Test if Rng is a random-number generator. The overload taking a ElementType also makes sure that the Rng generates values of that type.

A random-number generator has at least the following features:

• it's an InputRange
• it has a 'bool isUniformRandom' field readable in CTFE

Test if Rng is seedable. The overload taking a SeedType also makes sure that the Rng can be seeded with SeedType.

A seedable random-number generator has the following additional features:

• it has a 'seed(ElementType)' function

Linear Congruential generator.

Define LinearCongruentialEngine generators with well-chosen parameters.  MinstdRand0 implements Park and Miller's "minimal standard" generator that uses 16807 for the multiplier. MinstdRand implements a variant that has slightly better spectral behavior by using the multiplier 48271. Both generators are rather simplistic.

// seed with a constant

auto rnd0 = MinstdRand0(1);
auto n = rnd0.front; // same for each run

// Seed with an unpredictable value

rnd0.seed(unpredictableSeed);
n = rnd0.front; // different across runs

The Mersenne Twister generator.

A MersenneTwisterEngine instantiated with the parameters of the original engine MT19937, generating uniformly-distributed 32-bit numbers with a period of 2 to the power of 19937. Recommended for random number generation unless memory is severely restricted, in which case a LinearCongruentialEngine would be the generator of choice.

// seed with a constant

Mt19937 gen;
auto n = gen.front; // same for each run

// Seed with an unpredictable value

gen.seed(unpredictableSeed);
n = gen.front; // different across runs

Xorshift generator using 32bit algorithm.

Implemented according to Xorshift RNGs.

Define XorshiftEngine generators with well-chosen parameters. See each bits examples of "Xorshift RNGs". Xorshift is a Xorshift128's alias because 128bits implementation is mostly used.

// Seed with a constant

auto rnd = Xorshift(1);
auto num = rnd.front;  // same for each run


// Seed with an unpredictable value

rnd.seed(unpredictableSeed());
num = rnd.front; // different across runs

A "good" seed for initializing random number engines. Initializing with  unpredictableSeed makes engines generate different random number sequences every run.

auto rnd = Random(unpredictableSeed);
auto n = rnd.front;
...

The "default", "favorite", "suggested" random number generator type on the current platform. It is an alias for one of the previously-defined generators. You may want to use it if (1) you need to generate some nice random numbers, and (2) you don't care for the minutiae of the method being used.

Global random number generator used by various functions in this module whenever no generator is specified. It is allocated per-thread and initialized to an unpredictable value for each thread.

Generates a number between a and b. The boundaries parameter controls the shape of the interval (open vs. closed on either side). Valid values for boundaries are "[]", "(]", "[)", and "()". The default interval is closed to the left and open to the right. The version that does not take urng uses the default generator rndGen.

auto gen = Random(unpredictableSeed);
// Generate an integer in [0, 1023]

auto a = uniform(0, 1024, gen);
// Generate a float in [0, 1$(RPAREN)

auto a = uniform(0.0f, 1.0f, gen);

Generates a uniformly-distributed number in the range [T.min, T.max] for any integral type T. If no random number generator is passed, uses the default rndGen.

Returns a uniformly selected member of enum E. If no random number generator is passed, uses the default rndGen.

Generates a uniform probability distribution of size n, i.e., an array of size n of positive numbers of type F that sum to 1. If useThis is provided, it is used as storage.

Shuffles elements of r using gen as a shuffler. r must be a random-access range with length.

Partially shuffles the elements of r such that upon returning r[0..n] is a random subset of r and is randomly ordered. r[n..r.length] will contain the elements not in r[0..n]. These will be in an undefined order, but will not be random in the sense that their order after  partialShuffle returns will not be independent of their order before  partialShuffle was called.

r must be a random-access range with length. n must be less than or equal to r.length.

Rolls a  dice with relative probabilities stored in proportions. Returns the index in proportions that was chosen.

auto x = dice(0.5, 0.5);   // x is 0 or 1 in equal proportions

auto y = dice(50, 50);     // y is 0 or 1 in equal proportions

auto z = dice(70, 20, 10); // z is 0 70% of the time, 1 20% of the time,

                           // and 2 10% of the time

Covers a given range r in a random manner, i.e. goes through each element of r once and only once, just in a random order. r must be a random-access range with length.

If no random number generator is passed to randomCover, the thread-global RNG rndGen will be used internally.

int[] a = [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ];
foreach (e; randomCover(a))
{
    writeln(e);
}

int[] a = [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ];
foreach (e; randomCover(a, Random(unpredictableSeed)))  // correct!

{
    writeln(e);
}

foreach (e; randomCover(a, rndGen))  // DANGEROUS!! rndGen gets copied by value

{
    writeln(e);
}

foreach (e; randomCover(a, rndGen))  // ... so this second random cover

{                                    // will output the same sequence as

    writeln(e);                      // the previous one.

}

Selects a random subsample out of r, containing exactly n elements. The order of elements is the same as in the original range. The total length of r must be known. If total is passed in, the total number of sample is considered to be total. Otherwise,  RandomSample uses r.length.

 RandomSample implements Jeffrey Scott Vitter's Algorithm D (see Vitter 1984, 1987), which selects a sample of size n in O(n) steps and requiring O(n) random variates, regardless of the size of the data being sampled. The exception to this is if traversing k elements on the input range is itself an O(k) operation (e.g. when sampling lines from an input file), in which case the sampling calculation will inevitably be of O(total).

 RandomSample will throw an exception if total is verifiably less than the total number of elements available in the input, or if n > total.

If no random number generator is passed to randomSample, the thread-global RNG rndGen will be used internally.

int[] a = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ];
// Print 5 random elements picked off from a

foreach (e; randomSample(a, 5))
{
    writeln(e);
}

int[] a = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ];
foreach (e; randomSample(a, 5, Random(unpredictableSeed)))  // correct!

{
    writeln(e);
}

foreach (e; randomSample(a, 5, rndGen))  // DANGEROUS!! rndGen gets

{                                        // copied by value

    writeln(e);
}

foreach (e; randomSample(a, 5, rndGen))  // ... so this second random

{                                        // sample will select the same

    writeln(e);                          // values as the previous one.

}