A S3 class for vectors of 64bit integers

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', '%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 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

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 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.

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

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.

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)

Maintainer: Michael Chirico michaelchirico4@gmail.com

Authors:

• Jens Oehlschlägel

Other contributors:

• Leonardo Silvestri [contributor]

• Ofek Shilon [contributor]

See Also

integer() in base R

Examples

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)

  ## 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)

Test if two integer64 vectors are all.equal

Description

A utility to compare integer64 objects 'x' and 'y' testing for ‘near equality’, see all.equal().

Usage

## S3 method for class 'integer64'
all.equal(
  target,
  current,
  tolerance = sqrt(.Machine$double.eps),
  scale = NULL,
  countEQ = FALSE,
  formatFUN = function(err, what) format(err),
  ...,
  check.attributes = TRUE
)

Arguments

Details

In all.equal.numeric() the type integer is treated as a proper subset of double i.e. does not complain about comparing integer with double. Following this logic all.equal.integer64 treats integer as a proper subset of integer64 and does not complain about comparing integer with integer64. double also compares without warning as long as the values are within lim.integer64(), if double are bigger all.equal.integer64 complains about the ⁠all.equal.integer64 overflow warning⁠. For further details see all.equal().

Value

Either ‘TRUE’ (‘NULL’ for ‘attr.all.equal’) or a vector of ‘mode’ ‘"character"’ describing the differences between ‘target’ and ‘current’.

Note

all.equal() only dispatches to this method if the first argument is integer64, calling all.equal() with a non-integer64 first and a integer64 second argument gives undefined behavior!

See Also

all.equal()

Examples

  all.equal(as.integer64(1:10), as.integer64(0:9))
  all.equal(as.integer64(1:10), as.integer(1:10))
  all.equal(as.integer64(1:10), as.double(1:10))
  all.equal(as.integer64(1), as.double(1e300))

Coerce from integer64

Description

Methods to coerce integer64 to other atomic types. 'as.bitstring' coerces to a human-readable bit representation (strings of zeroes and ones). The methods format(), as.character(), as.double(), as.logical(), as.integer() do what you would expect.

Usage

as.bitstring(x, ...)

## S3 method for class 'integer64'
as.double(x, keep.names = FALSE, ...)

## S3 method for class 'integer64'
as.integer(x, ...)

## S3 method for class 'integer64'
as.logical(x, ...)

## S3 method for class 'integer64'
as.character(x, ...)

## S3 method for class 'integer64'
as.bitstring(x, ...)

## S3 method for class 'bitstring'
print(x, ...)

## S3 method for class 'integer64'
as.list(x, ...)

Arguments

Value

as.bitstring returns a string of class 'bitstring'.

The other methods return atomic vectors of the expected types

See Also

as.integer64.character() integer64()

Examples

  as.character(lim.integer64())
  as.bitstring(lim.integer64())
  as.bitstring(as.integer64(c(
   -2,-1,NA,0:2
  )))

integer64: Coercing to data.frame column

Description

Coercing integer64 vector to data.frame.

Usage

## S3 method for class 'integer64'
as.data.frame(x, ...)

Arguments

Details

'as.data.frame.integer64' is rather not intended to be called directly, but it is required to allow integer64 as data.frame columns.

Value

a one-column data.frame containing an integer64 vector

Note

This is currently very slow – any ideas for improvement?

See Also

cbind.integer64() integer64()

Examples

  as.data.frame.integer64(as.integer64(1:12))
  data.frame(a=1:12, b=as.integer64(1:12))

Coerce to integer64

Description

Methods to coerce from other atomic types to integer64.

Usage

as.integer64(x, ...)

## S3 method for class ''NULL''
as.integer64(x, ...)

## S3 method for class 'integer64'
as.integer64(x, ...)

## S3 method for class 'double'
as.integer64(x, keep.names = FALSE, ...)

## S3 method for class 'integer'
as.integer64(x, ...)

## S3 method for class 'logical'
as.integer64(x, ...)

## S3 method for class 'character'
as.integer64(x, ...)

## S3 method for class 'factor'
as.integer64(x, ...)

## S3 method for class 'bitstring'
as.integer64(x, ...)

NA_integer64_

Arguments

Format

An object of class integer64 of length 1.

Details

as.integer64.character is realized using C function strtoll which does not support scientific notation. Instead of '1e6' use '1000000'. as.integer64.bitstring evaluates characters '0' and ' ' as zero-bit, all other one byte characters as one-bit, multi-byte characters are not allowed, strings shorter than 64 characters are treated as if they were left-padded with '0', strings longer than 64 bytes are mapped to NA_INTEGER64 and a warning is emitted.

Value

The other methods return atomic vectors of the expected types

See Also

as.character.integer64() integer64()

Examples

as.integer64(as.character(lim.integer64()))
as.integer64(
  structure(c("1111111111111111111111111111111111111111111111111111111111111110",
              "1111111111111111111111111111111111111111111111111111111111111111",
              "1000000000000000000000000000000000000000000000000000000000000000",
              "0000000000000000000000000000000000000000000000000000000000000000",
              "0000000000000000000000000000000000000000000000000000000000000001",
              "0000000000000000000000000000000000000000000000000000000000000010"
  ), class = "bitstring")
)
as.integer64(
 structure(c("............................................................... ",
             "................................................................",
             ".                                                               ",
             "",
             ".",
             "10"
  ), class = "bitstring")
)

Function for measuring algorithmic performance of high-level and low-level integer64 functions

Description

Function for measuring algorithmic performance of high-level and low-level integer64 functions

Usage

benchmark64(nsmall = 2L^16L, nbig = 2L^25L, timefun = repeat.time)

optimizer64(
  nsmall = 2L^16L,
  nbig = 2L^25L,
  timefun = repeat.time,
  what = c("match", "%in%", "duplicated", "unique", "unipos", "table", "rank",
    "quantile"),
  uniorder = c("original", "values", "any"),
  taborder = c("values", "counts"),
  plot = TRUE
)

Arguments

Details

benchmark64 compares the following scenarios for the following use cases:

Note that the timings for the cached variants do not contain the time costs of building the cache, except for the timing of the exemplary user session, where the cache costs are included in order to evaluate amortization.

Value

benchmark64 returns a matrix with elapsed seconds, different high-level tasks in rows and different scenarios to solve the task in columns. The last row named 'SESSION' contains the elapsed seconds of the exemplary sesssion.

optimizer64 returns a dimensioned list with one row for each high-level function timed and two columns named after the values of the nsmall and nbig sample sizes. Each list cell contains a matrix with timings, low-level-methods in rows and three measurements c("prep","both","use") in columns. If it can be measured separately, prep contains the timing of preparatory work such as sorting and hashing, and use contains the timing of using the prepared work. If the function timed does both, preparation and use, the timing is in both.

Functions

• benchmark64(): compares high-level integer64 functions against the integer functions from Base R

• optimizer64(): compares for each high-level integer64 function the Base R integer function with several low-level integer64 functions with and without caching

See Also

integer64()

Examples

message("this small example using system.time does not give serious timings\n
this we do this only to run regression tests")
benchmark64(nsmall=2^7, nbig=2^13, timefun=function(expr)system.time(expr, gcFirst=FALSE))
optimizer64(nsmall=2^7, nbig=2^13, timefun=function(expr)system.time(expr, gcFirst=FALSE)
, plot=FALSE
)
## Not run: 
message("for real measurement of sufficiently large datasets run this on your machine")
benchmark64()
optimizer64()

## End(Not run)
message("let's look at the performance results on Core i7 Lenovo T410 with 8 GB RAM")
data(benchmark64.data)
print(benchmark64.data)

matplot(log2(benchmark64.data[-1,1]/benchmark64.data[-1,])
, pch=c("3", "6", "h", "s", "o", "a")
, xlab="tasks [last=session]"
, ylab="log2(relative speed) [bigger is better]"
)
matplot(t(log2(benchmark64.data[-1,1]/benchmark64.data[-1,]))
, type="b", axes=FALSE
, lwd=c(rep(1, 14), 3)
, xlab="context"
, ylab="log2(relative speed) [bigger is better]"
)
axis(1
, labels=c("32-bit", "64-bit", "hash", "sortorder", "order", "hash+sortorder")
, at=1:6
)
axis(2)
data(optimizer64.data)
print(optimizer64.data)
oldpar <- par(no.readonly = TRUE)
par(mfrow=c(2,1))
par(cex=0.7)
for (i in 1:nrow(optimizer64.data)){
 for (j in 1:2){
   tim <- optimizer64.data[[i,j]]
  barplot(t(tim))
  if (rownames(optimizer64.data)[i]=="match")
   title(paste("match", colnames(optimizer64.data)[j], "in", colnames(optimizer64.data)[3-j]))
  else if (rownames(optimizer64.data)[i]=="%in%")
   title(paste(colnames(optimizer64.data)[j], "%in%", colnames(optimizer64.data)[3-j]))
  else
   title(paste(rownames(optimizer64.data)[i], colnames(optimizer64.data)[j]))
 }
}
par(mfrow=c(1,1))

Results of performance measurement on a Core i7 Lenovo T410 8 GB RAM under Windows 7 64bit

Description

These are the results of calling benchmark64()

Usage

data(benchmark64.data)

Format

The format is:

num [1:16, 1:6] 2.55e-05 2.37 2.39 1.28 1.39 ...
- attr(*, "dimnames")=List of 2
..$ : chr [1:16] "cache" "match(s,b)" "s %in% b" "match(b,s)" ...
..$ : chr [1:6] "32-bit" "64-bit" "hashcache" "sortordercache" ...

Examples

data(benchmark64.data)
print(benchmark64.data)
matplot(log2(benchmark64.data[-1,1]/benchmark64.data[-1,])
, pch=c("3", "6", "h", "s", "o", "a")
, xlab="tasks [last=session]"
, ylab="log2(relative speed) [bigger is better]"
)
matplot(t(log2(benchmark64.data[-1,1]/benchmark64.data[-1,]))
, axes=FALSE
, type="b"
, lwd=c(rep(1, 14), 3)
, xlab="context"
, ylab="log2(relative speed) [bigger is better]"
)
axis(1
, labels=c("32-bit", "64-bit", "hash", "sortorder", "order", "hash+sortorder")
, at=1:6
)
axis(2)

Turning base R functions into S3 generics for bit64

Description

Turn those base functions S3 generic which are used in bit64

Usage

from:to
is.double(x)
match(x, table, ...)
x %in% table
rank(x, ...)
order(...)

## Default S3 method:
is.double(x)

## S3 method for class 'integer64'
is.double(x)

## S3 method for class 'integer64'
mtfrm(x)

## Default S3 method:
match(x, table, ...)

## Default S3 method:
x %in% table

## Default S3 method:
rank(x, ...)

## Default S3 method:
order(...)

Arguments

Details

The following functions are turned into S3 generics in order to dispatch methods for integer64():

• :

• is.double()

• match()

• %in%

• rank()

• order()

Value

invisible()

Note

• is.double() returns FALSE for integer64

• : currently only dispatches at its first argument, thus as.integer64(1):9 works but 1:as.integer64(9) doesn't

• match() currently only dispatches at its first argument and expects its second argument also to be integer64, otherwise throws an error. Beware of something like match(2, as.integer64(0:3))

• %in% currently only dispatches at its first argument and expects its second argument also to be integer64, otherwise throws an error. Beware of something like 2 %in% as.integer64(0:3)

• order() currently only orders a single argument, trying more than one raises an error

See Also

bit64(), S3

Examples

 is.double(as.integer64(1))
    as.integer64(1):9
 match(as.integer64(2), as.integer64(0:3))
 as.integer64(2) %in% as.integer64(0:3)

 unique(as.integer64(c(1,1,2)))
 rank(as.integer64(c(1,1,2)))


 order(as.integer64(c(1,NA,2)))

Concatenating integer64 vectors

Description

The ususal functions 'c', 'cbind' and 'rbind'

Usage

## S3 method for class 'integer64'
c(..., recursive = FALSE)

## S3 method for class 'integer64'
cbind(...)

## S3 method for class 'integer64'
rbind(...)

Arguments

Value

c() returns a integer64 vector of the total length of the input

cbind() and rbind() return a integer64 matrix

Note

R currently only dispatches generic 'c' to method 'c.integer64' if the first argument is 'integer64'

See Also

rep.integer64() seq.integer64() as.data.frame.integer64() integer64()

Examples

  c(as.integer64(1), 2:6)
  cbind(1:6, as.integer(1:6))
  rbind(1:6, as.integer(1:6))

Atomic Caching

Description

Functions for caching results attached to atomic objects

Usage

newcache(x)

jamcache(x)

cache(x)

setcache(x, which, value)

getcache(x, which)

remcache(x)

## S3 method for class 'cache'
print(x, all.names = FALSE, pattern, ...)

Arguments

Details

A cache is an environment attached to an atomic object with the attribute name 'cache'. It contains at least a reference to the atomic object that carries the cache. This is used when accessing the cache to detect whether the object carrying the cache has been modified meanwhile.

Value

See details

Functions

• newcache(): creates a new cache referencing x

• jamcache(): forces x to have a cache

• cache(): returns the cache attached to x if it is not found to be outdated

• setcache(): assigns a value into the cache of x

• getcache(): gets cache value 'which' from x

• remcache(): removes the cache from x

See Also

bit::still.identical() for testing whether to symbols point to the same RAM.

Functions that get and set small cache-content automatically when a cache is present: bit::na.count(), bit::nvalid(), bit::is.sorted(), bit::nunique() and bit::nties()

Setting big caches with a relevant memory footprint requires a conscious decision of the user: hashcache, sortcache, ordercache, sortordercache

Functions that use big caches: match.integer64(), %in%.integer64, duplicated.integer64(), unique.integer64(), unipos(), table.integer64(), keypos(), tiepos(), rank.integer64(), prank(), qtile(), quantile.integer64(), median.integer64(), and summary.integer64()

Examples

  x <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
  y <- x
  still.identical(x,y)
  y[1] <- NA
  still.identical(x,y)
  mycache <- newcache(x)
  ls(mycache)
  mycache
  rm(mycache)
  jamcache(x)
  cache(x)
  x[1] <- NA
  cache(x)
  getcache(x, "abc")
  setcache(x, "abc", 1)
  getcache(x, "abc")
  remcache(x)
  cache(x)

Cumulative Sums, Products, Extremes and lagged differences

Description

Cumulative Sums, Products, Extremes and lagged differences

Usage

## S3 method for class 'integer64'
diff(x, lag = 1L, differences = 1L, ...)

## S3 method for class 'integer64'
cummin(x)

## S3 method for class 'integer64'
cummax(x)

## S3 method for class 'integer64'
cumsum(x)

## S3 method for class 'integer64'
cumprod(x)

Arguments

Value

cummin(), cummax() , cumsum() and cumprod() return a integer64 vector of the same length as their input

diff() returns a integer64 vector shorter by lag*differences elements

See Also

sum.integer64() integer64()

Examples

  cumsum(rep(as.integer64(1), 12))
  diff(as.integer64(c(0,1:12)))
  cumsum(as.integer64(c(0, 1:12)))
  diff(cumsum(as.integer64(c(0,0,1:12))), differences=2)

Determine Duplicate Elements of integer64

Description

duplicated() determines which elements of a vector or data frame are duplicates of elements with smaller subscripts, and returns a logical vector indicating which elements (rows) are duplicates.

Usage

## S3 method for class 'integer64'
duplicated(x, incomparables = FALSE, nunique = NULL, method = NULL, ...)

Arguments

Details

This function automatically chooses from several low-level functions considering the size of x and the availability of a cache.

Suitable methods are

• hashdup (hashing)

• sortorderdup (fast ordering)

• orderdup (memory saving ordering).

Value

duplicated(): a logical vector of the same length as x.

See Also

duplicated(), unique.integer64()

Examples

x <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
duplicated(x)

stopifnot(identical(duplicated(x),  duplicated(as.integer(x))))

Extract or Replace Parts of an integer64 vector

Description

Methods to extract and replace parts of an integer64 vector.

Usage

## S3 method for class 'integer64'
x[i, ...]

## S3 replacement method for class 'integer64'
x[...] <- value

## S3 method for class 'integer64'
x[[...]]

## S3 replacement method for class 'integer64'
x[[...]] <- value

Arguments

Value

A vector or scalar of class 'integer64'

Note

You should not subscript non-existing elements and not use NAs as subscripts. The current implementation returns 9218868437227407266 instead of NA.

See Also

[ integer64()

Examples

  as.integer64(1:12)[1:3]
  x <- as.integer64(1:12)
  dim(x) <- c(3,4)
  x
  x[]
  x[,2:3]

Unary operators and functions for integer64 vectors

Description

Unary operators and functions for integer64 vectors.

Usage

## S3 method for class 'integer64'
format(x, justify = "right", ...)

## S3 method for class 'integer64'
sign(x)

## S3 method for class 'integer64'
abs(x)

## S3 method for class 'integer64'
sqrt(x)

## S3 method for class 'integer64'
log(x, base = NULL)

## S3 method for class 'integer64'
log10(x)

## S3 method for class 'integer64'
log2(x)

## S3 method for class 'integer64'
trunc(x, ...)

## S3 method for class 'integer64'
floor(x)

## S3 method for class 'integer64'
ceiling(x)

## S3 method for class 'integer64'
signif(x, digits = 6L)

## S3 method for class 'integer64'
scale(x, center = TRUE, scale = TRUE)

## S3 method for class 'integer64'
round(x, digits = 0L)

## S3 method for class 'integer64'
is.na(x)

## S3 method for class 'integer64'
is.finite(x)

## S3 method for class 'integer64'
is.infinite(x)

## S3 method for class 'integer64'
is.nan(x)

## S3 method for class 'integer64'
!x

Arguments

Value

format() returns a character vector

is.na() and ! return a logical vector

sqrt(), log(), log2() and log10() return a double vector

sign(), abs(), floor(), ceiling(), trunc() and round() return a vector of class 'integer64'

signif() is not implemented

See Also

xor.integer64() integer64()

Examples

  sqrt(as.integer64(1:12))

Big caching of hashing, sorting, ordering

Description

Functions to create cache that accelerates many operations

Usage

hashcache(x, nunique = NULL, ...)

sortcache(x, has.na = NULL)

sortordercache(x, has.na = NULL, stable = NULL)

ordercache(x, has.na = NULL, stable = NULL, optimize = "time")

Arguments

Details

The result of relative expensive operations hashmap(), bit::ramsort(), bit::ramsortorder(), and bit::ramorder() can be stored in a cache in order to avoid multiple excutions. Unless in very specific situations, the recommended method is hashsortorder only.

Value

x with a cache() that contains the result of the expensive operations, possible together with small derived information (such as nunique.integer64()) and previously cached results.

Note

Note that we consider storing the big results from sorting and/or ordering as a relevant side-effect, and therefore storing them in the cache should require a conscious decision of the user.

See Also

cache() for caching functions and nunique.integer64() for methods benefiting from small caches

Examples

  x <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
  sortordercache(x)

Hashing for 64bit integers

Description

This is an explicit implementation of hash functionality that underlies matching and other functions in R. Explicit means that you can create, store and use hash functionality directly. One advantage is that you can re-use hashmaps, which avoid re-building hashmaps again and again.

Usage

hashfun(x, ...)

## S3 method for class 'integer64'
hashfun(x, minfac = 1.41, hashbits = NULL, ...)

hashmap(x, ...)

## S3 method for class 'integer64'
hashmap(x, nunique = NULL, minfac = 1.41, hashbits = NULL, cache = NULL, ...)

hashpos(cache, ...)

## S3 method for class 'cache_integer64'
hashpos(cache, x, nomatch = NA_integer_, ...)

hashrev(cache, ...)

## S3 method for class 'cache_integer64'
hashrev(cache, x, nomatch = NA_integer_, ...)

hashfin(cache, ...)

## S3 method for class 'cache_integer64'
hashfin(cache, x, ...)

hashrin(cache, ...)

## S3 method for class 'cache_integer64'
hashrin(cache, x, ...)

hashdup(cache, ...)

## S3 method for class 'cache_integer64'
hashdup(cache, ...)

hashuni(cache, ...)

## S3 method for class 'cache_integer64'
hashuni(cache, keep.order = FALSE, ...)

hashupo(cache, ...)

## S3 method for class 'cache_integer64'
hashupo(cache, keep.order = FALSE, ...)

hashtab(cache, ...)

## S3 method for class 'cache_integer64'
hashtab(cache, ...)

hashmaptab(x, ...)

## S3 method for class 'integer64'
hashmaptab(x, nunique = NULL, minfac = 1.5, hashbits = NULL, ...)

hashmapuni(x, ...)

## S3 method for class 'integer64'
hashmapuni(x, nunique = NULL, minfac = 1.5, hashbits = NULL, ...)

hashmapupo(x, ...)

## S3 method for class 'integer64'
hashmapupo(x, nunique = NULL, minfac = 1.5, hashbits = NULL, ...)

Arguments

Details

Value

See Details

See Also

match(), runif64()

Examples

x <- as.integer64(sample(c(NA, 0:9)))
y <- as.integer64(sample(c(NA, 1:9), 10, TRUE))
hashfun(y)
hx <- hashmap(x)
hy <- hashmap(y)
ls(hy)
hashpos(hy, x)
hashrev(hx, y)
hashfin(hy, x)
hashrin(hx, y)
hashdup(hy)
hashuni(hy)
hashuni(hy, keep.order=TRUE)
hashmapuni(y)
hashupo(hy)
hashupo(hy, keep.order=TRUE)
hashmapupo(y)
hashtab(hy)
hashmaptab(y)

stopifnot(identical(match(as.integer(x),as.integer(y)),hashpos(hy, x)))
stopifnot(identical(match(as.integer(x),as.integer(y)),hashrev(hx, y)))
stopifnot(identical(as.integer(x) %in% as.integer(y), hashfin(hy, x)))
stopifnot(identical(as.integer(x) %in% as.integer(y), hashrin(hx, y)))
stopifnot(identical(duplicated(as.integer(y)), hashdup(hy)))
stopifnot(identical(as.integer64(unique(as.integer(y))), hashuni(hy, keep.order=TRUE)))
stopifnot(identical(sort(hashuni(hy, keep.order=FALSE)), sort(hashuni(hy, keep.order=TRUE))))
stopifnot(identical(y[hashupo(hy, keep.order=FALSE)], hashuni(hy, keep.order=FALSE)))
stopifnot(identical(y[hashupo(hy, keep.order=TRUE)], hashuni(hy, keep.order=TRUE)))
stopifnot(identical(hashpos(hy, hashuni(hy, keep.order=TRUE)), hashupo(hy, keep.order=TRUE)))
stopifnot(identical(hashpos(hy, hashuni(hy, keep.order=FALSE)), hashupo(hy, keep.order=FALSE)))
stopifnot(identical(hashuni(hy, keep.order=FALSE), hashtab(hy)$values))
stopifnot(identical(as.vector(table(as.integer(y), useNA="ifany"))
, hashtab(hy)$counts[order.integer64(hashtab(hy)$values)]))
stopifnot(identical(hashuni(hy, keep.order=TRUE), hashmapuni(y)))
stopifnot(identical(hashupo(hy, keep.order=TRUE), hashmapupo(y)))
stopifnot(identical(hashtab(hy), hashmaptab(y)))

    ## Not run: 
    message("explore speed given size of the hasmap in 2^hashbits and size of the data")
    message("more hashbits means more random access and less collisions")
    message("i.e. more data means less random access and more collisions")
    bits <- 24
    b <- seq(-1, 0, 0.1)
    tim <- matrix(NA, length(b), 2, dimnames=list(b, c("bits","bits+1")))
    for (i in 1:length(b)){
      n <- as.integer(2^(bits+b[i]))
      x <- as.integer64(sample(n))
      tim[i,1] <- repeat.time(hashmap(x, hashbits=bits))[3]
      tim[i,2] <- repeat.time(hashmap(x, hashbits=bits+1))[3]
      print(tim)
      matplot(b, tim)
    }
    message("we conclude that n*sqrt(2) is enough to avoid collisions")
    
## End(Not run)

Identity function for class 'integer64'

Description

This will discover any deviation between objects containing integer64 vectors.

Usage

identical.integer64(
  x,
  y,
  num.eq = FALSE,
  single.NA = FALSE,
  attrib.as.set = TRUE,
  ignore.bytecode = TRUE,
  ignore.environment = FALSE,
  ignore.srcref = TRUE,
  ...
)

Arguments

Details

This is simply a wrapper to identical() with default arguments ⁠num.eq = FALSE, single.NA = FALSE⁠.

Value

A single logical value, TRUE or FALSE, never NA and never anything other than a single value.

See Also

==.integer64 identical() integer64()

Examples

  i64 <- as.double(NA); class(i64) <- "integer64"
  identical(i64-1, i64+1)
  identical.integer64(i64-1, i64+1)

Small cache access methods

Description

These methods are packaged here for methods in packages bit64 and ff.

Usage

## S3 method for class 'integer64'
na.count(x, ...)

## S3 method for class 'integer64'
nvalid(x, ...)

## S3 method for class 'integer64'
is.sorted(x, ...)

## S3 method for class 'integer64'
nunique(x, ...)

## S3 method for class 'integer64'
nties(x, ...)

Arguments

Details

All these functions benefit from a sortcache(), ordercache() or sortordercache(). na.count(), nvalid() and nunique() also benefit from a hashcache().

Value

is.sorted returns a logical scalar, the other methods return an integer scalar.

Functions

• na.count(integer64): returns the number of NAs

• nvalid(integer64): returns the number of valid data points, usually length() minus na.count.

• is.sorted(integer64): checks for sortedness of x (NAs sorted first)

• nunique(integer64): returns the number of unique values

• nties(integer64): returns the number of tied values.

Note

If a cache() exists but the desired value is not cached, then these functions will store their result in the cache. We do not consider this a relevant side-effect, since these small cache results do not have a relevant memory footprint.

See Also

cache() for caching functions and sortordercache() for functions creating big caches

Examples

 x <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
 length(x)
 na.count(x)
 nvalid(x)
 nunique(x)
 nties(x)
 table.integer64(x)
 x

Extract Positions in redundant dimension table

Description

keypos returns the positions of the (fact table) elements that participate in their sorted unique subset (dimension table)

Usage

keypos(x, ...)

## S3 method for class 'integer64'
keypos(x, method = NULL, ...)

Arguments

Details

NAs are sorted first in the dimension table, see ramorder.integer64().

This function automatically chooses from several low-level functions considering the size of x and the availability of a cache.

Suitable methods are

• sortorderkey (fast ordering)

• orderkey (memory saving ordering).

Value

an integer vector of the same length as x containing positions relative to sort(unique(x), na.last=FALSE)

See Also

unique.integer64() for the unique subset and match.integer64() for finding positions in a different vector.

Examples

x <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
keypos(x)

stopifnot(identical(keypos(x),  match.integer64(x, sort(unique(x), na.last=FALSE))))

64-bit integer matching

Description

match returns a vector of the positions of (first) matches of its first argument in its second. %in% is a more intuitive interface as a binary operator, which returns a logical vector indicating if there is a match or not for its left operand.

Usage

## S3 method for class 'integer64'
match(x, table, nomatch = NA_integer_, nunique = NULL, method = NULL, ...)

## S3 method for class 'integer64'
x %in% table, ...

Arguments

Details

These functions automatically choose from several low-level functions considering the size of x and table and the availability of caches.

Suitable methods for ⁠%in%.integer64⁠ are

• hashpos (hash table lookup)

• hashrev (reverse lookup)

• sortorderpos (fast ordering)

• orderpos (memory saving ordering).

Suitable methods for match.integer64 are

• hashfin (hash table lookup)

• hashrin (reverse lookup)

• sortfin (fast sorting)

• orderfin (memory saving ordering).

Value

A vector of the same length as x.

match: An integer vector giving the position in table of the first match if there is a match, otherwise nomatch.

If x[i] is found to equal table[j] then the value returned in the i-th position of the return value is j, for the smallest possible j. If no match is found, the value is nomatch.

%in%: A logical vector, indicating if a match was located for each element of x: thus the values are TRUE or FALSE and never NA.

See Also

match()

Examples

x <- as.integer64(c(NA, 0:9), 32)
table <- as.integer64(c(1:9, NA))
match.integer64(x, table)
"%in%.integer64"(x, table)

x <- as.integer64(sample(c(rep(NA, 9), 0:9), 32, TRUE))
table <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
stopifnot(identical(match.integer64(x, table), match(as.integer(x), as.integer(table))))
stopifnot(identical("%in%.integer64"(x, table), as.integer(x) %in% as.integer(table)))

## Not run: 
    message("check when reverse hash-lookup beats standard hash-lookup")
    e <- 4:24
    timx <- timy <- matrix(NA, length(e), length(e), dimnames=list(e,e))
    for (iy in seq_along(e))
    for (ix in 1:iy){
        nx <- 2^e[ix]
        ny <- 2^e[iy]
        x <- as.integer64(sample(ny, nx, FALSE))
        y <- as.integer64(sample(ny, ny, FALSE))
        #hashfun(x, bits=as.integer(5))
        timx[ix,iy] <- repeat.time({
        hx <- hashmap(x)
        py <- hashrev(hx, y)
        })[3]
        timy[ix,iy] <- repeat.time({
        hy <- hashmap(y)
        px <- hashpos(hy, x)
        })[3]
        #identical(px, py)
        print(round(timx[1:iy,1:iy]/timy[1:iy,1:iy], 2), na.print="")
    }

    message("explore best low-level method given size of x and table")
    B1 <- 1:27
    B2 <- 1:27
    tim <- array(NA, dim=c(length(B1), length(B2), 5)
 , dimnames=list(B1, B2, c("hashpos","hashrev","sortpos1","sortpos2","sortpos3")))
    for (i1 in B1)
    for (i2 in B2)
    {
      b1 <- B1[i1]
      b2 <- B1[i2]
      n1 <- 2^b1
      n2 <- 2^b2
      x1 <- as.integer64(c(sample(n2, n1-1, TRUE), NA))
      x2 <- as.integer64(c(sample(n2, n2-1, TRUE), NA))
      tim[i1,i2,1] <- repeat.time({h <- hashmap(x2);hashpos(h, x1);rm(h)})[3]
      tim[i1,i2,2] <- repeat.time({h <- hashmap(x1);hashrev(h, x2);rm(h)})[3]
      s <- clone(x2); o <- seq_along(s); ramsortorder(s, o)
      tim[i1,i2,3] <- repeat.time(sortorderpos(s, o, x1, method=1))[3]
      tim[i1,i2,4] <- repeat.time(sortorderpos(s, o, x1, method=2))[3]
      tim[i1,i2,5] <- repeat.time(sortorderpos(s, o, x1, method=3))[3]
      rm(s,o)
      print(apply(tim, 1:2, function(ti)if(any(is.na(ti)))NA else which.min(ti)))
    }

## End(Not run)

Working with integer64 arrays and matrices

Description

These functions and methods facilitate working with integer64 objects stored in matrices. As ever, the primary motivation for having tailor-made functions here is that R's methods often receive input from bit64 and treat the vectors as doubles, leading to unexpected and/or incorrect results.

Usage

colSums(x, na.rm = FALSE, dims = 1L)

## Default S3 method:
colSums(x, na.rm = FALSE, dims = 1L)

## S3 method for class 'integer64'
colSums(x, na.rm = FALSE, dims = 1L)

rowSums(x, na.rm = FALSE, dims = 1L)

## Default S3 method:
rowSums(x, na.rm = FALSE, dims = 1L)

## S3 method for class 'integer64'
rowSums(x, na.rm = FALSE, dims = 1L)

## S3 method for class 'integer64'
aperm(a, perm, ...)

Arguments

Details

As of now, the colSums() and rowSums() methods are implemented as wrappers around equivalent apply() approaches, because re-using the default routine (and then applying integer64 to the result) does not work for objects with missing elements. Ideally this would eventually get its own dedicated C routine mimicking that of colSums() for integers; feature requests and PRs welcome.

aperm() is required for apply() to work, in general, otherwise FUN gets applied to a class-stripped version of the input.

Examples

A = as.integer64(1:6)
dim(A) = 3:2

colSums(A)
rowSums(A)
aperm(A, 2:1)

Results of performance measurement on a Core i7 Lenovo T410 8 GB RAM under Windows 7 64bit

Description

These are the results of calling optimizer64()

Usage

data(optimizer64.data)

Format

The format is:

List of 16
 $ : num [1:9, 1:3] 0 0 1.63 0.00114 2.44 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:9] "match" "match.64" "hashpos" "hashrev" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 $ : num [1:10, 1:3] 0 0 0 1.62 0.00114 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:10] "%in%" "match.64" "%in%.64" "hashfin" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 $ : num [1:10, 1:3] 0 0 0.00105 0.00313 0.00313 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:10] "duplicated" "duplicated.64" "hashdup" "sortorderdup1" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 $ : num [1:15, 1:3] 0 0 0 0.00104 0.00104 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:15] "unique" "unique.64" "hashmapuni" "hashuni" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 $ : num [1:14, 1:3] 0 0 0 0.000992 0.000992 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:14] "unique" "unipos.64" "hashmapupo" "hashupo" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 $ : num [1:13, 1:3] 0 0 0 0 0.000419 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:13] "tabulate" "table" "table.64" "hashmaptab" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 $ : num [1:7, 1:3] 0 0 0 0.00236 0.00714 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:7] "rank" "rank.keep" "rank.64" "sortorderrnk" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 $ : num [1:6, 1:3] 0 0 0.00189 0.00714 0 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:6] "quantile" "quantile.64" "sortqtl" "orderqtl" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 $ : num [1:9, 1:3] 0 0 0.00105 1.17 0 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:9] "match" "match.64" "hashpos" "hashrev" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 $ : num [1:10, 1:3] 0 0 0 0.00104 1.18 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:10] "%in%" "match.64" "%in%.64" "hashfin" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 $ : num [1:10, 1:3] 0 0 1.64 2.48 2.48 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:10] "duplicated" "duplicated.64" "hashdup" "sortorderdup1" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 $ : num [1:15, 1:3] 0 0 0 1.64 1.64 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:15] "unique" "unique.64" "hashmapuni" "hashuni" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 $ : num [1:14, 1:3] 0 0 0 1.62 1.62 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:14] "unique" "unipos.64" "hashmapupo" "hashupo" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 $ : num [1:13, 1:3] 0 0 0 0 0.32 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:13] "tabulate" "table" "table.64" "hashmaptab" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 $ : num [1:7, 1:3] 0 0 0 2.96 10.69 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:7] "rank" "rank.keep" "rank.64" "sortorderrnk" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 $ : num [1:6, 1:3] 0 0 1.62 10.61 0 ...
  ..- attr(*, "dimnames")=List of 2
  .. ..$ : chr [1:6] "quantile" "quantile.64" "sortqtl" "orderqtl" ...
  .. ..$ : chr [1:3] "prep" "both" "use"
 - attr(*, "dim")= int [1:2] 8 2
 - attr(*, "dimnames")=List of 2
  ..$ : chr [1:8] "match" "%in%" "duplicated" "unique" ...
  ..$ : chr [1:2] "65536" "33554432"

Examples

data(optimizer64.data)
print(optimizer64.data)
oldpar <- par(no.readonly = TRUE)
par(mfrow=c(2,1))
par(cex=0.7)
for (i in 1:nrow(optimizer64.data)){
 for (j in 1:2){
   tim <- optimizer64.data[[i,j]]
  barplot(t(tim))
  if (rownames(optimizer64.data)[i]=="match")
   title(paste("match", colnames(optimizer64.data)[j], "in", colnames(optimizer64.data)[3-j]))
  else if (rownames(optimizer64.data)[i]=="%in%")
   title(paste(colnames(optimizer64.data)[j], "%in%", colnames(optimizer64.data)[3-j]))
  else
   title(paste(rownames(optimizer64.data)[i], colnames(optimizer64.data)[j]))
 }
}
par(mfrow=c(1,1))

integer64: Maintaining S3 class attribute

Description

Maintaining integer64 S3 class attribute.

Usage

minusclass(class, whichclass)

Arguments

Value

NULL or a character vector of class attributes

See Also

oldClass() integer64()

Examples

  plusclass("inheritingclass","integer64")
  minusclass(c("inheritingclass","integer64"), "integer64")

(P)ercent (Rank)s

Description

Function prank.integer64 projects the values ⁠[min..max]⁠ via ranks ⁠[1..n]⁠ to ⁠[0..1]⁠. qtile.integer64() is the inverse function of 'prank.integer64' and projects ⁠[0..1]⁠ to ⁠[min..max]⁠.

Usage

prank(x, ...)

## S3 method for class 'integer64'
prank(x, method = NULL, ...)

Arguments

Details

Function prank.integer64 is based on rank.integer64().

Value

prank returns a numeric vector of the same length as x.

See Also

rank.integer64() for simple ranks and qtile() for the inverse function quantiles.

Examples

x <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
prank(x)

x <- x[!is.na(x)]
stopifnot(identical(x,  unname(qtile(x, probs=prank(x)))))

(Q)uan(Tile)s

Description

Function prank.integer64() projects the values ⁠[min..max]⁠ via ranks ⁠[1..n]⁠ to ⁠[0..1]⁠.

Usage

qtile(x, probs = seq(0, 1, 0.25), ...)

## S3 method for class 'integer64'
qtile(x, probs = seq(0, 1, 0.25), names = TRUE, method = NULL, ...)

## S3 method for class 'integer64'
quantile(
  x,
  probs = seq(0, 1, 0.25),
  na.rm = FALSE,
  names = TRUE,
  type = 0L,
  ...
)

## S3 method for class 'integer64'
median(x, na.rm = FALSE, ...)

## S3 method for class 'integer64'
mean(x, na.rm = FALSE, ...)

## S3 method for class 'integer64'
summary(object, ...)

Arguments

Details

qtile.ineger64 is the inverse function of 'prank.integer64' and projects ⁠[0..1]⁠ to ⁠[min..max]⁠.

Functions quantile.integer64 with type=0 and median.integer64 are convenience wrappers to qtile.

Function qtile behaves very similar to quantile.default with type=1 in that it only returns existing values, it is mostly symmetric but it is using 'round' rather than 'floor'.

Note that this implies that median.integer64 does not interpolate for even number of values (interpolation would create values that could not be represented as 64-bit integers).

This function automatically chooses from several low-level functions considering the size of x and the availability of a cache.

Suitable methods are

• sortqtl (fast sorting)

• orderqtl (memory saving ordering).

Value

prank returns a numeric vector of the same length as x.

qtile returns a vector with elements from x at the relative positions specified by probs.

See Also

rank.integer64() for simple ranks and quantile() for quantiles.

Examples

x <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
qtile(x, probs=seq(0, 1, 0.25))
quantile(x, probs=seq(0, 1, 0.25), na.rm=TRUE)
median(x, na.rm=TRUE)
summary(x)

x <- x[!is.na(x)]
stopifnot(identical(x,  unname(qtile(x, probs=prank(x)))))

Low-level intger64 methods for in-RAM sorting and ordering

Description

Fast low-level methods for sorting and ordering. The ..sortorder methods do sorting and ordering at once, which requires more RAM than ordering but is (almost) as fast as as sorting.

Usage

## S3 method for class 'integer64'
shellsort(x, has.na = TRUE, na.last = FALSE, decreasing = FALSE, ...)

## S3 method for class 'integer64'
shellsortorder(x, i, has.na = TRUE, na.last = FALSE, decreasing = FALSE, ...)

## S3 method for class 'integer64'
shellorder(x, i, has.na = TRUE, na.last = FALSE, decreasing = FALSE, ...)

## S3 method for class 'integer64'
mergesort(x, has.na = TRUE, na.last = FALSE, decreasing = FALSE, ...)

## S3 method for class 'integer64'
mergeorder(x, i, has.na = TRUE, na.last = FALSE, decreasing = FALSE, ...)

## S3 method for class 'integer64'
mergesortorder(x, i, has.na = TRUE, na.last = FALSE, decreasing = FALSE, ...)

## S3 method for class 'integer64'
quicksort(
  x,
  has.na = TRUE,
  na.last = FALSE,
  decreasing = FALSE,
  restlevel = floor(1.5 * log2(length(x))),
  ...
)

## S3 method for class 'integer64'
quicksortorder(
  x,
  i,
  has.na = TRUE,
  na.last = FALSE,
  decreasing = FALSE,
  restlevel = floor(1.5 * log2(length(x))),
  ...
)

## S3 method for class 'integer64'
quickorder(
  x,
  i,
  has.na = TRUE,
  na.last = FALSE,
  decreasing = FALSE,
  restlevel = floor(1.5 * log2(length(x))),
  ...
)

## S3 method for class 'integer64'
radixsort(
  x,
  has.na = TRUE,
  na.last = FALSE,
  decreasing = FALSE,
  radixbits = 8L,
  ...
)

## S3 method for class 'integer64'
radixsortorder(
  x,
  i,
  has.na = TRUE,
  na.last = FALSE,
  decreasing = FALSE,
  radixbits = 8L,
  ...
)

## S3 method for class 'integer64'
radixorder(
  x,
  i,
  has.na = TRUE,
  na.last = FALSE,
  decreasing = FALSE,
  radixbits = 8L,
  ...
)

## S3 method for class 'integer64'
ramsort(
  x,
  has.na = TRUE,
  na.last = FALSE,
  decreasing = FALSE,
  stable = TRUE,
  optimize = c("time", "memory"),
  VERBOSE = FALSE,
  ...
)

## S3 method for class 'integer64'
ramsortorder(
  x,
  i,
  has.na = TRUE,
  na.last = FALSE,
  decreasing = FALSE,
  stable = TRUE,
  optimize = c("time", "memory"),
  VERBOSE = FALSE,
  ...
)

## S3 method for class 'integer64'
ramorder(
  x,
  i,
  has.na = TRUE,
  na.last = FALSE,
  decreasing = FALSE,
  stable = TRUE,
  optimize = c("time", "memory"),
  VERBOSE = FALSE,
  ...
)

Arguments

Details

See bit::ramsort()

Value

These functions return the number of NAs found or assumed during sorting

Note

Note that these methods purposely violate the functional programming paradigm: they are called for the side-effect of changing some of their arguments. The sort-methods change x, the order-methods change i, and the sortoder-methods change both x and i

See Also

bit::ramsort() for the generic, ramsort.default for the methods provided by package ff, sort.integer64() for the sort interface and sortcache() for caching the work of sorting

Examples

  x <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
  x
  message("ramsort example")
  s <- clone(x)
  ramsort(s)
  message("s has been changed in-place - whether or not ramsort uses an in-place algorithm")
  s
  message("ramorder example")
  s <- clone(x)
  o <- seq_along(s)
  ramorder(s, o)
  message("o has been changed in-place - s remains unchanged")
  s
  o
  s[o]
  message("ramsortorder example")
  o <- seq_along(s)
  ramsortorder(s, o)
  message("s and o have both been changed in-place - this is much faster")
  s
  o

Sample Ranks from integer64

Description

Returns the sample ranks of the values in a vector. Ties (i.e., equal values) are averaged and missing values propagated.

Usage

## S3 method for class 'integer64'
rank(x, method = NULL, ...)

Arguments

Details

This function automatically chooses from several low-level functions considering the size of x and the availability of a cache. Suitable methods are

• sortorderrnk() (fast ordering)

• orderrnk() (memory saving ordering).

Value

A numeric vector of the same length as x.

See Also

order.integer64(), rank() and prank() for percent rank.

Examples

x <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
rank.integer64(x)

stopifnot(identical(rank.integer64(x),  rank(as.integer(x)
, na.last="keep", ties.method = "average")))

Replicate elements of integer64 vectors

Description

Replicate elements of integer64 vectors

Arguments

Value

rep() returns a integer64 vector

See Also

c.integer64() rep.integer64() as.data.frame.integer64() integer64()

Examples

  rep(as.integer64(1:2), 6)
  rep(as.integer64(1:2), c(6,6))
  rep(as.integer64(1:2), length.out=6)

integer64: random numbers

Description

Create uniform random 64-bit integers within defined range

Usage

runif64(
  n,
  min = lim.integer64()[1L],
  max = lim.integer64()[2L],
  replace = TRUE
)

Arguments

Details

For each random integer we call R's internal C interface unif_rand() twice. Each call is mapped to 2^32 unsigned integers. The two 32-bit patterns are concatenated to form the new integer64. This process is repeated until the result is not a NA_INTEGER64_.

Value

a integer64 vector

See Also

runif(), hashfun()

Examples

  runif64(12)
  runif64(12, -16, 16)
  runif64(12, 0, as.integer64(2^60)-1)  # not 2^60-1 !
  var(runif(1e4))
  var(as.double(runif64(1e4, 0, 2^40))/2^40)  # ~ = 1/12 = .08333

  table(sample(16, replace=FALSE))
  table(runif64(16, 1, 16, replace=FALSE))
  table(sample(16, replace=TRUE))
  table(runif64(16, 1, 16, replace=TRUE))

integer64: Sequence Generation

Description

Generating sequence of integer64 values

Arguments

Details

seq.integer64 does coerce its arguments 'from', 'to' and 'by' to integer64. If not provided, the argument 'by' is automatically determined as +1 or -1, but the size of 'by' is not calculated as in seq() (because this might result in a non-integer value).

Value

an integer64 vector with the generated sequence

Note

In base R : currently is not generic and does not dispatch, see section "Limitations inherited from Base R" in integer64()

See Also

c.integer64() rep.integer64() as.data.frame.integer64() integer64()

Examples

  # colon not activated: as.integer64(1):12
  seq(as.integer64(1), 12, 2)
  seq(as.integer64(1), by=2, length.out=6)

High-level intger64 methods for sorting and ordering

Description

Fast high-level methods for sorting and ordering. These are wrappers to ramsort.integer64() and friends and do not modify their arguments.

Usage

## S3 method for class 'integer64'
sort(
  x,
  decreasing = FALSE,
  has.na = TRUE,
  na.last = TRUE,
  stable = TRUE,
  optimize = c("time", "memory"),
  VERBOSE = FALSE,
  ...
)

## S3 method for class 'integer64'
order(
  ...,
  na.last = TRUE,
  decreasing = FALSE,
  has.na = TRUE,
  stable = TRUE,
  optimize = c("time", "memory"),
  VERBOSE = FALSE
)

Arguments

Details

see sort() and order()

Value

sort returns the sorted vector and vector returns the order positions.

See Also

sort(), sortcache()

Examples

  x <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
  x
  sort(x)
  message("the following has default optimize='time' which is faster but requires more RAM
, this calls 'ramorder'")
  order.integer64(x)
  message("slower with less RAM, this calls 'ramsortorder'")
  order.integer64(x, optimize="memory")

Searching and other uses of sorting for 64bit integers

Description

This is roughly an implementation of hash functionality but based on sorting instead on a hashmap. Since sorting is more informative than hashing we can do some more interesting things.

Usage

sortnut(sorted, ...)

## S3 method for class 'integer64'
sortnut(sorted, ...)

ordernut(table, order, ...)

## S3 method for class 'integer64'
ordernut(table, order, ...)

sortfin(sorted, x, ...)

## S3 method for class 'integer64'
sortfin(sorted, x, method = NULL, ...)

orderfin(table, order, x, ...)

## S3 method for class 'integer64'
orderfin(table, order, x, method = NULL, ...)

orderpos(table, order, x, ...)

## S3 method for class 'integer64'
orderpos(table, order, x, nomatch = NA, method = NULL, ...)

sortorderpos(sorted, order, x, ...)

## S3 method for class 'integer64'
sortorderpos(sorted, order, x, nomatch = NA, method = NULL, ...)

orderdup(table, order, ...)

## S3 method for class 'integer64'
orderdup(table, order, method = NULL, ...)

sortorderdup(sorted, order, ...)

## S3 method for class 'integer64'
sortorderdup(sorted, order, method = NULL, ...)

sortuni(sorted, nunique, ...)

## S3 method for class 'integer64'
sortuni(sorted, nunique, ...)

orderuni(table, order, nunique, ...)

## S3 method for class 'integer64'
orderuni(table, order, nunique, keep.order = FALSE, ...)

sortorderuni(table, sorted, order, nunique, ...)

## S3 method for class 'integer64'
sortorderuni(table, sorted, order, nunique, ...)

orderupo(table, order, nunique, ...)

## S3 method for class 'integer64'
orderupo(table, order, nunique, keep.order = FALSE, ...)

sortorderupo(sorted, order, nunique, keep.order = FALSE, ...)

## S3 method for class 'integer64'
sortorderupo(sorted, order, nunique, keep.order = FALSE, ...)

ordertie(table, order, nties, ...)

## S3 method for class 'integer64'
ordertie(table, order, nties, ...)

sortordertie(sorted, order, nties, ...)

## S3 method for class 'integer64'
sortordertie(sorted, order, nties, ...)

sorttab(sorted, nunique, ...)

## S3 method for class 'integer64'
sorttab(sorted, nunique, ...)

ordertab(table, order, nunique, ...)

## S3 method for class 'integer64'
ordertab(table, order, nunique, denormalize = FALSE, keep.order = FALSE, ...)

sortordertab(sorted, order, ...)

## S3 method for class 'integer64'
sortordertab(sorted, order, denormalize = FALSE, ...)

orderkey(table, order, na.skip.num = 0L, ...)

## S3 method for class 'integer64'
orderkey(table, order, na.skip.num = 0L, ...)

sortorderkey(sorted, order, na.skip.num = 0L, ...)

## S3 method for class 'integer64'
sortorderkey(sorted, order, na.skip.num = 0L, ...)

orderrnk(table, order, na.count, ...)

## S3 method for class 'integer64'
orderrnk(table, order, na.count, ...)

sortorderrnk(sorted, order, na.count, ...)

## S3 method for class 'integer64'
sortorderrnk(sorted, order, na.count, ...)

sortqtl(sorted, na.count, probs, ...)

## S3 method for class 'integer64'
sortqtl(sorted, na.count, probs, ...)

orderqtl(table, order, na.count, probs, ...)

## S3 method for class 'integer64'
orderqtl(table, order, na.count, probs, ...)

Arguments

Details

The functions sortfin, orderfin, orderpos and sortorderpos each offer three algorithms for finding x in table.

With method=1L each value of x is searched independently using binary search, this is fastest for small tables.

With method=2L the values of x are first sorted and then searched using doubly exponential search, this is the best allround method.

With method=3L the values of x are first sorted and then searched using simple merging, this is the fastest method if table is huge and x has similar size and distribution of values.

With method=NULL the functions use a heuristic to determine the fastest algorithm.

The functions orderdup and sortorderdup each offer two algorithms for setting the truth values in the return vector.

With method=1L the return values are set directly which causes random write access on a possibly large return vector.

With method=2L the return values are first set in a smaller bit-vector – random access limited to a smaller memory region – and finally written sequentially to the logical output vector.

With method=NULL the functions use a heuristic to determine the fastest algorithm.

Value

see details

See Also

match()

Examples

 message("check the code of 'optimizer64' for examples:")
 print(optimizer64)

Summary functions for integer64 vectors

Description

Summary functions for integer64 vectors. Function 'range' without arguments returns the smallest and largest value of the 'integer64' class.

Usage

## S3 method for class 'integer64'
any(..., na.rm = FALSE)

## S3 method for class 'integer64'
all(..., na.rm = FALSE)

## S3 method for class 'integer64'
sum(..., na.rm = FALSE)

## S3 method for class 'integer64'
prod(..., na.rm = FALSE)

## S3 method for class 'integer64'
min(..., na.rm = FALSE)

## S3 method for class 'integer64'
max(..., na.rm = FALSE)

## S3 method for class 'integer64'
range(..., na.rm = FALSE, finite = FALSE)

lim.integer64()

Arguments

Details

The numerical summary methods always return integer64. Therefore the methods for min,max and range do not return ⁠+Inf,-Inf⁠ on empty arguments, but ⁠+9223372036854775807, -9223372036854775807⁠ (in this sequence). The same is true if only NAs are submitted with argument na.rm=TRUE.

lim.integer64 returns these limits in proper order ⁠-9223372036854775807, +9223372036854775807⁠ and without a warning().

Value

all() and any() return a logical scalar

range() returns a integer64 vector with two elements

min(), max(), sum() and prod() return a integer64 scalar

See Also

mean.integer64() cumsum.integer64() integer64()

Examples

  lim.integer64()
  range(as.integer64(1:12))

Cross Tabulation and Table Creation for integer64

Description

table.integer64 uses the cross-classifying integer64 vectors to build a contingency table of the counts at each combination of vector values.

Usage

table.integer64(
  ...,
  return = c("table", "data.frame", "list"),
  order = c("values", "counts"),
  nunique = NULL,
  method = NULL,
  dnn = list.names(...),
  deparse.level = 1L
)

Arguments

Details

This function automatically chooses from several low-level functions considering the size of x and the availability of a cache.

Suitable methods are

• hashmaptab (simultaneously creating and using a hashmap)

• hashtab (first creating a hashmap then using it)

• sortordertab (fast ordering)

• ordertab (memory saving ordering).

If the argument dnn is not supplied, the internal function list.names is called to compute the 'dimname names'. If the arguments in ... are named, those names are used. For the remaining arguments, deparse.level = 0 gives an empty name, deparse.level = 1 uses the supplied argument if it is a symbol, and deparse.level = 2 will deparse the argument.

Arguments exclude, useNA, are not supported, i.e. NAs are always tabulated, and, different from table() they are sorted first if order="values".

Value

By default (with return="table") table() returns a contingency table, an object of class "table", an array of integer values. Note that unlike S the result is always an array, a 1D array if one factor is given. Note also that for multidimensional arrays this is a dense return structure which can dramatically increase RAM requirements (for large arrays with high mutual information, i.e. many possible input combinations of which only few occur) and that table() is limited to 2^31 possible combinations (e.g. two input vectors with 46340 unique values only). Finally note that the tabulated values or value-combinations are represented as dimnames and that the implied conversion of values to strings can cause severe performance problems since each string needs to be integrated into R's global string cache.

You can use the other ⁠return=⁠ options to cope with these problems, the potential combination limit is increased from 2^31 to 2^63 with these options, RAM is only required for observed combinations and string conversion is avoided.

With return="data.frame" you get a dense representation as a data.frame() (like that resulting from as.data.frame(table(...))) where only observed combinations are listed (each as a data.frame row) with the corresponding frequency counts (the latter as component named by responseName). This is the inverse of xtabs().

With return="list" you also get a dense representation as a simple list() with components

• values a integer64 vector of the technically tabulated values, for 1D this is the tabulated values themselves, for kD these are the values representing the potential combinations of input values

• counts the frequency counts

• dims only for kD: a list with the vectors of the unique values of the input dimensions

Note

Note that by using as.integer64.factor() we can also input factors into table.integer64 – only the levels() get lost.

See Also

table() for more info on the standard version coping with Base R's data types, tabulate() which can faster tabulate integers with a limited range ⁠[1L .. nL not too big]⁠, unique.integer64() for the unique values without counting them and unipos.integer64() for the positions of the unique values.

Examples

message("pure integer64 examples")
x <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
y <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
z <- sample(c(rep(NA, 9), letters), 32, TRUE)
table.integer64(x)
table.integer64(x, order="counts")
table.integer64(x, y)
table.integer64(x, y, return="data.frame")

message("via as.integer64.factor we can use 'table.integer64' also for factors")
table.integer64(x, as.integer64(as.factor(z)))

Extract Positions of Tied Elements

Description

tiepos returns the positions of those elements that participate in ties.

Usage

tiepos(x, ...)

## S3 method for class 'integer64'
tiepos(x, nties = NULL, method = NULL, ...)

Arguments

Details

This function automatically chooses from several low-level functions considering the size of x and the availability of a cache.

Suitable methods are

• sortordertie (fast ordering)

• ordertie (memory saving ordering).

Value

an integer vector of positions

See Also

rank.integer64() for possibly tied ranks and unipos.integer64() for positions of unique values.

Examples

x <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
tiepos(x)

stopifnot(identical(tiepos(x),  (1:length(x))[duplicated(x) | rev(duplicated(rev(x)))]))

Extract Positions of Unique Elements

Description

unipos returns the positions of those elements returned by unique().

Usage

unipos(x, incomparables = FALSE, order = c("original", "values", "any"), ...)

## S3 method for class 'integer64'
unipos(
  x,
  incomparables = FALSE,
  order = c("original", "values", "any"),
  nunique = NULL,
  method = NULL,
  ...
)

Arguments

Details

This function automatically chooses from several low-level functions considering the size of x and the availability of a cache.

Suitable methods are

• hashmapupo (simultaneously creating and using a hashmap)

• hashupo (first creating a hashmap then using it)

• sortorderupo (fast ordering)

• orderupo (memory saving ordering).

The default order="original" collects unique values in the order of the first appearance in x like in unique(), this costs extra processing. order="values" collects unique values in sorted order like in table(), this costs extra processing with the hash methods but comes for free. order="any" collects unique values in undefined order, possibly faster. For hash methods this will be a quasi random order, for sort methods this will be sorted order.

Value

an integer vector of positions

See Also

unique.integer64() for unique values and match.integer64() for general matching.

Examples

x <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
unipos(x)
unipos(x, order="values")

stopifnot(identical(unipos(x),  (1:length(x))[!duplicated(x)]))
stopifnot(identical(unipos(x),  match.integer64(unique(x), x)))
stopifnot(identical(unipos(x, order="values"),  match.integer64(unique(x, order="values"), x)))
stopifnot(identical(unique(x),  x[unipos(x)]))
stopifnot(identical(unique(x, order="values"),  x[unipos(x, order="values")]))

Extract Unique Elements from integer64

Description

unique returns a vector like x but with duplicate elements/rows removed.

Usage

## S3 method for class 'integer64'
unique(
  x,
  incomparables = FALSE,
  order = c("original", "values", "any"),
  nunique = NULL,
  method = NULL,
  ...
)

Arguments

Details

This function automatically chooses from several low-level functions considering the size of x and the availability of a cache.

Suitable methods are

• hashmapuni (simultaneously creating and using a hashmap)

• hashuni (first creating a hashmap then using it)

• sortuni (fast sorting for sorted order only)

• sortorderuni (fast ordering for original order only)

• orderuni (memory saving ordering).

The default order="original" returns unique values in the order of the first appearance in x like in unique(), this costs extra processing. order="values" returns unique values in sorted order like in table(), this costs extra processing with the hash methods but comes for free. order="any" returns unique values in undefined order, possibly faster. For hash methods this will be a quasi random order, for sort methods this will be sorted order.

Value

For a vector, an object of the same type of x, but with only one copy of each duplicated element. No attributes are copied (so the result has no names).

See Also

unique() for the generic, unipos() which gives the indices of the unique elements and table.integer64() which gives frequencies of the unique elements.

Examples

x <- as.integer64(sample(c(rep(NA, 9), 1:9), 32, TRUE))
unique(x)
unique(x, order="values")

stopifnot(identical(unique(x),  x[!duplicated(x)]))
stopifnot(identical(unique(x),  as.integer64(unique(as.integer(x)))))
stopifnot(identical(unique(x, order="values")
,  as.integer64(sort(unique(as.integer(x)), na.last=FALSE))))

Binary operators for integer64 vectors

Description

Binary operators for integer64 vectors.

Usage

binattr(e1, e2)

## S3 method for class 'integer64'
e1 + e2

## S3 method for class 'integer64'
e1 - e2

## S3 method for class 'integer64'
e1 %/% e2

## S3 method for class 'integer64'
e1 %% e2

## S3 method for class 'integer64'
e1 * e2

## S3 method for class 'integer64'
e1 ^ e2

## S3 method for class 'integer64'
e1 / e2

## S3 method for class 'integer64'
e1 == e2

## S3 method for class 'integer64'
e1 != e2

## S3 method for class 'integer64'
e1 < e2

## S3 method for class 'integer64'
e1 <= e2

## S3 method for class 'integer64'
e1 > e2

## S3 method for class 'integer64'
e1 >= e2

## S3 method for class 'integer64'
e1 & e2

## S3 method for class 'integer64'
e1 | e2

## S3 method for class 'integer64'
xor(x, y)

Arguments

Value

&, |, xor(), !=, ==, <, <=, >, >= return a logical vector

^ and / return a double vector

+, -, *, %/%, %% return a vector of class 'integer64'

See Also

format.integer64() integer64()

Examples

  as.integer64(1:12) - 1
  options(integer64_semantics="new")
  d <- 2.5
  i <- as.integer64(5)
  d/i  # new 0.5
  d*i  # new 13
  i*d  # new 13
  options(integer64_semantics="old")
  d/i  # old: 0.4
  d*i  # old: 10
  i*d  # old: 13