| Brobdingnag-package {Brobdingnag} | R Documentation |
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.
| 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.
Robin K. S. Hankin <r.hankin@noc.soton.ac.uk>
googol <- as.brob(1e100)
googolplex <- 10^googol
f <- function(n){exp(n)*n^n*sqrt(2*pi*n)}
f(googol) # close to factorial(googol)