# randomfast

Generates random numbers for a discrete distribution in constant time.

Controller: **CodeCogs**

## Dependents

## Interface

C++

Excel

## Class RandomFast

This random generator is an alternative of Discrete/RandomSample, and is optimised for discrete sampling of large distribution when you require constant time random number generation. However, due to rounding errors with this approach, if your distribution is very large, then you should use Discrete/RandomSample for more accuracy. This statistical distribution can take only discrete values, with a probability function that has a distribution function and population mean## Example

The following example displays 20 random floating point numbers from a discrete distribution. It uses two different generators to achieve this. The first generator uses a particular value to initialize the seed, while the second one is using the system timer. Notice that it was necessary to divide the timer with the MERSENNEDIV value in order to keep the seed in the (0, 1) interval. Since the seed of the first generator is never changed, the first 10 numbers will always remain the same. However since the second generator is initialized via the system timer, the next 10 numbers will obviously vary with each execution of the program, Also notice the declaration of the probability array P and value array V. They are used as constructor arguments when declaring the generators to specify the probabilities P[i] associated to each value V[i] in the values table. Always make sure that the components of P sum up to 1.#include <iostream.h> #include <conio.h> #include <time.h> #include <codecogs/stats/dists/discrete/discrete/randomfast.h> void main() { double P[4] = { 0.1, 0.1, 0.2, 0.6 }; double V[4] = { 3.14, 2.71, 0.33, 12.57 }; Stats::Dist::Discrete::Discrete::RandomFast A(4, P, V, false, 0.762); Stats::Dist::Discrete::Discrete::RandomFast B(4, P, false, time(0) / MERSENNEDIV); for (int i = 0; i < 10; ++i) cout << A.genReal() << " "; cout << endl; getch(); cout << endl; for (int i = 0; i < 10; ++i) cout << B.genReal() << " "; cout << endl getch(); }Below you will find 10 numbers corresponding to the output of the first generator :

12.57 0.33 2.71 0.33 12.57 3.14 12.57 12.57 0.33 12.57

## Speed

The average running time for generating 100,000,000 random numbers using this class on a 750MHz microprocessor is 8 seconds.## Warning

Due to rounding errors, this class is not suited for use with very large number of input probability values, i.e. when n exceeds 10,000 values, the accuracy of the random numbers deteriorates.## References

- MathWorld, http://mathworld.wolfram.com/DiscreteDistribution.html
- The Newran03 random number generator library of Robert Davies, http://www.robertnz.net/nr03doc.htm

### Authors

*Will Bateman*

##### Source Code

Source code is available when you buy a Commercial licence.

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## Members of RandomFast

#### RandomFast

Constructor that sets up the class variables and initializes the associated random number generator with the given seed.RandomFast( int `n`T* `p`bool `normalise``= true`

double `s``= 0.7323`

) *[constructor]*n The number of values p The probability array of length n (should sum up to 1) normalise Normalises the probabilities defined in p (Default=true) s Default value = 0.7323

#### RandomFast

Constructor that sets up the class variables and initializes the associated random number generator with the given seed.RandomFast( int `n`T* `prob`T* `val`double `s``= 0.59012`

bool `makecopy``= false`

) *[constructor]*n The number of values prob The probability array of length n val The set of values the generator may return s Default value = 0.59012 makecopy Default value = false

## RandomFast::init

#### RandomFast::init

template<class T> voidRandomFast<T>::init( | int | n | |

T* | p | ||

bool | normalise | ) |

normalise Default Value = true

## SampleFast

intsampleFast( | int | N | |

double* | p | ||

bool | normalise` = true` | ||

double | seed` = 0.1234` | ) |

#include <time.h> ... sample(N, p, time(0) / MERSENNEDIV);If you require more advance behaviour, we strongly recommend that directly use the underlying class randomsample that is provided with this module.

### Parameters

N the number of rates in custom distribution p an array of *N*rates that define the occurrence rate of each event.normalise Default Value = true seed sets the initial seed for the random generator. Only used in the first call to this function

### Returns

- this function returns an index in the range 0 to (N-1), which act as an index into the array define in
*p*.

##### Source Code

Source code is available when you buy a Commercial licence.

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