| Title: | A Pseudo-Random Number Generator |
| Version: | 0.0.2.1.2 |
| Description: | Provides functions for generating pseudo-random numbers that follow a uniform distribution [0,1]. Randomness tests were conducted using the National Institute of Standards and Technology test suitehttps://csrc.nist.gov/pubs/sp/800/22/r1/upd1/final, along with additional tests. The sequence generated depends on the initial values and parameters. The package includes a linear congruence map as the decision map and three chaotic maps to generate the pseudo-random sequence, which follow a uniform distribution. Other distributions can be generated from the uniform distribution using the Inversion Principle Method and BOX-Muller transformation. Small perturbations in seed values result in entirely different sequences of numbers due to the sensitive nature of the maps being used. The chaotic nature of the maps helps achieve randomness in the generator. Additionally, the generator is capable of producing random bits. |
| License: | MIT + file LICENSE |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.2.3 |
| Suggests: | testthat (≥ 3.0.0), nortest |
| Config/testthat/edition: | 3 |
| NeedsCompilation: | no |
| Packaged: | 2024-09-06 17:44:26 UTC; pervaiz |
| Author: | Sajad Ahmad Mir 
[aut, cre],
Dr. Puneet Sharma
[aut] |
| Maintainer: | Sajad Ahmad Mir <maths.acad24@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2024-09-06 18:00:02 UTC |
Baker map
Description
this is a chaotic map with the sensitive for the parameter value greater than 0.5
Usage
baker_map(x0, a)
Arguments
x0 |
seed value |
a |
parameter of the map range is greater than 0.5 |
Value
for 0<=x=<1/2 the map returns 2ax for 1/2<=x<=1 the map returns a(2x-1)mod1
Examples
baker_map(0.3,0.56)
Linear congruence map
Description
the map is a member of the family of the maps f(x)=(ax+b) mod(n)
Usage
linear_con(x0)
Arguments
x0 |
seed value |
Value
the map gives an integer ax+b mod(n)
Examples
linear_con(5)
Logistic map
Description
This is the most used chaotic map . The map is sensitive for the value of the parameter greater than 3.568
Usage
logistic_map(x0, a)
Arguments
x0 |
the seed value range from 0 to 1 |
a |
the parameter ranging from 3.5 to 4 |
Value
the map returns the a*x(1-x) for input x
Examples
logistic_map(0.26,3.5)
Random Bit generator
Description
this function generates random bits of desired length
Usage
prbits(n, Time = TRUE)
Arguments
n |
number of bits required |
Time |
it is a boolean value of TRUE/FALSE if we want to generate time dependent random bits.i.e each time we call the function with same input different output will be generated. |
Value
returns a vector of random bits of length n
Examples
prbits(2)
prbits(2)
prbits(2,Time=FALSE)
prbits(2,Time=FALSE)
prbits(10)
Cauchy distribution
Description
This function generates random numbers from standard cauchy distribution
Usage
prcauchy(n, Time = TRUE)
Arguments
n |
How many numbers we want |
Time |
time dependent or not |
Value
a vector of n numbers from cauchy distribution
Examples
prcauchy(10)
prcauchy(10,Time=TRUE)
prcauchy(10,Time=TRUE)
Exponentail distribution
Description
This function generates random numbers from exponentail distribution
Usage
prexp(n, Time = TRUE)
Arguments
n |
how many numbers we need |
Time |
time dependent or not |
Value
a vector of n numbers from exponential distribution
Examples
prexp(10)
prexp(10)
prexp(10,FALSE)
prexp(10,FALSE)
Generating numbers form Normal distribution here we use Box Muler transform to obtain normal random variable
Description
Generating numbers form Normal distribution here we use Box Muler transform to obtain normal random variable
Usage
prnorm(n)
Arguments
n |
number required |
Value
a list of pseudo random numbers from normal distribution
Examples
prnorm(10)
prnorm(100)
Uniformly Pseudo random number generator
Description
this function generates random numbers which follow uniform distribution [0,1]
Usage
prunf(
N = 100,
Time = TRUE,
n0 = 5,
x00 = 0.5362,
x01 = 0.357,
x02 = 0.235,
a1 = 3.69,
a2 = 0.7
)
Arguments
N |
How many numbers are required |
Time |
if enabled TRUE the numbers are time dependent |
n0 |
seed value of linear congruence map it can take value of any natural number |
x00 |
seed value of saw-tooth map values from 0 to 1 |
x01 |
seed value of logistic map values from 0 to 1 |
x02 |
seed value of baker map |
a1 |
parameter of logistic map the value takes from 3.5 to 4 |
a2 |
parameter of baker map the value it takes values greater than or equalt to 0.5 |
Value
gives a vector of pseudo random numbers generated of desired length
Examples
prunf(10)
prunf(10,Time=TRUE)
prunf(10,Time=TRUE)
prunf(10,Time=TRUE)
prunf(10,2)
prunf(10,Time=TRUE,2)
prunf(10,Time=TRUE,2)
prunf(10,5,0.52)
prunf(15,2,0.352)
prunf(10,2,0.652,0.235)
prunf(10,Time=TRUE,2,0.652,0.235)
prunf(9,7,0.52,0.4235,0.389)
prunf(10,Time=TRUE,2,0.752,0.235,0.351,3.8)
Saw tooth map
Description
saw tooth map is a family of maps as f(x)=b*x mod1
Usage
saw_tooth(x0)
Arguments
x0 |
seed value ranging from 0 to 1 |
Value
(3*x) mod(1)
Examples
saw_tooth(0.6)
stime function
Description
This function is used to generate a time of the system to be used for generating time dependent random numbers precise upto micro-seconds
Usage
stime()
Value
t fractional value of the time
Examples
stime()