brob {Brobdingnag}

Brobdingnagian numbers

Description

Create, coerce to or test for a Brobdingnagian object

Usage

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

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.

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

See Also

glub

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)))