Package 'Brobdingnag' reference manual

Title:	Very Large Numbers in R
Description:	Very large numbers in R. Real numbers are held using their natural logarithms, plus a logical flag indicating sign. Functionality for complex numbers is also provided. The package includes a vignette that gives a step-by-step introduction to using S4 methods.
Authors:	Robin K. S. Hankin [aut, cre]
Maintainer:	Robin K. S. Hankin <[email protected]>
License:	GPL
Version:	1.2-9-1
Built:	2024-12-12 06:13:56 UTC
Source:	https://github.com/robinhankin/brobdingnag

Very Large Numbers in R

Description

Very large numbers in R. Real numbers are held using their natural logarithms, plus a logical flag indicating sign. Functionality for complex numbers is also provided. The package includes a vignette that gives a step-by-step introduction to using S4 methods.

Details

The DESCRIPTION file:

Package:	Brobdingnag
Type:	Package
Title:	Very Large Numbers in R
Version:	1.2-9-1
Authors@R:	person(given=c("Robin", "K. S."), family="Hankin", role = c("aut","cre"), email="[email protected]", comment = c(ORCID = "0000-0001-5982-0415"))
Maintainer:	Robin K. S. Hankin <[email protected]>
Depends:	R (>= 2.13.0), methods, Matrix (>= 1.5-0)
Description:	Very large numbers in R. Real numbers are held using their natural logarithms, plus a logical flag indicating sign. Functionality for complex numbers is also provided. The package includes a vignette that gives a step-by-step introduction to using S4 methods.
Suggests:	cubature, testthat, knitr, markdown, rmarkdown
VignetteBuilder:	knitr
License:	GPL
URL:	https://github.com/RobinHankin/Brobdingnag, https://robinhankin.github.io/Brobdingnag/
Repository:	https://robinhankin.r-universe.dev
RemoteUrl:	https://github.com/robinhankin/brobdingnag
RemoteRef:	HEAD
RemoteSha:	e5a42707bdf3bae16a23c414affe52a3d5be7eb9
Author:	Robin K. S. Hankin [aut, cre] (<https://orcid.org/0000-0001-5982-0415>)

Index of help topics:

Arith-methods           Methods for Function Arith in package
                        Brobdingnag
Brobdingnag-package     Very Large Numbers in R
Compare-methods         Methods for Function Compare in Package
                        Brobdingnag
Re                      Real and imaginary manipulation
[.brob                  Extract or Replace Parts of brobs or glubs
abs                     Various logarithmic and circular functions for
                        brobs
as.numeric              Coerces to numeric or complex form
brob                    Brobdingnagian numbers
brob-class              Class "brob"
brobmat                 Brobdingnagian matrices
brobmat-class           Class '"brobmat"'
brobmat.mult            Brobdingagian matrix arithmetic
cbrob                   Combine Brobdingnagian vectors
getP                    Get and set methods for brob objects
glub                    Glubbdubdribian numbers: complex numbers with
                        Brobdingnagian real and imaginary parts
glub-class              Class "glub"
index-class             Class '"index"'
infinite                Infinite brobs and glubs
length                  Get lengths of brobs and glubs
logic.brob              Logical operations on brobs
plot                    Basic plotting of Brobs
print.brob              Methods for printing brobs and glubs
sum                     Various summary statistics for brobs and glubs
swift-class             Class "swift"

Real numbers are represented by two objects: a real, holding the logarithm of their absolute values; and a logical, indicating the sign. Multiplication and exponentiation are easy: the challenge is addition. This is achieved using the (trivial) identity $\log(e^x+e^y)=x+\log(1+e^{y-x})$ where, WLOG, $y<x$ .

Complex numbers are stored as a pair of brobs: objects of class glub.

The package is a simple example of S4 methods.

However, it could be viewed as a cautionary tale: the underlying R concepts are easy yet the S4 implementation is long and difficult. I would not recommend using S4 methods for a package as simple as this; S3 methods would have been perfectly adequate. I would suggest that S4 methods should only be used when S3 methods are demonstrably inadequate.

Author(s)

Robin K. S. Hankin [aut, cre] (<https://orcid.org/0000-0001-5982-0415>)

Maintainer: Robin K. S. Hankin <[email protected]>

References

R. K. S. Hankin 2007. “Very Large Numbers in R: Introducing Package Brobdingnag”. R News, volume 7, number 3, pages 15-16

Examples

googol <- as.brob(10)^100

googol
googol + googol/2

1/(googol + 1e99)

(1:10)^googol

googolplex <- 10^googol

googolplex

googolplex * googol  # practically the same as googolplex (!)



googol <- as.brob(10)^100

googol
googol + googol/2

1/(googol + 1e99)

(1:10)^googol

googolplex <- 10^googol

googolplex

googolplex * googol  # practically the same as googolplex (!)

Methods for Function Arith in package Brobdingnag

Description

Methods for Arithmetic functions in package Brobdingnag: +, -, *, /, ^

Note

The unary arithmetic functions (viz “+” and “-”) do no coercion.

The binary arithmetic functions coerce numeric <op> brob to brob; and numeric <op> glub, complex <op> brob, and brob <op> glub, to glub.

Author(s)

Robin K. S. Hankin

Examples

x <- as.brob(1:10)
y <- 1e10

x+y

as.numeric((x+y)-1e10)

x^(1/y)



x <- as.brob(1:10)
y <- 1e10

x+y

as.numeric((x+y)-1e10)

x^(1/y)

Coerces to numeric or complex form

Description

Coerces an object of class brob to numeric, or an object of class glub to complex

Arguments

`x`	Object of class `brob` or `glub`
`...`	Further arguments (currently ignored)

Details

Function as.numeric() coerces a brob to numeric; if given a glub, the imaginary component is ignored (and a warning given).

Function as.complex() coerces to complex.

Note

If $\left|x\right|$ is greater than .Machine$double.xmax, then as.numeric(x) returns Inf or -Inf but no warning is given.

Author(s)

Robin K. S. Hankin

Examples

a <- as.brob(1:10)
a <- cbrob(a, as.brob(10)^1e26)
a
as.numeric(a)

as.complex(10i + a)

a <- as.brob(1:10)
a <- cbrob(a, as.brob(10)^1e26)
a
as.numeric(a)

as.complex(10i + a)

Brobdingnagian numbers

Description

Create, coerce to or test for a Brobdingnagian object

Usage

brob(x = double(), positive)
as.brob(x)
is.brob(x)
brob(x = double(), positive)
as.brob(x)
is.brob(x)

Arguments

`x`	Quantity to be tested, coerced in to Brobdingnagian form
`positive`	In function `brob()`, logical indicating whether the number is positive (actually, positive or zero)

Details

Function as.brob() is the user's workhorse: use this to coerce numeric vectors to brobs.

Function is.brob() tests for its arguments being of class brob.

Function brob() takes argument x and returns a brob formally equal to $e^x$ ; set argument positive to FALSE to return $-e^x$ . Thus calling function exp(x) simply returns brob(x). This function is not really intended for the end user: it is confusing and includes no argument checking. In general numerical work, use function as.brob() instead, although be aware that if you really really want $e^{10^7}$ , you should use brob(1e7); this would be an exact representation.

Note

Complex numbers are stored as a pair of brobs: objects of class glub.

The package is a simple example of S4 methods. However, it could be viewed as a cautionary tale: the underlying R concepts are easy yet the S4 implementation is long and difficult. I would not recommend using S4 methods for a package as simple as this; S3 methods would have been perfectly adequate. I would suggest that S4 methods should only be used when S3 methods are demonstrably inadequate.

The package has poor handling of NA and NaN. Currently, as.brob(1) + as.brob(c(1,NA)) returns an error.

Author(s)

Robin K. S, Hankin

Examples


googol <- as.brob(10)^100
googolplex <- 10^googol

(googolplex/googol) / googolplex
#  Thus googolplex/googol == googolplex (!)


# use cbrob() instead of c() when Brobdingnagian numbers are involved:
cbrob(4,exp(as.brob(1e55)))


googol <- as.brob(10)^100
googolplex <- 10^googol

(googolplex/googol) / googolplex
#  Thus googolplex/googol == googolplex (!)


# use cbrob() instead of c() when Brobdingnagian numbers are involved:
cbrob(4,exp(as.brob(1e55)))

Class “brob”

Description

The formal S4 class for Brobdingnagian numbers

Objects from the Class

Objects can be created by calls of the form new("brob", ...) but this is not encouraged. Use functions brob() and, especially, as.brob() instead.

Slots

x:: Object of class "numeric" holding the log of the absolute value of the number to be represented
positive:: Object of class "logical" indicating whether the number is positive (see Note, below)

Extends

Class "swift", directly.

Note

Slot positive indicates non-negativity, as zero is conventionally considered to be “positive”.

Author(s)

Robin K. S. Hankin

Examples

new("brob",x=5,positive=TRUE)  # not intended for the user

as.brob(5)  # Standard user-oriented idiom
new("brob",x=5,positive=TRUE)  # not intended for the user

as.brob(5)  # Standard user-oriented idiom

Brobdingnagian matrices

Description

Basic matrix arithmetic for Brobdingnagian numbers. Matrix addition, multiplication extraction and replacement implemented but not the determinant or matrix inverse.

Usage

brobmat(..., positive)
newbrobmat(x,positive)
as.brobmat(x)
is.brobmat(x)
brobmat_to_brob(x)
diag(x,...)
## S3 method for class 'brobmat'
print(x,...)
t(x,...)
brobmat(..., positive)
newbrobmat(x,positive)
as.brobmat(x)
is.brobmat(x)
brobmat_to_brob(x)
diag(x,...)
## S3 method for class 'brobmat'
print(x,...)
t(x,...)

Arguments

`x`	Argument
`...`	Further arguments
`positive`	Logical, indicating whether an element is positive

Details

Basic arithmetic for Brobdingnagian matrices.

To create a Brobdingnagian matrix, use as.brobmat(); function brobmat() can be confusing.

Function brobmat() is like brob() in that it interprets its first argument as the exponent (but creates a matrix); the sign of the entry is given by Boolean argument positive. Note that brobmat() accepts a Brobdingnagian vector as primary argument, and in this case the sign is respected.

Function as.brobmat() coerces a numeric matrix to a brobmat.

Value

Generally return a brobmat or brob.

Author(s)

Robin K. S. Hankin

Examples


(M <- brobmat(-10:19,5,6))
all(M > 0)  # should be TRUE (sic)

as.brobmat(matrix(-10:19,5,6))

(M <- brobmat(-10:19,5,6))
all(M > 0)  # should be TRUE (sic)

as.brobmat(matrix(-10:19,5,6))

Class `"brobmat"`

Description

The brobmat class provides basic Brobdingnagian arithmetic for matrices.

Objects from the Class

Objects can be created by calls of the form new("brobmat", ...), although functions brobmat(), as.brobmat() are more user-friendly.

Slots

x:: Object of class "matrix" that specifes the exponent
positive:: Object of class "logical" that specifies the sign

Methods

[: signature(x = "brobmat", i = "ANY", j = "ANY"): ...
[: signature(x = "brobmat", i = "index", j = "index"): ...
[: signature(x = "brobmat", i = "index", j = "missing"): ...
[: signature(x = "brobmat", i = "missing", j = "index"): ...
[: signature(x = "brobmat", i = "missing", j = "missing"): ...
[: signature(x = "brobmat", i = "matrix", j = "missing"): ...
[<-: signature(x = "brobmat", i = "index", j = "index"): ...
[<-: signature(x = "brobmat", i = "index", j = "missing"): ...
[<-: signature(x = "brobmat", i = "missing", j = "index"): ...
[<-: signature(x = "brobmat", i = "matrix", j = "missing"): ...
[<-: signature(x = "brobmat", i = "missing", j = "missing"): ...
%*%: signature(x = "ANY", y = "brobmat"): ...
%*%: signature(x = "brobmat", y = "ANY"): ...
%*%: signature(x = "brobmat", y = "brobmat"): ...
Arith: signature(e1 = "ANY", e2 = "brobmat"): ...
Arith: signature(e1 = "brob", e2 = "brobmat"): ...
Arith: signature(e1 = "brobmat", e2 = "ANY"): ...
Arith: signature(e1 = "brobmat", e2 = "brob"): ...
Arith: signature(e1 = "brobmat", e2 = "brobmat"): ...
Arith: signature(e1 = "brobmat", e2 = "missing"): ...
as.matrix: signature(x = "brobmat"): ...
as.vector: signature(x = "brobmat"): ...
coerce: signature(from = "brobmat", to = "matrix"): ...
colnames: signature(x = "brobmat"): ...
colnames<-: signature(x = "brobmat"): ...
Compare: signature(e1 = "ANY", e2 = "brobmat"): ...
Compare: signature(e1 = "brobmat", e2 = "ANY"): ...
Compare: signature(e1 = "brobmat", e2 = "brobmat"): ...
diag: signature(x = "brobmat"): ...
dimnames: signature(x = "brobmat"): ...
dimnames<-: signature(x = "brobmat"): ...
getP: signature(x = "brobmat"): ...
getX: signature(x = "brobmat"): ...
length: signature(x = "brobmat"): ...
Math: signature(x = "brobmat"): ...
ncol: signature(x = "brobmat"): ...
nrow: signature(x = "brobmat"): ...
rownames: signature(x = "brobmat"): ...
rownames<-: signature(x = "brobmat"): ...
show: signature(object = "brobmat"): ...
t: signature(x = "brobmat"): ...

Author(s)

Robin K. S. Hankin

References

Brobdingnag R News paper

Examples

showClass("brobmat")
showClass("brobmat")

Brobdingagian matrix arithmetic

Description

Basic arithmetic for Brobdingnagian matrices

Usage

brobmat.mult(e1, e2)
brobmat.add(e1, e2)
brobmat.mult(e1, e2)
brobmat.power(e1, e2)
brobmat.inverse(e1)
brobmat.greater(e1, e2)
brobmat.equal(e1, e2)
getat(e1,e2)
brobmat.mult(e1, e2)
brobmat.add(e1, e2)
brobmat.mult(e1, e2)
brobmat.power(e1, e2)
brobmat.inverse(e1)
brobmat.greater(e1, e2)
brobmat.equal(e1, e2)
getat(e1,e2)

Arguments

e1, e2

Arguments coerced to brobmat

Details

These functions are helper functions used by the brobmat Arith group and are not designed to be user-friendly. Function getat() is a helper function that sets attributes such as dimnames of returned values.

Value

Return a brobmat, or logical for the comparison operators.

Author(s)

Robin K. S. Hankin

Examples

a <- brobmat(1:54,6,9)
rownames(a) <- letters[1:6]
a + 1e30
a-a

b <- as.brobmat(matrix(rnorm(27),9,3))
colnames(b) <- month.abb[1:3]

a %*% b

a <- brobmat(1:54,6,9)
rownames(a) <- letters[1:6]
a + 1e30
a-a

b <- as.brobmat(matrix(rnorm(27),9,3))
colnames(b) <- month.abb[1:3]

a %*% b

Combine Brobdingnagian vectors

Description

Combine Brobdingnagian or Glubdubbdribian vectors through concatenation

Usage

cbrob(x, ...)
cbrob(x, ...)

Arguments

`x`	Brobdingnagian vector
`...`	Other arguments coerced to brob form

Details

If any argument has class glub, all arguments are coerced to glubs. Otherwise, if any argument has class brob, all arguments are coerced to brobs.

Function cbrob() operates recursively, calling .cPair() repeatedly. Function .cPair() uses S4 method dispatch to call either .Brob.cpair() or .Glub.cpair() according to the classes of the arguments.

Note

As of R-2.4.0, it is apparently not possible to use S4 methods to redefine c() to coerce to class brob form and concatenate as expected. This would seem to be a reasonable interpretation of c() from the user's perspective.

Conceptually, the operation is simple: concatenate the value slot and the positive slot separately, then call brob() on the two resulting vectors. When concatenating glub objects, the real and imaginary components (being brobs) are concatenated using .Brob.cpair()

The choice of name—cbrob()—is not entirely logical. Because it operates consistently on brob and glub objects, it might be argued that cSwift() would be a more appropriate name.

Author(s)

Robin K. S. Hankin; original idea due to John Chambers

Examples

a <- as.brob(2)^1e-40
cbrob(1:4,4:1,a)
cbrob(1:4,a,1i)
a <- as.brob(2)^1e-40
cbrob(1:4,4:1,a)
cbrob(1:4,a,1i)

Methods for Function Compare in Package Brobdingnag

Description

Methods for comparison (greater than, etc) in package Brobdingnag

Note

As for min() and max(), comparison is not entirely straightforward in the presence of NAs.

The low-level workhorses are .Brob.equal() for equality and .Brob.greater() for ‘strictly greater than’. All other comparisons are calculated by combining these two.

Comparison [function .Brob.compare()] explicitly tests for a zero length argument and if given one returns logical(0) to match base behaviour.

Examples

  a <- as.brob(10)^(0.5 + 97:103)
  a < 1e100
  a <- as.brob(10)^(0.5 + 97:103)
  a < 1e100

Real and imaginary manipulation

Description

Get or set real and imaginary components of brobs or glubs.

Usage

## S4 method for signature 'glub'
Re(z)
## S4 method for signature 'glub'
Im(z)
## S4 method for signature 'glub'
Mod(z)
## S4 method for signature 'glub'
Conj(z)
## S4 method for signature 'glub'
Arg(z)
Re(z) <- value
Im(z) <- value
## S4 method for signature 'glub'
Re(z)
## S4 method for signature 'glub'
Im(z)
## S4 method for signature 'glub'
Mod(z)
## S4 method for signature 'glub'
Conj(z)
## S4 method for signature 'glub'
Arg(z)
Re(z) <- value
Im(z) <- value

Arguments

`z`	object of class `glub` (or, in the case of `Im<-()` or `Im(z) <- value`, class `brob`)
`value`	object of class `numeric` or `brob`

Value

Functions Re() and Im() return an object of class brob; functions Re<-() and Im<-() return an object of class glub

Author(s)

Robin K. S. Hankin

Examples

a <- cbrob(1:10,brob(1e100))
Im(a) <- 11:1
a


a <- cbrob(1:10,brob(1e100))
Im(a) <- 11:1
a

Extract or Replace Parts of brobs or glubs

Description

Methods for "[" and "[<-", i.e., extraction or subsetting of brobs and glubs.

Arguments

`x`	Object of class brob or glub
`i`	elements to extract or replace
`value`	replacement value

Value

Always returns an object of the same class as x.

Note

If x is a numeric vector and y a brob, one might expect typing x[1] <- y to result in x being a brob. This is impossible, according to John Chambers.

Author(s)

Robin K. S. Hankin

Examples

a <- as.brob(10)^c(-100,0,100,1000,1e32)

a[4]

a[4] <- 1e100

a

a <- as.brob(10)^c(-100,0,100,1000,1e32)

a[4]

a[4] <- 1e100

a

Get and set methods for brob objects

Description

Get and set methods for brobs: sign and value

Usage

getP(x)
getX(x)
sign(x) <- value
getP(x)
getX(x)
sign(x) <- value

Arguments

`x`	Brobdingnagian object
`value`	In function `sign<-()`, Boolean specifying whehter the brob object is positive

Author(s)

Robin K. S. Hankin

Examples

x <- as.brob(-10:10)
sign(x) <- TRUE
x <- as.brob(-10:10)
sign(x) <- TRUE

Glubbdubdribian numbers: complex numbers with Brobdingnagian real and imaginary parts

Description

Create, coerce to or test for a Glubbdubdribian object

Usage

glub(real = double(), imag = double())
as.glub(x)
is.glub(x)
glub(real = double(), imag = double())
as.glub(x)
is.glub(x)

Arguments

`real`, `imag`	Real and imaginary components of complex number: must be Brobdingnagian numbers
`x`	object to be coerced to or tested for Glubbdubdribian form

Details

A Glubbdubdribian number is the Brobdingnagian equivalent of a complex number.

Function glub() takes two arguments that are coerced to Brobdingnagian numbers and returns a Glubbdubdribian number. This function is not really intended for the end user: it is confusing and includes no argument checking. Use function as.glub() instead.

Function as.glub() is the user's workhorse: use this to coerce numeric or complex vectors to Glubbdubdribian form.

Function is.glub() tests for its arguments being Glubbdubdribian.

Note

Function glub() uses recycling inherited from cbind().

Author(s)

Robin K. S. Hankin

Examples

a <- as.glub(1:10 + 5i)
a^2 - a*a

f <- function(x){sin(x) +x^4 - 1/x}
as.complex(f(a)) - f(as.complex(a))   # should be zero (in the first
                                      # term, f() works with glubs and coerces to
                                      # complex; in the second, f()
                                      # works with complex numbers directly)
a <- as.glub(1:10 + 5i)
a^2 - a*a

f <- function(x){sin(x) +x^4 - 1/x}
as.complex(f(a)) - f(as.complex(a))   # should be zero (in the first
                                      # term, f() works with glubs and coerces to
                                      # complex; in the second, f()
                                      # works with complex numbers directly)

Class "glub"

Description

Complex Brobdingnagian numbers

Objects from the Class

A glub object holds two slots, both brobs, representing the real and imaginary components of a complex vector.

Slots

real:: Object of class "brob" representing the real component
imag:: Object of class "brob" representing the imaginary component

Extends

Class "swift", directly.

Methods

.cPair: signature(x = "brob", y = "glub"): ...
.cPair: signature(x = "ANY", y = "glub"): ...
.cPair: signature(x = "glub", y = "glub"): ...
.cPair: signature(x = "glub", y = "ANY"): ...
.cPair: signature(x = "glub", y = "brob"): ...
Im<-: signature(x = "glub"): ...
Re<-: signature(x = "glub"): ...

Author(s)

Robin K. S. Hankin

Examples

a <- as.brob(45)
new("glub",real=a, imag=a)

as.brob(5+5i)   # standard R idiom; imaginary component discarded
as.glub(5+5i)   # returns a Glubbdubdribian object


a <- as.brob(45)
new("glub",real=a, imag=a)

as.brob(5+5i)   # standard R idiom; imaginary component discarded
as.glub(5+5i)   # returns a Glubbdubdribian object

Class `"index"`

Description

A virtual class for matrix extraction, copied from the Matrix package.

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

[: signature(x = "brobmat", i = "index", j = "index"): ...
[: signature(x = "brobmat", i = "index", j = "missing"): ...
[: signature(x = "brobmat", i = "missing", j = "index"): ...
[<-: signature(x = "brobmat", i = "index", j = "index"): ...
[<-: signature(x = "brobmat", i = "index", j = "missing"): ...
[<-: signature(x = "brobmat", i = "missing", j = "index"): ...

Author(s)

Bates and Maechler, I guess

References

Douglas Bates and Martin Maechler (2019). Matrix: Sparse and Dense Matrix Classes and Methods. R package version 1.2-18. https://CRAN.R-project.org/package=Matrix

Examples

showClass("index")
showClass("index")

Infinite brobs and glubs

Description

Brobdingnagian and Glubbdubdribian infinity

Usage

## S4 method for signature 'brob'
is.infinite(x)
## S4 method for signature 'glub'
is.infinite(x)
## S4 method for signature 'brob'
is.finite(x)
## S4 method for signature 'glub'
is.finite(x)
## S4 method for signature 'brob'
is.infinite(x)
## S4 method for signature 'glub'
is.infinite(x)
## S4 method for signature 'brob'
is.finite(x)
## S4 method for signature 'glub'
is.finite(x)

Arguments

`x`	vector of class brob or glub

Details

For a Brobdingnagian number, is.infinite() returns TRUE if the exponent is infinite.

A Glubbdubdribian number is infinite if either the real or imaginary component is infinite.

Function is.finite() is simply the logical negation of is.infinite().

Author(s)

Robin K. S. Hankin

Examples


is.infinite(brob(c(1,4,Inf)))

is.infinite(glub(3,Inf))
is.infinite(glub(Inf,3))


is.infinite(exp(1e300))
is.infinite(brob(1e300))
# (Brobdingnagian infinity is bigger than regular infinity ;-)


is.infinite(brob(c(1,4,Inf)))

is.infinite(glub(3,Inf))
is.infinite(glub(Inf,3))


is.infinite(exp(1e300))
is.infinite(brob(1e300))
# (Brobdingnagian infinity is bigger than regular infinity ;-)

Get lengths of brobs and glubs

Description

Get lengths of brob and glub vectors

Usage

## S4 method for signature 'brob'
length(x)
## S4 method for signature 'glub'
length(x)
## S4 method for signature 'brob'
length(x)
## S4 method for signature 'glub'
length(x)

Arguments

`x`	vector of class brob or glub

Author(s)

Robin K. S. Hankin

Examples

x <- as.brob(-10:10)
length(x)
x <- as.brob(-10:10)
length(x)

Logical operations on brobs

Description

Logical operations on brobs are not supported

Note

The S4 group generic “Logic” appeared in R-2.4.0-patched.

Carrying out logical operations in this group will call .Brob.logic(), which reports an error.

Negation, “!”, is not part of this group: attempting to negate a brob will not activate .Brob.logic(); an “invalid argument type” error is given instead.

Author(s)

Robin K. S. Hankin

Examples


## Not run: 
!brob(10)

## End(Not run)
## Not run: 
!brob(10)

## End(Not run)

Various logarithmic and circular functions for brobs

Description

Various elementary functions for brobs

Arguments

`x`	Object of class `brob` (or sometimes `glub`)
`base`	In function `log()`, the base of the logarithm

Details

For brobs: apart from abs(), log(), exp(), sinh() and cosh(), these functions return f(as.numeric(x)) so are numeric; the exceptional functions return brobs.

For glubs: mostly direct transliteration of the appropriate formula; one might note that log(z) is defined as glub(log(Mod(x)),Arg(x)).

Author(s)

Robin K. S. Hankin

Examples

exp(as.brob(3000))  #exp(3000) is represented with zero error
exp(as.brob(3000))  #exp(3000) is represented with zero error

Basic plotting of Brobs

Description

Plotting methods. Essentially, any brob is coerced to a numeric and any glub is coerced to a complex, and the argument or arguments are passed to plot().

Usage

plot(x, y, ...)
plot(x, y, ...)

Arguments

`x`, `y`	Brob or glub
`...`	Further arguments passed to `plot()`

Author(s)

Robin K. S. Hankin

Examples

plot(as.brob(1:10))
plot(as.brob(1:10))

Methods for printing brobs and glubs

Description

Methods for printing brobs and glubs nicely using exponential notation

Usage

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

Arguments

`x`	An object of class `brob` or `glub`
`...`	Further arguments (currently ignored)

Author(s)

Robin K. S. Hankin

Examples

a <- as.brob(1:5)
dput(a)
a

a <- as.brob(1:5)
dput(a)
a

Various summary statistics for brobs and glubs

Description

Various summary statistics for brobs and glubs

Arguments

`x`, `...`	Objects of class `brob` or, in the case of `sum()` and `prob()`, class `glub`
`na.rm`	Boolean, with default `FALSE` meaning to interpret `NA`s literally and `TRUE` meaning to ignore any such elements

Details

For a brob object, being NA is not entirely straightforward. The S4 method for is.na is too “strict” for some of the functions considered here. Consider max(a) where a includes only positive, fully specified, elements, and elements with known negative sign and exponents that include NA values. Here, max(a) is unambiguously determined.

Similar logic applies to min() and, by extension, range().

Note

Function prod() is very slow for long glub vectors. It has to compute four Brobdingnagian products and two Brobdingnagian sums per element of its argument, and this takes a long time.

Author(s)

Robin K. S. Hankin

Examples

a <- as.brob(1:10)
max(cbrob(1:10,brob(NA,FALSE)))
a <- as.brob(1:10)
max(cbrob(1:10,brob(NA,FALSE)))

Class "swift"

Description

A (virtual) class that extends brob and glub objects

Objects from the Class

A virtual Class: No objects may be created from it.

Methods

No methods defined with class "swift" in the signature.

Author(s)

Robin K. S. Hankin

Package 'Brobdingnag'

Help Index

Very Large Numbers in R

Description

Details

Author(s)

References

Examples

Methods for Function Arith in package Brobdingnag

Description

Note

Author(s)

Examples

Coerces to numeric or complex form

Description

Arguments

Details

Note

Author(s)

Examples

Brobdingnagian numbers

Description

Usage

Arguments

Details

Note

Author(s)

See Also

Examples

Class “brob”

Description

Objects from the Class

Slots

Extends

Note

Author(s)

See Also

Examples

Brobdingnagian matrices

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Class "brobmat"

Description

Objects from the Class

Slots

Methods

Author(s)

References

See Also

Examples

Brobdingagian matrix arithmetic

Description

Usage

Arguments

Details

Value

Author(s)

Examples

Combine Brobdingnagian vectors

Description

Usage

Arguments

Details

Note

Author(s)

Examples

Methods for Function Compare in Package Brobdingnag

Description

Note

Examples

Real and imaginary manipulation

Description

Usage

Arguments

Value

Class `"brobmat"`

Class `"index"`