The RandomTools[QuadraticCongruence] subpackage contains functions for creating pseudo-random number generators using the Quadratic Congruence algorithm.  The integers $x_1,x_2$, ... are generated using the quadratic recurrence

where $n$ is a product of two primes and $x_0$, the seed, may be specified by the user.  They use the least significant bits of the x's to form the random numbers.

The Quadratic Congruential Generator creates generators using primes of length either 10, 12, 15 or 16 digits. These generators can be used for every day scientific applications.

Each command in the RandomTools[QuadraticCongruence] subpackage can be accessed by using either the long form or the short form of the command name in the command calling sequence.

As the underlying implementation of the RandomTools[QuadraticCongruence] subpackage is a module, it is also possible to use the form RandomTools:-QuadraticCongruence:-command to access a command from the package. For more information, see Module Members.

To display the help page for a particular QuadraticCongruence command, see Getting Help with a Command in a Package.

$\mathrm{with}\left(\mathrm{RandomTools}\left[\mathrm{QuadraticCongruence}\right]\right)$

$\left[\mathrm{NewGenerator}\right]$

$\mathrm{die}≔\mathrm{NewGenerator}\left(\mathrm{range}=1..6\right)$

$\mathrm{die}≔\mathbf{proc}\left(\right)x≔\mathrm{irem}\left(x\^2\,n\right)\;\mathrm{irem}\left(x\,6\right)\+1\mathbf{end\; proc}$

$\mathrm{die}\left(\right)$

$6$

$\mathrm{die}\left(\right)$

$2$

$\mathrm{seq}\left(\mathrm{die}\left(\right)\,i=1..10\right)$

$2,5,5,1,3,2,5,4,4,5$

$R≔\mathrm{NewGenerator}\left(\mathrm{range}=0..{10}^{10}\right)$

$R≔\mathbf{proc}\left(\right)\mathbf{local}y\&semi;x≔\mathrm{irem}\left(x\&Hat;2\&comma;n\right)\&semi;y≔\mathrm{irem}\left(x\&comma;10000000000\right)\&semi;\mathbf{while}y<10000000001\mathbf{do}x≔\mathrm{irem}\left(x\&Hat;2\&comma;n\right)\&semi;y≔10000000000\&ast;y\&plus;\mathrm{irem}\left(x\&comma;10000000000\right)\mathbf{end\; do}\&semi;\mathrm{irem}\left(y\&comma;10000000001\right)\mathbf{end\; proc}$

$m≔R\left(\right)$

$m≔742625902$

$e≔-10$

$e≔\mathrm{-10}$

$\mathrm{Float}\left(m\&comma;e\right)$

$0.0742625902$

$\mathrm{seq}\left(\mathrm{Float}\left(R\left(\right)\&comma;e\right)\&comma;i=1..5\right)$

$0.9305361902,0.0805966638,0.4297131736,0.5949740789,0.0017230061$