tango.math.random.Random
Random number generators
This is an attempt at having a good flexible and easy to use random number
generator.
ease of use:
simple Random (non threadsafe) and RandomSync (threadsafe) types to
create new generators (for heavy use a good idea is one Random object per thread)
several distributions can be requested like this
rand.distributionD!(type)(paramForDistribution)
the type can often be avoided if the parameters make it clear.
From it single numbers can be generated with .getRandom(), and variables
initialized either with call style (var) or with .randomize(var).
Utility functions to generate numbers directly are also available.
The choice to put all the distribution in a single object that caches them
has made (for example) the gamma distribution very easy to implement.
sample usage:
auto r=new Random();
int i; float f; real rv; real[100] ar0; real[] ar=ar0[];
// initialize with uniform distribution
i=r.uniform!(int);
f=r.uniform!(float);
rv=r.uniform!(real);
foreach (ref el;ar)
el=r.uniform!(real);
// another way to do all the previous in one go:
r(i)(f)(rv)(ar);
// unfortunetely one cannot use directly ar0...
// uniform distribution 0..10
i=r.uniformR(10);
f=r.uniformR(10.0f);
rv=r.uniformR(10.0L);
foreach (ref el;ar)
el=r.uniformR(10.0L);
// another way to do all the previous in one go:
r.uniformRD(10)(i)(f)(r)(ar);
// uniform numbers in [5;10
i=r.uniformR2(5,10);
// uniform numbers in (5;10)
f=r.uniformR2(5.0f,10.0f);
rv=r.uniformR2(5.0L,10.0L);
foreach (ref el;ar)
el=r.uniformR2(5.0L,10.0L);
// another way to do all the previous in one go:
r.uniformR2D(5.0L,10.0L)(i)(f)(r)(ar);
// uniform distribution -10..10
i=r.uniformRSymm(10);
// well you get it...
r.uniformRSymmD(10)(i)(f)(r)(ar);
// any distribution can be stored
auto r2=r.uniformRSymmD(10);
// and used later
r2(ar);
// complex distributions (normal,exp,gamma) are produced for the requested type
r.normalSource!(float)()(f);
// with sigma=2
r.normalD(2.0f)(f);
// and can be used also to initialize other types
r.normalSource!(float)()(r)(ar);
r.normalD(2.0f)(r)(ar);
// but this is different from
r.normalSource!(real)()(i)(r)(ar);
r.normalD(2.0L)(i)(r)(ar);
// as the source generates numbers of its type that then are simply cast to
// the type needed.
// Uniform distribution (as its creation for different types has no overhead)
// is never cast, so that (for example) bounds exclusion for floats is really
// guaranteed.
// For the other distribution using a distribution of different type than
// the variable should be done with care, as underflow/overflow might ensue.
//
// Some utility functions are also available
int i2=r.uniform!(int)();
int i2=r.randomize(i); // both i and i2 are initialized to the same value
float f2=r.normalSigma(3.0f);
)
)
flexibility:
Quality:
- the default Source combines two surces that pass all statistical tests
(KISS+CMWC)
(P. L'Ecuyer and R. Simard, ACM Transactions on Mathematical Software (2007),
33, 4, Article 22, for KISS, see CMWC engine for the other)
- floating point uniform generator always initializes the full mantissa, the
only flaw is a (*very* small) predilection of 0 as least important bit
(IEEE rounds to 0 in case of tie).
Using a method that initializes the full mantissa was shown to improve the
quality of subsequntly derived normal distribued numbers
(Thomas et al. Gaussian random number generators. Acm Comput Surv (2007)
vol. 39 (4) pp. 11)
Ziggurat method, a very fast and accurate method was used for both Normal and
exp distributed numbers.
gamma distribued numbers uses a method recently proposed by Marsaglia and
Tsang. The method is very fast, and should be good.
My (Fawzi's) feeling is that the transformation h(x)=(1+d*x)^3 might lose
a couple of bits of precision in some cases, but it is unclear if this
might become visible in (*very* extensive) tests or not.
the basic source can be easily be changed with something else
Efficiency:
very fast methods have been used, and some effort has been put into
optimizing some of them, but not all, but the interface has been choosen
so that close to optimal implementation can be provided through the same
interface.
Normal and Exp sources allocated only upon request: no memory waste, but
a (*very* small) speed hit, that can be avoided by storing the source in
a variable and using it (not going through the RandomG)
)
Annoyances:
License:
BSD style:
Version:
Initial release: July 2008
author:
Fawzi Mohamed
- template isFloat(T)
- if T is a float
- alias DefaultEngine = tango.math.random.engines.KissCmwc.KissCmwc!(32u, 987655670LU).KissCmwc;
- The default engine, a reasonably collision free, with good statistical properties
not easy to invert, and with a relatively small key (but not too small)
- class RandomG(SourceT = DefaultEngine);
- Class that represents a random number generator.
Normally you should get random numbers either with call-like interface:
auto r=new Random(); r(i)(j)(k);
or with randomize
r.randomize(i); r.randomize(j); r.randomize(k);
if you use this you should be able to easily switch distribution later,
as all distributions support this interface, and can be built on the top of RandomG
auto r2=r.NormalSource!(float)(); r2(i)(j)(k);
there are utility methods within random for the cases in which you do not
want to build a special distribution for just a few numbers
- this(bool randomInit = true);
- Creates and seeds a new generator
- RandomG seed();
- if source.canSeed seeds the generator using the shared rand generator
(use urandom directly if available?)
- RandomG seed(scope uint delegate() seedSource);
- if source.canSeed seeds the generator using the given source of uints
- uint next();
uint next(uint to);
uint next(uint from, uint to);
RandomG!(Sync!(DefaultEngine)) instance();
- compatibility with old Random, deprecate??
- T uniform(T, bool boundCheck = true)();
- uniform distribution on the whole range of integer types, and on
the (0;1) range for floating point types. Floating point guarantees the initialization
of the full mantissa, but due to rounding effects it might have *very* small
dependence due to rounding effects on the least significant bit (in case of tie 0 is favored).
if boundCheck is false in the floating point case bounds might be included (but with a
lower propability than other numbers)
- T uniformR(T, bool boundCheck = true)(T to);
- uniform distribution on the range [0;to) for integer types, and on
the (0;to) range for floating point types. Same caveat as uniform(T) apply
- T uniformRSymm(T, bool boundCheck = true, bool excludeZero = isFloat!(T))(T to, int iter = 2000);
- uniform distribution on the range (-to;to) for integer types, and on
the (-to;0)(0;to) range for floating point types if boundCheck is true.
If boundCheck=false the range changes to [-to;0)u(0;to] with a slightly
lower propability at the bounds for floating point numbers.
excludeZero controls if 0 is excluded or not (by default float exclude it,
ints no). Please note that the probability of 0 in floats is very small due
Cannot be used on unsigned types.
In here there is probably one of the few cases where c handling of modulo of negative
numbers is handy
- T uniformR2(T, bool boundCheck = true)(T from, T to);
- uniform distribution [from;to) for integers, and (from;to) for floating point numbers.
if boundCheck is false the bounds are included in the floating point number distribution.
the range for int and long is limited to only half the possible range
(it could be worked around using long aritmethic for int, and doing a carry by hand for long,
but I think it is seldomly needed, for int you are better off using long when needed)
- T uniformEl(T)(const(T[]) arr);
- returns a random element of the given array (which must be non empty)
- U randomizeUniform(U, bool boundCheck)(ref U a);
- randomizes the given array and returns it (for some types this is potentially
more efficient, both from the use of random numbers and speedwise)
- U randomizeUniformR(U, V, bool boundCheck = true)(ref U a, V to);
- randomizes the given array and returns it (for some types this is potentially
more efficient, both from the use of random numbers and speedwise)
- U randomizeUniformR2(U, V, W, bool boundCheck = true)(ref U a, V from, W to);
- randomizes the given variable and returns it (for some types this is potentially
more efficient, both from the use of random numbers and speedwise)
- U randomizeUniformRSymm(U, V, bool boundCheck = true, bool excludeZero = isFloat!(BaseTypeOfArrays!(U)))(ref U a, V to);
- randomizes the given variable like uniformRSymm and returns it
(for some types this is potentially more efficient, both from the use of
random numbers and speedwise)
- RandG spawn(RandG = RandomG)();
- returns another (mostly indipendent, depending on seed size) random generator
- struct UniformDistribution(T, bool boundCheck);
- uniform distribution on the whole range for integers, and on (0;1) for floats
with boundCheck=true this is equivalent to r itself, here just for completness
- UniformDistribution opCall(U, S...)(ref U a, S args);
- chainable call style initialization of variables (thorugh a call to randomize)
- T getRandom();
- returns a random number
- U randomize(U)(ref U a);
- initialize el
- struct UniformRDistribution(T, bool boundCheck);
- uniform distribution on the subrange [0;to) for integers, (0;to) for floats
- UniformRDistribution create(RandomG r, T to);
- initializes the probability distribution
- UniformRDistribution opCall(U)(ref U a);
- chainable call style initialization of variables (thorugh a call to randomize)
- T getRandom();
- returns a random number
- U randomize(U)(ref U a);
- initialize el
- struct UniformRSymmDistribution(T, bool boundCheck = true, bool excludeZero = isFloat!(T));
- uniform distribution on the subrange (-to;to) for integers, (-to;0)u(0;to) for floats
excludeZero controls if the zero should be excluded, boundCheck if the boundary should
be excluded for floats
- UniformRSymmDistribution create(RandomG r, T to);
- initializes the probability distribution
- UniformRSymmDistribution opCall(U)(ref U a);
- chainable call style initialization of variables (thorugh a call to randomize)
- T getRandom();
- returns a random number
- U randomize(U)(ref U a);
- initialize el
- struct UniformR2Distribution(T, bool boundCheck);
- uniform distribution on the subrange (-to;to) for integers, (0;to) for floats
- UniformR2Distribution create(RandomG r, T from, T to);
- initializes the probability distribution
- UniformR2Distribution opCall(U, S...)(ref U a, S args);
- chainable call style initialization of variables (thorugh a call to randomize)
- T getRandom();
- returns a random number
- U randomize(U)(ref U a);
- initialize a
- struct GammaDistribution(T);
- gamma distribution f=x^(alpha-1)*exp(-x/theta)/(gamma(alpha)*theta^alpha)
alpha has to be bigger than 1, for alpha<1 use gammaD(alpha)=gammaD(alpha+1)*pow(r.uniform!(T),1/alpha)
from Marsaglia and Tsang, ACM Transaction on Mathematical Software, Vol. 26, N. 3
2000, p 363-372
- GammaDistribution opCall(U, S...)(ref U a, S args);
- chainable call style initialization of variables (thorugh a call to randomize)
- T getRandom(T a = alpha, T t = theta);
- returns a single random number
- U randomize(U)(ref U b, T a = alpha, T t = theta);
- initializes b with gamma distribued random numbers
- U randomizeOp(U, S)(S delegate(T) op, ref U b, T a = alpha, T t = theta);
- maps op on random numbers (of type T) and initializes b with it
- NormalSource!(RandomG, T) normalSource(T)();
- generators of normal numbers (sigma=1,mu=0) of the given type
f=exp(-x*x/(2*sigma^2))/(sqrt(2 pi)*sigma)
- ExpSource!(RandomG, T) expSource(T)();
- generators of exp distribued numbers (beta=1) of the given type
f=1/beta*exp(-x/beta)
- NormalSource!(RandomG, T).NormalDistribution normalD(T)(T sigma = cast(T)1, T mu = cast(T)0);
- generators of normal numbers with a different default sigma/mu
f=exp(-x*x/(2*sigma^2))/(sqrt(2 pi)*sigma)
- ExpSource!(RandomG, T).ExpDistribution expD(T)(T beta);
- exponential distribued numbers with a different default beta
f=1/beta*exp(-x/beta)
- GammaDistribution!(T) gammaD(T)(T alpha = cast(T)1, T theta = cast(T)1);
- gamma distribued numbers with the given default alpha
- UniformDistribution!(T, true) uniformD(T)();
- uniform distribution on the whole integer range, and on (0;1) for floats
should return simply this??
- UniformDistribution!(T, false) uniformBoundsD(T)();
- uniform distribution on the whole integer range, and on [0;1] for floats
- UniformRDistribution!(T, true) uniformRD(T)(T to);
- uniform distribution [0;to) for ints, (0:to) for reals
- UniformRDistribution!(T, false) uniformRBoundsD(T)(T to);
- uniform distribution [0;to) for ints, [0:to] for reals
- UniformRSymmDistribution!(T, true, isFloat!(T)) uniformRSymmD(T)(T to);
- uniform distribution (-to;to) for ints and (-to;0)u(0;to) for reals
- UniformRSymmDistribution!(T, false, isFloat!(T)) uniformRSymmBoundsD(T)(T to);
- uniform distribution (-to;to) for ints and [-to;0)u(0;to] for reals
- UniformR2Distribution!(T, true) uniformR2D(T)(T from, T to);
- uniform distribution [from;to) for ints and (from;to) for reals
- UniformR2Distribution!(T, false) uniformR2BoundsD(T)(T from, T to);
- uniform distribution [from;to) for ints and [from;to] for reals
- T normal(T)();
- returns a normal distribued number
- T normalSigma(T)(T sigma);
- returns a normal distribued number with the given sigma
- T normalSigmaMu(T)(T sigma, T mu);
- returns a normal distribued number with the given sigma and mu
- T exp(T)();
- returns an exp distribued number
- T expBeta(T)(T beta);
- returns an exp distribued number with the given scale beta
- T gamma(T)(T alpha = cast(T)1, T sigma = cast(T)1);
- returns a gamma distribued number
from Marsaglia and Tsang, ACM Transaction on Mathematical Software, Vol. 26, N. 3
2000, p 363-372
- string toString();
- writes the current status in a string
- size_t fromString(const(char[]) s);
- reads the current status from a string (that should have been trimmed)
returns the number of chars read
- RandomG opCall(U)(ref U a);
- chainable call style initialization of variables (thorugh a call to randomize)
- T getRandom(T)();
- returns a random number
- U randomize(U)(ref U a);
- initialize el
- alias Random = RandomG!().RandomG;
- make the default random number generator type
(a non threadsafe random number generator) easily available
you can safely expect a new instance of this to be indipendent from all the others
- alias RandomSync = RandomG!(Sync!(KissCmwc!(32u, 987655670LU))).RandomG;
- default threadsafe random number generator type
- static RandomSync rand;
- shared locked (threadsafe) random number generator
initialized with urandom if available, with time otherwise
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