24. Random generators {VeryLargeIntegers}

Random Generators of vli Objects

Description

Random generators of vli (Very Large Integer) objects following different probability distributions.

Usage

rvlidigits(d)

rvliunif(x, y)

## Default S3 method:
rvliunif(x, y)

## S3 method for class 'numeric'
rvliunif(x, y)

## S3 method for class 'vli'
rvliunif(x, y)

rvlibin(n, p)

## Default S3 method:
rvlibin(n, p)

## S3 method for class 'numeric'
rvlibin(n, p)

## S3 method for class 'vli'
rvlibin(n, p)

rvlinegbin(s, p)

## Default S3 method:
rvlinegbin(s, p)

## S3 method for class 'numeric'
rvlinegbin(s, p)

## S3 method for class 'vli'
rvlinegbin(s, p)

rvliprime(y, iter = 10, test = "MR")

## Default S3 method:
rvliprime(y, iter = 10, test = "MR")

## S3 method for class 'numeric'
rvliprime(y, iter = 10, test = "MR")

## S3 method for class 'vli'
rvliprime(y, iter = 10, test = "MR")

Arguments

d

number of digits of the vli class object being generated; numeric

x

lower bound for the object of class vli being generated; object of class vli or 32 bits integer

y

upper bound for the object of class vli being generated; object of class vli or 32 bits integer

n

number of independent Bernoulli trials; object of class vli 32 bits integer

p

probability of success; numeric

s

number of successes; vli class object or 32 bits integer

iter

number of iterations for each number to be tested; numeric

test

chosen primality test: "F" for the Fermat Test, "SS" for the Solovay-Strassen Test or "MR" (by default) for the Miller-Rabin Test; character

Details

The function rvlidigits(d) returns a vli object of d digits randomly generated following the uniform distribution. It is the most efficient way of generating random vli objects.

The function rvliunif(x, y) returns a vli object randomly generated following the Uniform distribution with parameters x and y.

The function rvlibin(n, p) returns a vli object randomly generated following the Binomial distribution with parameters n and p, where n is the number of Bernoulli trials and p the probability of success.

The function rvlinegbin(x, y) returns a vli object randomly generated following the Negative Binomial distribution with parameters s and p, where s is the number of successes and p the probability of success.

The function rvliprime(y, iter, test) returns a vli object randomly chosen from the set of primes up to y.

Value

objects of class vli in all cases:

rvlidigits(d) returns a object of class vli belonging to the interval [0, 10^d)

rvliunif(x, y) returns a object of class vli belonging to the interval [x, y)

rvlibin(n, p) returns a object of class vli belonging to the interval [0, n]

rvlinegbin(x, y) returns a object of class vli belonging to the interval [n, Inf)

rvliprime(y, iter, test) returns a object of class vli with the value of a prime number belonging to the interval [2, y)

Author(s)

Javier Leiva Cuadrado

Examples

rvlidigits(2000)
rvliunif(3425, as.vli("2061341345304562604342"))
rvlibin(100, 0.6)
rvlinegbin(as.vli("1000000"), 0.5)
rvliprime(as.vli("100000"), iter = 10, test = "MR")