std.random

import std.algorithm.comparison : among, equal;
import std.range : iota;

// seed a random generator with a constant
auto rnd = Random(42);

// Generate a uniformly-distributed integer in the range [0, 14]
// If no random generator is passed, the global `rndGen` would be used
auto i = uniform(0, 15, rnd);
assert(i >= 0 && i < 15);

// Generate a uniformly-distributed real in the range [0, 100)
auto r = uniform(0.0L, 100.0L, rnd);
assert(r >= 0 && r < 100);

// Sample from a custom type
enum Fruit { apple, mango, pear }
auto f = rnd.uniform!Fruit;
with(Fruit)
assert(f.among(apple, mango, pear));

// Generate a 32-bit random number
auto u = uniform!uint(rnd);
static assert(is(typeof(u) == uint));

// Generate a random number in the range in the range [0, 1)
auto u2 = uniform01(rnd);
assert(u2 >= 0 && u2 < 1);

// Select an element randomly
auto el = 10.iota.choice(rnd);
assert(0 <= el && el < 10);

// Throw a dice with custom proportions
// 0: 20%, 1: 10%, 2: 60%
auto val = rnd.dice(0.2, 0.1, 0.6);
assert(0 <= val && val <= 2);

auto rnd2 = MinstdRand0(42);

// Select a random subsample from a range
assert(10.iota.randomSample(3, rnd2).equal([7, 8, 9]));

// Cover all elements in an array in random order
version (D_LP64) // https://issues.dlang.org/show_bug.cgi?id=15147
    assert(10.iota.randomCover(rnd2).equal([7, 4, 2, 0, 1, 6, 8, 3, 9, 5]));
else
    assert(10.iota.randomCover(rnd2).equal([4, 8, 7, 3, 5, 9, 2, 6, 0, 1]));

// Shuffle an array
version (D_LP64) // https://issues.dlang.org/show_bug.cgi?id=15147
    assert([0, 1, 2, 4, 5].randomShuffle(rnd2).equal([2, 0, 4, 5, 1]));
else
    assert([0, 1, 2, 4, 5].randomShuffle(rnd2).equal([4, 2, 5, 0, 1]));

enum bool isUniformRNG(Rng, ElementType);

enum bool isUniformRNG(Rng);

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

Examples:

struct NoRng
{
    @property uint front() {return 0;}
    @property bool empty() {return false;}
    void popFront() {}
}
static assert(!isUniformRNG!(NoRng));

struct validRng
{
    @property uint front() {return 0;}
    @property bool empty() {return false;}
    void popFront() {}

    enum isUniformRandom = true;
}
static assert(isUniformRNG!(validRng, uint));
static assert(isUniformRNG!(validRng));

enum bool isSeedable(Rng, SeedType);

enum bool isSeedable(Rng);

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

Examples:

struct validRng
{
    @property uint front() {return 0;}
    @property bool empty() {return false;}
    void popFront() {}

    enum isUniformRandom = true;
}
static assert(!isSeedable!(validRng, uint));
static assert(!isSeedable!(validRng));

struct seedRng
{
    @property uint front() {return 0;}
    @property bool empty() {return false;}
    void popFront() {}
    void seed(uint val){}
    enum isUniformRandom = true;
}
static assert(isSeedable!(seedRng, uint));
static assert(!isSeedable!(seedRng, ulong));
static assert(isSeedable!(seedRng));

struct LinearCongruentialEngine(UIntType, UIntType a, UIntType c, UIntType m) if (isUnsigned!UIntType);

Linear Congruential generator. When m = 0, no modulus is used.

Examples:

Declare your own linear congruential engine

alias CPP11LCG = LinearCongruentialEngine!(uint, 48271, 0, 2_147_483_647);

// seed with a constant
auto rnd = CPP11LCG(42);
auto n = rnd.front; // same for each run
writeln(n); // 2027382

Examples:

Declare your own linear congruential engine

// glibc's LCG
alias GLibcLCG = LinearCongruentialEngine!(uint, 1103515245, 12345, 2_147_483_648);

// Seed with an unpredictable value
auto rnd = GLibcLCG(unpredictableSeed);
auto n = rnd.front; // different across runs

Examples:

Declare your own linear congruential engine

// Visual C++'s LCG
alias MSVCLCG = LinearCongruentialEngine!(uint, 214013, 2531011, 0);

// seed with a constant
auto rnd = MSVCLCG(1);
auto n = rnd.front; // same for each run
writeln(n); // 2745024

enum bool isUniformRandom;

Mark this as a Rng

enum bool hasFixedRange;

Does this generator have a fixed range? (true).

enum UIntType min;

Lowest generated value (1 if c == 0, 0 otherwise).

enum UIntType max;

Highest generated value (modulus - 1).

enum UIntType multiplier;

enum UIntType increment;

enum UIntType modulus;

The parameters of this distribution. The random number is x = (x * multipler + increment) % modulus.

pure nothrow @nogc @safe this(UIntType x0);

Constructs a LinearCongruentialEngine generator seeded with x0.

pure nothrow @nogc @safe void seed(UIntType x0 = 1);

(Re)seeds the generator.

pure nothrow @nogc @safe void popFront();

Advances the random sequence.

const pure nothrow @nogc @property @safe UIntType front();

Returns the current number in the random sequence.

const pure nothrow @nogc @property @safe typeof(this) save();

enum bool empty;

Always false (random generators are infinite ranges).

alias MinstdRand0 = LinearCongruentialEngine!(uint, 16807u, 0u, 2147483647u).LinearCongruentialEngine;

alias MinstdRand = LinearCongruentialEngine!(uint, 48271u, 0u, 2147483647u).LinearCongruentialEngine;

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.

Examples:

// seed with a constant
auto rnd0 = MinstdRand0(1);
auto n = rnd0.front;
 // same for each run
writeln(n); // 16807

// Seed with an unpredictable value
rnd0.seed(unpredictableSeed);
n = rnd0.front; // different across runs

struct MersenneTwisterEngine(UIntType, size_t w, size_t n, size_t m, size_t r, UIntType a, size_t u, UIntType d, size_t s, UIntType b, size_t t, UIntType c, size_t l, UIntType f) if (isUnsigned!UIntType);

The Mersenne Twister generator.

Examples:

// seed with a constant
Mt19937 gen;
auto n = gen.front; // same for each run
writeln(n); // 3499211612

// Seed with an unpredictable value
gen.seed(unpredictableSeed);
n = gen.front; // different across runs

enum bool isUniformRandom;

Mark this as a Rng

enum size_t wordSize;

enum size_t stateSize;

enum size_t shiftSize;

enum size_t maskBits;

enum UIntType xorMask;

enum size_t temperingU;

enum UIntType temperingD;

enum size_t temperingS;

enum UIntType temperingB;

enum size_t temperingT;

enum UIntType temperingC;

enum size_t temperingL;

enum UIntType initializationMultiplier;

Parameters for the generator.

enum UIntType min;

Smallest generated value (0).

enum UIntType max;

Largest generated value.

enum UIntType defaultSeed;

The default seed value.

pure nothrow @nogc @safe this(UIntType value);

Constructs a MersenneTwisterEngine object.

pure nothrow @nogc @safe void seed()(UIntType value = defaultSeed);

Seeds a MersenneTwisterEngine object.

Note This seed function gives 2^w starting points (the lowest w bits of the value provided will be used). To allow the RNG to be started in any one of its internal states use the seed overload taking an InputRange.

void seed(T)(T range)
if (isInputRange!T && is(immutable(ElementType!T) == immutable(UIntType)));

Seeds a MersenneTwisterEngine object using an InputRange.

Throws:

Exception if the InputRange didn't provide enough elements to seed the generator. The number of elements required is the 'n' template parameter of the MersenneTwisterEngine struct.

pure nothrow @nogc @safe void popFront();

Advances the generator.

const pure nothrow @nogc @property @safe UIntType front();

Returns the current random value.

const pure nothrow @nogc @property @safe typeof(this) save();

enum bool empty;

Always false.

alias Mt19937 = MersenneTwisterEngine!(uint, 32LU, 624LU, 397LU, 31LU, 2567483615u, 11LU, 4294967295u, 7LU, 2636928640u, 15LU, 4022730752u, 18LU, 1812433253u).MersenneTwisterEngine;

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.

Examples:

// seed with a constant
Mt19937 gen;
auto n = gen.front; // same for each run
writeln(n); // 3499211612

// Seed with an unpredictable value
gen.seed(unpredictableSeed);
n = gen.front; // different across runs

alias Mt19937_64 = MersenneTwisterEngine!(ulong, 64LU, 312LU, 156LU, 31LU, 13043109905998158313LU, 29LU, 6148914691236517205LU, 17LU, 8202884508482404352LU, 37LU, 18444473444759240704LU, 43LU, 6364136223846793005LU).MersenneTwisterEngine;

A MersenneTwisterEngine instantiated with the parameters of the original engine MT19937-64, generating uniformly-distributed 64-bit numbers with a period of 2 to the power of 19937.

Examples:

// Seed with a constant
auto gen = Mt19937_64(12345);
auto n = gen.front; // same for each run
writeln(n); // 6597103971274460346

// Seed with an unpredictable value
gen.seed(unpredictableSeed!ulong);
n = gen.front; // different across runs

struct XorshiftEngine(UIntType, uint nbits, int sa, int sb, int sc) if (isUnsigned!UIntType && !(sa > 0 && (sb > 0) && (sc > 0)));

template XorshiftEngine(UIntType, int bits, int a, int b, int c) if (isUnsigned!UIntType && (a > 0) && (b > 0) && (c > 0))

Xorshift generator. Implemented according to Xorshift RNGs (Marsaglia, 2003) when the size is small. For larger sizes the generator uses Sebastino Vigna's optimization of using an index to avoid needing to rotate the internal array.

Period is 2 ^^ nbits - 1 except for a legacy 192-bit uint version (see note below).

Parameters:

UIntType	Word size of this xorshift generator and the return type of opCall.
nbits	The number of bits of state of this generator. This must be a positive multiple of the size in bits of UIntType. If nbits is large this struct may occupy slightly more memory than this so it can use a circular counter instead of shifting the entire array.
sa	The direction and magnitude of the 1st shift. Positive means left, negative means right.
sb	The direction and magnitude of the 2nd shift. Positive means left, negative means right.
sc	The direction and magnitude of the 3rd shift. Positive means left, negative means right.

Note For historical compatibility when nbits == 192 and UIntType is uint a legacy hybrid PRNG is used consisting of a 160-bit xorshift combined with a 32-bit counter. This combined generator has period equal to the least common multiple of 2^^160 - 1 and 2^^32.

Previous versions of XorshiftEngine did not provide any mechanism to specify the directions of the shifts, taking each shift as an unsigned magnitude. For backwards compatibility, because three shifts in the same direction cannot result in a full-period XorshiftEngine, when all three of sa, sb, sc, are positive XorshiftEngine` treats them as unsigned magnitudes and uses shift directions to match the old behavior of XorshiftEngine.

Not every set of shifts results in a full-period xorshift generator. The template does not currently at compile-time perform a full check for maximum period but in a future version might reject parameters resulting in shorter periods.

Examples:

alias Xorshift96  = XorshiftEngine!(uint, 96,  10, 5,  26);
auto rnd = Xorshift96(42);
auto num = rnd.front;  // same for each run
writeln(num); // 2704588748

enum bool isUniformRandom;

Mark this as a Rng

enum auto empty;

Always false (random generators are infinite ranges).

enum UIntType min;

Smallest generated value.

enum UIntType max;

Largest generated value.

pure nothrow @nogc @safe this()(UIntType x0);

Constructs a XorshiftEngine generator seeded with x0.

Parameters:

UIntType x0

value used to deterministically initialize internal state

pure nothrow @nogc @safe void seed()(UIntType x0);

(Re)seeds the generator.

Parameters:

UIntType x0

value used to deterministically initialize internal state

const pure nothrow @nogc @property @safe UIntType front();

Returns the current number in the random sequence.

pure nothrow @nogc @safe void popFront();

Advances the random sequence.

const pure nothrow @nogc @property @safe typeof(this) save();

Captures a range state.

alias Xorshift32 = XorshiftEngine!(uint, 32u, 13, -17, 15).XorshiftEngine;

alias Xorshift64 = XorshiftEngine!(uint, 64u, 10, -13, -10).XorshiftEngine;

alias Xorshift96 = XorshiftEngine!(uint, 96u, 10, -5, -26).XorshiftEngine;

alias Xorshift128 = XorshiftEngine!(uint, 128u, 11, -8, -19).XorshiftEngine;

alias Xorshift160 = XorshiftEngine!(uint, 160u, 2, -1, -4).XorshiftEngine;

alias Xorshift192 = XorshiftEngine!(uint, 192u, -2, 1, 4).XorshiftEngine;

alias Xorshift = XorshiftEngine!(uint, 128u, 11, -8, -19).XorshiftEngine;

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.

Examples:

// Seed with a constant
auto rnd = Xorshift(1);
auto num = rnd.front;  // same for each run
writeln(num); // 1405313047

// Seed with an unpredictable value
rnd.seed(unpredictableSeed);
num = rnd.front; // different across rnd

nothrow @nogc @property @trusted uint unpredictableSeed();

template unpredictableSeed(UIntType) if (isUnsigned!UIntType)

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

Returns:

A single unsigned integer seed value, different on each successive call

Note In general periodically 'reseeding' a PRNG does not improve its quality and in some cases may harm it. For an extreme example the Mersenne Twister has 2 ^^ 19937 - 1 distinct states but after seed(uint) is called it can only be in one of 2 ^^ 32 distinct states regardless of how excellent the source of entropy is.

Examples:

auto rnd = Random(unpredictableSeed);
auto n = rnd.front;
static assert(is(typeof(n) == uint));

alias Random = MersenneTwisterEngine!(uint, 32LU, 624LU, 397LU, 31LU, 2567483615u, 11LU, 4294967295u, 7LU, 2636928640u, 15LU, 4022730752u, 18LU, 1812433253u).MersenneTwisterEngine;

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.

nothrow @nogc @property ref @safe Random rndGen();

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.

Returns:

A singleton instance of the default random number generator

Examples:

import std.algorithm.iteration : sum;
import std.range : take;
auto rnd = rndGen;
assert(rnd.take(3).sum > 0);

auto uniform(string boundaries = "[)", T1, T2)(T1 a, T2 b)
if (!is(CommonType!(T1, T2) == void));

auto uniform(string boundaries = "[)", T1, T2, UniformRandomNumberGenerator)(T1 a, T2 b, ref UniformRandomNumberGenerator urng)
if (isFloatingPoint!(CommonType!(T1, T2)) && isUniformRNG!UniformRandomNumberGenerator);

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.

Parameters:

T1 a	lower bound of the uniform distribution
T2 b	upper bound of the uniform distribution
UniformRandomNumberGenerator urng	(optional) random number generator to use; if not specified, defaults to rndGen

Returns:

A single random variate drawn from the uniform distribution between a and b, whose type is the common type of these parameters

Examples:

auto rnd = Random(unpredictableSeed);

// Generate an integer in [0, 1023]
auto a = uniform(0, 1024, rnd);
assert(0 <= a && a < 1024);

// Generate a float in [0, 1)
auto b = uniform(0.0f, 1.0f, rnd);
assert(0 <= b && b < 1);

// Generate a float in [0, 1]
b = uniform!"[]"(0.0f, 1.0f, rnd);
assert(0 <= b && b <= 1);

// Generate a float in (0, 1)
b = uniform!"()"(0.0f, 1.0f, rnd);
assert(0 < b && b < 1);

Examples:

Create an array of random numbers using range functions and UFCS

import std.array : array;
import std.range : generate, takeExactly;

int[] arr = generate!(() => uniform(0, 100)).takeExactly(10).array;
writeln(arr.length); // 10
assert(arr[0] >= 0 && arr[0] < 100);

auto uniform(T, UniformRandomNumberGenerator)(ref UniformRandomNumberGenerator urng)
if (!is(T == enum) && (isIntegral!T || isSomeChar!T) && isUniformRNG!UniformRandomNumberGenerator);

auto uniform(T)()
if (!is(T == enum) && (isIntegral!T || isSomeChar!T));

auto uniform(E, UniformRandomNumberGenerator)(ref UniformRandomNumberGenerator urng)
if (is(E == enum) && isUniformRNG!UniformRandomNumberGenerator);

auto uniform(E)()
if (is(E == enum));

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

If an enum is used as type, the random variate is drawn with equal probability from any of the possible values of the enum E.

Parameters:

UniformRandomNumberGenerator urng

(optional) random number generator to use; if not specified, defaults to rndGen

Returns:

Random variate drawn from the uniform distribution across all possible values of the integral, character or enum type T.

Examples:

auto rnd = MinstdRand0(42);

writeln(rnd.uniform!ubyte); // 102
writeln(rnd.uniform!ulong); // 4838462006927449017

enum Fruit { apple, mango, pear }
version (D_LP64) // https://issues.dlang.org/show_bug.cgi?id=15147
writeln(rnd.uniform!Fruit); // Fruit.mango

T uniform01(T = double)()
if (isFloatingPoint!T);

T uniform01(T = double, UniformRNG)(ref UniformRNG rng)
if (isFloatingPoint!T && isUniformRNG!UniformRNG);

Generates a uniformly-distributed floating point number of type T in the range [0, 1). If no random number generator is specified, the default RNG rndGen will be used as the source of randomness.

uniform01 offers a faster generation of random variates than the equivalent uniform!"[)"(0.0, 1.0) and so may be preferred for some applications.

Parameters:

UniformRNG rng

(optional) random number generator to use; if not specified, defaults to rndGen

Returns:

Floating-point random variate of type T drawn from the uniform distribution across the half-open interval [0, 1).

Examples:

import std.math.operations : feqrel;

auto rnd = MinstdRand0(42);

// Generate random numbers in the range in the range [0, 1)
auto u1 = uniform01(rnd);
assert(u1 >= 0 && u1 < 1);

auto u2 = rnd.uniform01!float;
assert(u2 >= 0 && u2 < 1);

// Confirm that the random values with the initial seed 42 are 0.000328707 and 0.524587
assert(u1.feqrel(0.000328707) > 20);
assert(u2.feqrel(0.524587) > 20);

F[] uniformDistribution(F = double)(size_t n, F[] useThis = null)
if (isFloatingPoint!F);

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.

Examples:

import std.algorithm.iteration : reduce;
import std.math.operations : isClose;

auto a = uniformDistribution(5);
writeln(a.length); // 5
assert(isClose(reduce!"a + b"(a), 1));

a = uniformDistribution(10, a);
writeln(a.length); // 10
assert(isClose(reduce!"a + b"(a), 1));

ref auto choice(Range, RandomGen = Random)(Range range, ref RandomGen urng)
if (isRandomAccessRange!Range && hasLength!Range && isUniformRNG!RandomGen);

ref auto choice(Range)(Range range);

ref auto choice(Range, RandomGen = Random)(ref Range range, ref RandomGen urng)
if (isRandomAccessRange!Range && hasLength!Range && isUniformRNG!RandomGen);

ref auto choice(Range)(ref Range range);

Returns a random, uniformly chosen, element e from the supplied Range range. If no random number generator is passed, the default rndGen is used.

Parameters:

Range range	a random access range that has the length property defined
RandomGen urng	(optional) random number generator to use; if not specified, defaults to rndGen

Returns:

A single random element drawn from the range. If it can, it will return a ref to the range element, otherwise it will return a copy.

Examples:

auto rnd = MinstdRand0(42);

auto elem  = [1, 2, 3, 4, 5].choice(rnd);
version (D_LP64) // https://issues.dlang.org/show_bug.cgi?id=15147
writeln(elem); // 3

Range randomShuffle(Range, RandomGen)(Range r, ref RandomGen gen)
if (isRandomAccessRange!Range && isUniformRNG!RandomGen);

Range randomShuffle(Range)(Range r)
if (isRandomAccessRange!Range);

Shuffles elements of r using gen as a shuffler. r must be a random-access range with length. If no RNG is specified, rndGen will be used.

Parameters:

Range r	random-access range whose elements are to be shuffled
RandomGen gen	(optional) random number generator to use; if not specified, defaults to rndGen

Returns:

The shuffled random-access range.

Examples:

auto rnd = MinstdRand0(42);

auto arr = [1, 2, 3, 4, 5].randomShuffle(rnd);
version (D_LP64) // https://issues.dlang.org/show_bug.cgi?id=15147
writeln(arr); // [3, 5, 2, 4, 1]

Range partialShuffle(Range, RandomGen)(Range r, in size_t n, ref RandomGen gen)
if (isRandomAccessRange!Range && isUniformRNG!RandomGen);

Range partialShuffle(Range)(Range r, in size_t n)
if (isRandomAccessRange!Range);

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. If no RNG is specified, rndGen will be used.

Parameters:

Range r	random-access range whose elements are to be shuffled
size_t n	number of elements of r to shuffle (counting from the beginning); must be less than r.length
RandomGen gen	(optional) random number generator to use; if not specified, defaults to rndGen

Returns:

The shuffled random-access range.

Examples:

auto rnd = MinstdRand0(42);

auto arr = [1, 2, 3, 4, 5, 6];
arr = arr.dup.partialShuffle(1, rnd);

version (D_LP64) // https://issues.dlang.org/show_bug.cgi?id=15147
assert(arr == [2, 1, 3, 4, 5, 6]); // 1<->2

arr = arr.dup.partialShuffle(2, rnd);
version (D_LP64) // https://issues.dlang.org/show_bug.cgi?id=15147
assert(arr == [1, 4, 3, 2, 5, 6]); // 1<->2, 2<->4

arr = arr.dup.partialShuffle(3, rnd);
version (D_LP64) // https://issues.dlang.org/show_bug.cgi?id=15147
assert(arr == [5, 4, 6, 2, 1, 3]); // 1<->5, 2<->4, 3<->6

size_t dice(Rng, Num)(ref Rng rnd, Num[] proportions...)
if (isNumeric!Num && isForwardRange!Rng);

size_t dice(R, Range)(ref R rnd, Range proportions)
if (isForwardRange!Range && isNumeric!(ElementType!Range) && !isArray!Range);

size_t dice(Range)(Range proportions)
if (isForwardRange!Range && isNumeric!(ElementType!Range) && !isArray!Range);

size_t dice(Num)(Num[] proportions...)
if (isNumeric!Num);

Get a random index into a list of weights corresponding to each index

Similar to rolling a die with relative probabilities stored in proportions. Returns the index in proportions that was chosen.

Note Usually, dice are 'fair', meaning that each side has equal probability to come up, in which case 1 + uniform(0, 6) can simply be used. In future Phobos versions, this function might get renamed to something like weightedChoice to avoid confusion.

Parameters:

Rng rnd	(optional) random number generator to use; if not specified, defaults to rndGen
Num[] proportions	forward range or list of individual values whose elements correspond to the probabilities with which to choose the corresponding index value

Returns:

Random variate drawn from the index values [0, ... proportions.length - 1], with the probability of getting an individual index value i being proportional to proportions[i].

Examples:

auto d6  = 1 + dice(1, 1, 1, 1, 1, 1); // fair dice roll
auto d6b = 1 + dice(2, 1, 1, 1, 1, 1); // double the chance to roll '1'

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

Examples:

auto rnd = MinstdRand0(42);
auto z = rnd.dice(70, 20, 10);
writeln(z); // 0
z = rnd.dice(30, 20, 40, 10);
writeln(z); // 2

struct RandomCover(Range, UniformRNG = void) if (isRandomAccessRange!Range && (isUniformRNG!UniformRNG || is(UniformRNG == void)));

auto randomCover(Range, UniformRNG)(Range r, auto ref UniformRNG rng)
if (isRandomAccessRange!Range && isUniformRNG!UniformRNG);

auto randomCover(Range)(Range r)
if (isRandomAccessRange!Range);

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.

Parameters:

Range r	random-access range to cover
UniformRNG rng	(optional) random number generator to use; if not specified, defaults to rndGen

Returns:

Range whose elements consist of the elements of r, in random order. Will be a forward range if both r and rng are forward ranges, an input range otherwise.

Examples:

import std.algorithm.comparison : equal;
import std.range : iota;
auto rnd = MinstdRand0(42);

version (D_LP64) // https://issues.dlang.org/show_bug.cgi?id=15147
assert(10.iota.randomCover(rnd).equal([7, 4, 2, 0, 1, 6, 8, 3, 9, 5]));

struct RandomSample(Range, UniformRNG = void) if (isInputRange!Range && (isUniformRNG!UniformRNG || is(UniformRNG == void)));

auto randomSample(Range)(Range r, size_t n, size_t total)
if (isInputRange!Range);

auto randomSample(Range)(Range r, size_t n)
if (isInputRange!Range && hasLength!Range);

auto randomSample(Range, UniformRNG)(Range r, size_t n, size_t total, auto ref UniformRNG rng)
if (isInputRange!Range && isUniformRNG!UniformRNG);

auto randomSample(Range, UniformRNG)(Range r, size_t n, auto ref UniformRNG rng)
if (isInputRange!Range && hasLength!Range && isUniformRNG!UniformRNG);

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.

Parameters:

Range r	range to sample from
size_t n	number of elements to include in the sample; must be less than or equal to the total number of elements in r and/or the parameter total (if provided)
size_t total	(semi-optional) number of elements of r from which to select the sample (counting from the beginning); must be less than or equal to the total number of elements in r itself. May be omitted if r has the .length property and the sample is to be drawn from all elements of r.
UniformRNG rng	(optional) random number generator to use; if not specified, defaults to rndGen

Returns:

Range whose elements consist of a randomly selected subset of the elements of r, in the same order as these elements appear in r itself. Will be a forward range if both r and rng are forward ranges, an input range otherwise.

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.

Examples:

import std.algorithm.comparison : equal;
import std.range : iota;
auto rnd = MinstdRand0(42);
assert(10.iota.randomSample(3, rnd).equal([7, 8, 9]));

const @property bool empty();

@property ref auto front();

void popFront();

const @property typeof(this) save();

const @property size_t length();

Range primitives.

@property size_t index();

Returns the index of the visited record.