x:integer64 1 2 1 2 1 2 1 2 ... 
str(as.data.frame(y))
#> 'data.frame':	3 obs. of  4 variables:
#>  $ A:integer64 1 NA NA 
#>  $ B:integer64 2 NA NA 
#>  $ C:integer64 1 NA NA 
#>  $ D:integer64 2 NA NA 
str(data.frame(y))
#> 'data.frame':	3 obs. of  4 variables:
#>  $ A:integer64 1 NA NA 
#>  $ B:integer64 2 NA NA 
#>  $ C:integer64 1 NA NA 
#>  $ D:integer64 2 NA NA 
str(data.frame(I(y)))
#> 'data.frame':	3 obs. of  1 variable:
#>  $ y:integer64 1 NA NA 2 NA NA 1 NA ... 
d <- data.frame(x=x, y=runif(length(x), 0, 100))
d
#>    x          y
#> a  1 54.0294650
#> b  2 82.8379691
#> c  1 36.9443346
#> d  2 78.9029870
#> e  1 85.1345699
#> f  2 86.8393181
#> g  1 68.9746707
#> h  2 64.7483669
#> i  0 29.8988144
#> j  0 83.8488248
#> k  0 50.9581229
#> l  0  0.6297852
#> m  0 63.9481665
#> n 76 69.5749745
#> o 91 41.0609695
#> p 70 45.4798865
#> q 58 16.2794145
#> r 13 85.1599901
#> s  8 69.5091747
#> t 76 10.9175470
#> u 40 22.8045808
#> v 15  4.8925648
#> w  9 14.1299729
#> x  2 80.4662978
#> y  8 70.5601694
#> z 28 33.7272814
d$x
#> integer64
#>  [1] 1  2  1  2  1  2  1  2  0  0  0  0  0  76 91 70 58 13 8  76 40 15 9 
#> [24] 2  8  28

message("Using integer64 with csv files")
#> 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)
#> 'data.frame':	26 obs. of  2 variables:
#>  $ x:integer64 1 2 1 2 1 2 1 2 ... 
#>  $ y: num  54 82.8 36.9 78.9 85.1 ...
identical.integer64(d$x,e$x)
#> [1] TRUE

message("Serializing and unserializing integer64")
#> Serializing and unserializing integer64
dput(d, fi64)
e <- dget(fi64)
identical.integer64(d$x,e$x)
#> [1] TRUE
e <- d[,]
save(e, file=fi64)
rm(e)
load(file=fi64)
identical.integer64(d,e)
#> [1] TRUE

  if (FALSE) { # \dontrun{
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")
  } # }