Brobdingnag (version 1.2-2)

Brobdingnag-package: Brobdingnagian numbers: storing large numbers by their natural logarithms

Description

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

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 Rconcepts 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.

Details

ll{ Package: Brobdingnag Type: Package Version: 1.0-1 Date: 2006-09-21 License: GPL }

The user should coerce numeric vectors to brobs using as.brob(). The 4 arithmetic operations, concatenation, trig functions, comparisons, and so forth, should operate on brobs transparently.

The basic low-level function is brob(), which takes two vectors: a double for the value and a logical for the sign (defaulting to positive). Given x, function brob(x) returns $e^x$.

Functions as.glub() and glub() perform analogous operations for the complex plane.

Examples

googol <- as.brob(1e100)
googolplex <- 10^googol


f <- function(n){exp(n)*n^n*sqrt(2*pi*n)}

f(googol)   # close to factorial(googol)