In this post, I will present my first R package, available on CRAN. It makes use of Prime Factorization for computations.

This small R package was initially developed to compute hypergeometric probabilities which are used in Fisher’s exact test, for instance. It was also a way to get introduced with CRAN submission :’).

## Installation and Attachment

## Installation
install.packages("primefactr")
## Attachment
library("primefactr")

## Features

### Main feature

For instance, to compute $P(X = k) = \dfrac{\binom{K}{k}~\binom{N-K}{n-k}}{\binom{N}{n}} = \dfrac{K!~(N-K)!~n!~(N-n)!}{k!~(K-k)!~(n-k)!~(N-K-n+k)!~N!},$ you can use

f <- function(k, N, K, n) {
ComputeDivFact(c(K, (N-K), n, (N-n)),
c(k, (K-k), (n-k), (N-K-n+k), N))
}
f(4, 50, 5, 10)

## [1] 0.003964583

f(5, 50, 5, 10)

## [1] 0.0001189375

You can check the results here.

Let us now check large numbers:

f(k = 1000, N = 15100, K = 5000, n = 3100)

## [1] 0.009003809

A direct approach would require computing factorial(15100), while factorial(100) = 9.332622e+157.

### Implementation

This uses a Prime Factorization to simplify computations.

I code a number as follows, $number = \prod i^{code[i]},$ or, which is equivalent, $\log(number) = \sum code[i] \times \log(i).$ For example,

• $$5$$ is coded as (0, 0, 0, 0, 1),
• $$5!$$ is coded as (1, 1, 1, 1, 1),
• $$8!$$ is coded as (1, 1, 1, 1, 1, 1, 1, 1).

So, to compute $$8! / 5!$$, you just have to substract the code of $$5!$$ from the code of $$8!$$ which gives you (0, 0, 0, 0, 0, 1, 1, 1).

Then there is the step of Prime Factorization:

Factorization by 2:

• it becomes (0, 2, 1, 1, 0, 0, 1, 0) because $$8 = 4 \times 2$$ and $$6 = 3 \times 2$$,
• then it becomes (0, 4, 1, 0, 0, 0, 1, 0) because $$4 = 2^2$$.

This is already finished (this is a small example). You get that $$8! / 5! = 2^4 \times 3^1 \times 7^1$$. Let us verify:

cat(sprintf("%s == %s", factorial(8) / factorial(5), 2^4 * 3 * 7))

## 336 == 336

### Play with primes

You can also test if a number is a prime and get all prime numbers up to a certain number.

## Submission to CRAN

It was easier than I thought. I’ve just followed the instructions of the book R packages by Hadley Wickham. I had two notes:

1. It is my first submission.
2. File README.md cannot be checked without ‘pandoc’ being installed. For this note, I used the same comment as here and CRAN didn’t complain.