Very Large Numbers in R

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

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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

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

Maintainer: Robin K. S. Hankin <hankin.robin@gmail.com>

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
#> [1] +exp(230.26)
googol + googol/2
#> [1] +exp(230.66)

1/(googol + 1e99)
#> [1] +exp(-230.35)

(1:10)^googol
#>  [1] +exp(0)           +exp(6.9315e+99)  +exp(1.0986e+100) +exp(1.3863e+100)
#>  [5] +exp(1.6094e+100) +exp(1.7918e+100) +exp(1.9459e+100) +exp(2.0794e+100)
#>  [9] +exp(2.1972e+100) +exp(2.3026e+100)

googolplex <- 10^googol

googolplex
#> [1] +exp(2.3026e+100)

googolplex * googol  # practically the same as googolplex (!)
#> [1] +exp(2.3026e+100)