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Module Rand


module Rand: sig  end
Random number distributions

The idea here is to provide a variety of different random number distributions, for any math type you'd ever want to use, using any source of random numbers you'd ever need.

So, the *Dist modules are two-argument functors for the most part. The first parameter is one of the ones in the Math module (Or a user-provided one that has a compatible signature), that tells the code how to do basic math on a numeric type. The second parameter is a source of random numbers. Numbers generated by it are fiddled with by the Dist module to get the proper distribution.

There are several Source modules in the MtRand and FileRand packages, and SysSource in this file is a Source for the standard Random generator.

Each fully functorized module has two functions (min and max, aliases for Source.min and Source.max), and one class, rng. rng's constructor arguments vary depending on the distribution. The class has three methods: min and max, for the lowest and highest numbers an object will return, and genrand, which returns one random number according to the proper distribution.

Note that these distributions do not do any seeding of the underlying Source generator.

They also haven't been tested exceedingly well. Most of the implementations are based on algorithms and descriptions from Knuth's The Art of Computer Programming, but I might have made errors in the translation. One of these days I'll have to look into doing some real testing to make sure the distributions are accurate.


Example:

Set up a new module that works with ints using the Mersenne Twister:

module MyRNG = Rand.UniformDist2(Math.IntOps)(MtRand.IntSource)

Create a uniform RNG that returns values in the range $0\leq x<100$ and print one number:

let myrand = new MyRNG.rng 0 100 in print_int myrand#genrand; print_newline () \bigskip

module type RNGSource = sig  end
All sources must provide this signature: 
module S2USSource: functor (Ops : Math.Ops) -> functor (Source : sig  end) -> sig  end
A source that takes a source that returns numbers less than 0 and forces them to be positive 
module SysSource: sig  end
Source for the standard Random.int generator. 
module SysFloatSource: sig  end
module type IDIST = functor (Ops : sig  end) -> functor (Source : sig  end) -> sig  end
Some of the Distribution modules that work on integer ranges will implement this signature. 
module UniformDist: IDIST
new UniformDist.rng low high returns an object that will generate random numbers in the range low < x < high. 
module UniformDist2: IDIST
new UniformDist2.rng low high returns an object that will generate random numbers in the range low <= x < high. 
module type IFDIST = functor (Ops : sig  end) -> functor (Source : sig  end) -> sig  end
Module type for distributions that need a uniform float source but return integer types and whose rng class constructor takes one argument. 
module GeometricDist: IFDIST
new GeometricDist.rng mean returns an object that will generate random numbers in the geometric distribution using the given mean. 
module PoissonDist: IFDIST
new PoissonDist.rng mean returns an object that will generate random numbers in the Poisson distribution using the given mean. 
module type FDIST = functor (Source : sig  end) -> sig  end
Signature used by many distributions that work entirely with floats. 
module NormalDist: FDIST
new NormalDist.rng returns an object that will generate random floats in the normal distribution (Mean 0, standard deviation 1). 
module ExponentialDist: functor (Source : sig  end) -> sig  end
new ExponentialDist.rng mean returns an object that will generate random floats in an exponential distribution with the given mean.

Future possibilities for distributions include