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// Written in the D programming language.
/**
Facilities for random number generation. The old-style functions
$(D_PARAM rand_seed) and $(D_PARAM rand) will soon be deprecated as
they rely on global state and as such are subjected to various
thread-related issues.
The new-style generator objects hold their own state so they are
immune of threading issues. The generators feature a number of
well-known and well-documented methods of generating random
numbers. An overall fast and reliable means to generate random numbers
is the $(D_PARAM Mt19937) generator, which derives its name from
"$(LUCKY Mersenne Twister) with a period of 2 to the power of
19937". In memory-constrained situations, $(LUCKY linear congruential)
generators such as $(D MinstdRand0) and $(D MinstdRand) might be
useful. The standard library provides an alias $(D_PARAM Random) for
whichever generator it considers the most fit for the target
environment.
Example:
----
// Generate a uniformly-distributed integer in the range [0, 14]
auto i = uniform(0, 15);
// Generate a uniformly-distributed real in the range [0, 100$(RPAREN)
// using a specific random generator
Random gen;
auto r = uniform(0.0L, 100.0L, gen);
----
In addition to random number generators, this module features
distributions, which skew a generator's output statistical
distribution in various ways. So far the uniform distribution for
integers and real numbers have been implemented.
Source: $(PHOBOSSRC std/_random.d)
Macros:
WIKI = Phobos/StdRandom
Copyright: Copyright Andrei Alexandrescu 2008 - 2009.
License: <a href="http://www.boost.org/LICENSE_1_0.txt">Boost License 1.0</a>.
Authors: $(WEB erdani.org, Andrei Alexandrescu)
Masahiro Nakagawa (Xorshift randome generator)
Credits: The entire random number library architecture is derived from the
excellent $(WEB open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2461.pdf, C++0X)
random number facility proposed by Jens Maurer and contributed to by
researchers at the Fermi laboratory(excluding Xorshift).
*/
/*
Copyright Andrei Alexandrescu 2008 - 2009.
Distributed under the Boost Software License, Version 1.0.
(See accompanying file LICENSE_1_0.txt or copy at
http://www.boost.org/LICENSE_1_0.txt)
*/
module std.random;
import std.algorithm, std.c.time, std.conv, std.exception,
std.math, std.numeric, std.range, std.traits,
core.thread, core.time;
version(unittest) import std.typetuple;
// Segments of the code in this file Copyright (c) 1997 by Rick Booth
// From "Inner Loops" by Rick Booth, Addison-Wesley
// Work derived from:
/*
A C-program for MT19937, with initialization improved 2002/1/26.
Coded by Takuji Nishimura and Makoto Matsumoto.
Before using, initialize the state by using init_genrand(seed)
or init_by_array(init_key, key_length).
Copyright (C) 1997 - 2002, Makoto Matsumoto and Takuji Nishimura,
All rights reserved.
Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions
are met:
1. Redistributions of source code must retain the above copyright
notice, this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
notice, this list of conditions and the following disclaimer in the
documentation and/or other materials provided with the distribution.
3. The names of its contributors may not be used to endorse or promote
products derived from this software without specific prior written
permission.
THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR
CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
Any feedback is very welcome.
http://www.math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html
email: m-mat @ math.sci.hiroshima-u.ac.jp (remove space)
*/
version (Windows)
{
extern(Windows) int QueryPerformanceCounter(ulong *count);
}
version (Posix)
{
private import core.sys.posix.sys.time;
}
/**
* 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:
* $(UL
* $(LI it's an InputRange)
* $(LI it has a 'bool isUniformRandom' field readable in CTFE)
* )
*/
template isUniformRNG(Rng, ElementType)
{
enum bool isUniformRNG = isInputRange!Rng &&
is(typeof(Rng.front) == ElementType) &&
is(typeof(
{
static assert(Rng.isUniformRandom); //tag
}));
}
/**
* ditto
*/
template isUniformRNG(Rng)
{
enum bool isUniformRNG = isInputRange!Rng &&
is(typeof(
{
static assert(Rng.isUniformRandom); //tag
}));
}
/**
* Test if Rng is seedable. The overload
* taking a ElementType also makes sure that the Rng generates
* values of that type.
*
* A seedable random-number generator has the following additional features:
* $(UL
* $(LI it has a 'seed(ElementType)' function)
* )
*/
template isSeedable(Rng, ElementType)
{
enum bool isSeedable = isUniformRNG!(Rng, ElementType) &&
is(typeof(
{
Rng r = void; // can define a Rng object
r.seed(ElementType.init); // can seed a Rng
}));
}
///ditto
template isSeedable(Rng)
{
enum bool isSeedable = isUniformRNG!Rng &&
is(typeof(
{
Rng r = void; // can define a Rng object
r.seed(typeof(r.front).init); // can seed a Rng
}));
}
unittest
{
struct NoRng
{
@property uint front() {return 0;}
@property bool empty() {return false;}
void popFront() {}
}
assert(!isUniformRNG!(NoRng, uint));
assert(!isUniformRNG!(NoRng));
assert(!isSeedable!(NoRng, uint));
assert(!isSeedable!(NoRng));
struct NoRng2
{
@property uint front() {return 0;}
@property bool empty() {return false;}
void popFront() {}
enum isUniformRandom = false;
}
assert(!isUniformRNG!(NoRng2, uint));
assert(!isUniformRNG!(NoRng2));
assert(!isSeedable!(NoRng2, uint));
assert(!isSeedable!(NoRng2));
struct NoRng3
{
@property bool empty() {return false;}
void popFront() {}
enum isUniformRandom = true;
}
assert(!isUniformRNG!(NoRng3, uint));
assert(!isUniformRNG!(NoRng3));
assert(!isSeedable!(NoRng3, uint));
assert(!isSeedable!(NoRng3));
struct validRng
{
@property uint front() {return 0;}
@property bool empty() {return false;}
void popFront() {}
enum isUniformRandom = true;
}
assert(isUniformRNG!(validRng, uint));
assert(isUniformRNG!(validRng));
assert(!isSeedable!(validRng, uint));
assert(!isSeedable!(validRng));
struct seedRng
{
@property uint front() {return 0;}
@property bool empty() {return false;}
void popFront() {}
void seed(uint val){}
enum isUniformRandom = true;
}
assert(isUniformRNG!(seedRng, uint));
assert(isUniformRNG!(seedRng));
assert(isSeedable!(seedRng, uint));
assert(isSeedable!(seedRng));
}
/**
Linear Congruential generator.
*/
struct LinearCongruentialEngine(UIntType, UIntType a, UIntType c, UIntType m)
{
///Mark this as a Rng
enum bool isUniformRandom = true;
/// Does this generator have a fixed range? ($(D_PARAM true)).
enum bool hasFixedRange = true;
/// Lowest generated value ($(D 1) if $(D c == 0), $(D 0) otherwise).
enum UIntType min = ( c == 0 ? 1 : 0 );
/// Highest generated value ($(D modulus - 1)).
enum UIntType max = m - 1;
/**
The parameters of this distribution. The random number is $(D_PARAM x
= (x * multipler + increment) % modulus).
*/
enum UIntType multiplier = a;
///ditto
enum UIntType increment = c;
///ditto
enum UIntType modulus = m;
static assert(isIntegral!(UIntType));
static assert(m == 0 || a < m);
static assert(m == 0 || c < m);
static assert(m == 0 ||
(cast(ulong)a * (m-1) + c) % m == (c < a ? c - a + m : c - a));
// Check for maximum range
private static ulong gcd(ulong a, ulong b) {
while (b) {
auto t = b;
b = a % b;
a = t;
}
return a;
}
private static ulong primeFactorsOnly(ulong n) {
ulong result = 1;
ulong iter = 2;
for (; n >= iter * iter; iter += 2 - (iter == 2)) {
if (n % iter) continue;
result *= iter;
do {
n /= iter;
} while (n % iter == 0);
}
return result * n;
}
unittest {
static assert(primeFactorsOnly(100) == 10);
//writeln(primeFactorsOnly(11));
static assert(primeFactorsOnly(11) == 11);
static assert(primeFactorsOnly(7 * 7 * 7 * 11 * 15 * 11) == 7 * 11 * 15);
static assert(primeFactorsOnly(129 * 2) == 129 * 2);
// enum x = primeFactorsOnly(7 * 7 * 7 * 11 * 15);
// static assert(x == 7 * 11 * 15);
}
private static bool properLinearCongruentialParameters(ulong m,
ulong a, ulong c) {
if (m == 0)
{
static if (is(UIntType == uint))
{
// Assume m is uint.max + 1
m = (1uL << 32);
}
else
{
return false;
}
}
// Bounds checking
if (a == 0 || a >= m || c >= m) return false;
// c and m are relatively prime
if (c > 0 && gcd(c, m) != 1) return false;
// a - 1 is divisible by all prime factors of m
if ((a - 1) % primeFactorsOnly(m)) return false;
// if a - 1 is multiple of 4, then m is a multiple of 4 too.
if ((a - 1) % 4 == 0 && m % 4) return false;
// Passed all tests
return true;
}
// check here
static assert(c == 0 || properLinearCongruentialParameters(m, a, c),
"Incorrect instantiation of LinearCongruentialEngine");
/**
Constructs a $(D_PARAM LinearCongruentialEngine) generator seeded with
$(D x0).
*/
this(UIntType x0)
{
seed(x0);
}
/**
(Re)seeds the generator.
*/
void seed(UIntType x0 = 1)
{
static if (c == 0)
{
enforce(x0, "Invalid (zero) seed for "
~ LinearCongruentialEngine.stringof);
}
_x = modulus ? (x0 % modulus) : x0;
popFront();
}
/**
Advances the random sequence.
*/
void popFront()
{
static if (m)
{
static if (is(UIntType == uint) && m == uint.max)
{
immutable ulong
x = (cast(ulong) a * _x + c),
v = x >> 32,
w = x & uint.max;
immutable y = cast(uint)(v + w);
_x = (y < v || y == uint.max) ? (y + 1) : y;
}
else static if (is(UIntType == uint) && m == int.max)
{
immutable ulong
x = (cast(ulong) a * _x + c),
v = x >> 31,
w = x & int.max;
immutable uint y = cast(uint)(v + w);
_x = (y >= int.max) ? (y - int.max) : y;
}
else
{
_x = cast(UIntType) ((cast(ulong) a * _x + c) % m);
}
}
else
{
_x = a * _x + c;
}
}
/**
Returns the current number in the random sequence.
*/
@property UIntType front()
{
return _x;
}
///
@property typeof(this) save()
{
return this;
}
/**
Always $(D false) (random generators are infinite ranges).
*/
enum bool empty = false;
/**
Compares against $(D_PARAM rhs) for equality.
*/
bool opEquals(ref const LinearCongruentialEngine rhs) const
{
return _x == rhs._x;
}
private UIntType _x = m ? (a + c) % m : (a + c);
}
/**
Define $(D_PARAM LinearCongruentialEngine) generators with well-chosen
parameters. $(D MinstdRand0) implements Park and Miller's "minimal
standard" $(WEB
wikipedia.org/wiki/Park%E2%80%93Miller_random_number_generator,
generator) that uses 16807 for the multiplier. $(D MinstdRand)
implements a variant that has slightly better spectral behavior by
using the multiplier 48271. Both generators are rather simplistic.
Example:
----
// 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
----
*/
alias LinearCongruentialEngine!(uint, 16807, 0, 2147483647) MinstdRand0;
/// ditto
alias LinearCongruentialEngine!(uint, 48271, 0, 2147483647) MinstdRand;
unittest
{
assert(isForwardRange!MinstdRand);
assert(isUniformRNG!MinstdRand);
assert(isUniformRNG!MinstdRand0);
assert(isUniformRNG!(MinstdRand, uint));
assert(isUniformRNG!(MinstdRand0, uint));
assert(isSeedable!MinstdRand);
assert(isSeedable!MinstdRand0);
assert(isSeedable!(MinstdRand, uint));
assert(isSeedable!(MinstdRand0, uint));
// The correct numbers are taken from The Database of Integer Sequences
// http://www.research.att.com/~njas/sequences/eisBTfry00128.txt
auto checking0 = [
16807UL,282475249,1622650073,984943658,1144108930,470211272,
101027544,1457850878,1458777923,2007237709,823564440,1115438165,
1784484492,74243042,114807987,1137522503,1441282327,16531729,
823378840,143542612 ];
//auto rnd0 = MinstdRand0(1);
MinstdRand0 rnd0;
foreach (e; checking0)
{
assert(rnd0.front == e);
rnd0.popFront();
}
// Test the 10000th invocation
// Correct value taken from:
// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2461.pdf
rnd0.seed();
popFrontN(rnd0, 9999);
assert(rnd0.front == 1043618065);
// Test MinstdRand
auto checking = [48271UL,182605794,1291394886,1914720637,2078669041,
407355683];
//auto rnd = MinstdRand(1);
MinstdRand rnd;
foreach (e; checking)
{
assert(rnd.front == e);
rnd.popFront();
}
// Test the 10000th invocation
// Correct value taken from:
// http://www.open-std.org/jtc1/sc22/wg21/docs/papers/2007/n2461.pdf
rnd.seed();
popFrontN(rnd, 9999);
assert(rnd.front == 399268537);
}
/**
The $(LUCKY Mersenne Twister) generator.
*/
struct MersenneTwisterEngine(
UIntType, size_t w, size_t n, size_t m, size_t r,
UIntType a, size_t u, size_t s,
UIntType b, size_t t,
UIntType c, size_t l)
{
static assert(UIntType.min == 0);
///Mark this as a Rng
enum bool isUniformRandom = true;
/**
Parameter for the generator.
*/
enum size_t wordSize = w;
enum size_t stateSize = n;
enum size_t shiftSize = m;
enum size_t maskBits = r;
enum UIntType xorMask = a;
enum UIntType temperingU = u;
enum size_t temperingS = s;
enum UIntType temperingB = b;
enum size_t temperingT = t;
enum UIntType temperingC = c;
enum size_t temperingL = l;
/// Smallest generated value (0).
enum UIntType min = 0;
/// Largest generated value.
enum UIntType max =
w == UIntType.sizeof * 8 ? UIntType.max : (1u << w) - 1;
/// The default seed value.
enum UIntType defaultSeed = 5489u;
static assert(1 <= m && m <= n);
static assert(0 <= r && 0 <= u && 0 <= s && 0 <= t && 0 <= l);
static assert(r <= w && u <= w && s <= w && t <= w && l <= w);
static assert(0 <= a && 0 <= b && 0 <= c);
static assert(a <= max && b <= max && c <= max);
/**
Constructs a MersenneTwisterEngine object.
*/
this(UIntType value)
{
seed(value);
}
/**
Seeds a MersenneTwisterEngine object.
*/
void seed(UIntType value = defaultSeed)
{
static if (w == UIntType.sizeof * 8)
{
mt[0] = value;
}
else
{
static assert(max + 1 > 0);
mt[0] = value % (max + 1);
}
for (mti = 1; mti < n; ++mti) {
mt[mti] =
cast(UIntType)
(1812433253UL * (mt[mti-1] ^ (mt[mti-1] >> (w - 2))) + mti);
/* See Knuth TAOCP Vol2. 3rd Ed. P.106 for multiplier. */
/* In the previous versions, MSBs of the seed affect */
/* only MSBs of the array mt[]. */
/* 2002/01/09 modified by Makoto Matsumoto */
//mt[mti] &= ResultType.max;
/* for >32 bit machines */
}
popFront();
}
/**
Advances the generator.
*/
void popFront()
{
if (mti == size_t.max) seed();
enum UIntType
upperMask = ~((cast(UIntType) 1u <<
(UIntType.sizeof * 8 - (w - r))) - 1),
lowerMask = (cast(UIntType) 1u << r) - 1;
static immutable UIntType mag01[2] = [0x0UL, a];
ulong y = void;
if (mti >= n)
{
/* generate N words at one time */
int kk = 0;
const limit1 = n - m;
for (; kk < limit1; ++kk)
{
y = (mt[kk] & upperMask)|(mt[kk + 1] & lowerMask);
mt[kk] = cast(UIntType) (mt[kk + m] ^ (y >> 1)
^ mag01[cast(UIntType) y & 0x1U]);
}
const limit2 = n - 1;
for (; kk < limit2; ++kk)
{
y = (mt[kk] & upperMask)|(mt[kk + 1] & lowerMask);
mt[kk] = cast(UIntType) (mt[kk + (m -n)] ^ (y >> 1)
^ mag01[cast(UIntType) y & 0x1U]);
}
y = (mt[n -1] & upperMask)|(mt[0] & lowerMask);
mt[n - 1] = cast(UIntType) (mt[m - 1] ^ (y >> 1)
^ mag01[cast(UIntType) y & 0x1U]);
mti = 0;
}
y = mt[mti++];
/* Tempering */
y ^= (y >> temperingU);
y ^= (y << temperingS) & temperingB;
y ^= (y << temperingT) & temperingC;
y ^= (y >> temperingL);
_y = cast(UIntType) y;
}
/**
Returns the current random value.
*/
@property UIntType front()
{
if (mti == size_t.max) seed();
return _y;
}
///
@property typeof(this) save()
{
return this;
}
/**
Always $(D false).
*/
enum bool empty = false;
private UIntType mt[n];
private size_t mti = size_t.max; /* means mt is not initialized */
UIntType _y = UIntType.max;
}
/**
A $(D MersenneTwisterEngine) instantiated with the parameters of the
original engine $(WEB math.sci.hiroshima-u.ac.jp/~m-mat/MT/emt.html,
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 $(D
LinearCongruentialEngine) would be the generator of choice.
Example:
----
// 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
----
*/
alias MersenneTwisterEngine!(uint, 32, 624, 397, 31, 0x9908b0df, 11, 7,
0x9d2c5680, 15, 0xefc60000, 18)
Mt19937;
unittest
{
assert(isUniformRNG!Mt19937);
assert(isUniformRNG!(Mt19937, uint));
assert(isSeedable!Mt19937);
assert(isSeedable!(Mt19937, uint));
Mt19937 gen;
popFrontN(gen, 9999);
assert(gen.front == 4123659995);
}
unittest
{
uint a, b;
{
Mt19937 gen;
a = gen.front;
}
{
Mt19937 gen;
gen.popFront();
//popFrontN(gen, 1); // skip 1 element
b = gen.front;
}
assert(a != b);
}
/**
* Xorshift generator using 32bit algorithm.
*
* Implemented according to $(WEB www.jstatsoft.org/v08/i14/paper, Xorshift RNGs).
*
* $(BOOKTABLE $(TEXTWITHCOMMAS Supporting bits are below, $(D bits) means second parameter of XorshiftEngine.),
* $(TR $(TH bits) $(TH period))
* $(TR $(TD 32) $(TD 2^32 - 1))
* $(TR $(TD 64) $(TD 2^64 - 1))
* $(TR $(TD 96) $(TD 2^96 - 1))
* $(TR $(TD 128) $(TD 2^128 - 1))
* $(TR $(TD 160) $(TD 2^160 - 1))
* $(TR $(TD 192) $(TD 2^192 - 2^32))
* )
*/
struct XorshiftEngine(UIntType, UIntType bits, UIntType a, UIntType b, UIntType c)
{
static assert(bits == 32 || bits == 64 || bits == 96 || bits == 128 || bits == 160 || bits == 192,
"Supporting bits are 32, 64, 96, 128, 160 and 192. " ~ to!string(bits) ~ " is not supported.");
public:
///Mark this as a Rng
enum bool isUniformRandom = true;
/// Always $(D false) (random generators are infinite ranges).
enum empty = false;
/// Smallest generated value.
enum UIntType min = 0;
/// Largest generated value.
enum UIntType max = UIntType.max;
private:
enum Size = bits / 32;
static if (bits == 32) {
UIntType[Size] seeds_ = [2463534242];
} else static if (bits == 64) {
UIntType[Size] seeds_ = [123456789, 362436069];
} else static if (bits == 96) {
UIntType[Size] seeds_ = [123456789, 362436069, 521288629];
} else static if (bits == 128) {
UIntType[Size] seeds_ = [123456789, 362436069, 521288629, 88675123];
} else static if (bits == 160) {
UIntType[Size] seeds_ = [123456789, 362436069, 521288629, 88675123, 5783321];
} else { // 192bits
UIntType[Size] seeds_ = [123456789, 362436069, 521288629, 88675123, 5783321, 6615241];
UIntType value_;
}
public:
/**
* Constructs a $(D XorshiftEngine) generator seeded with $(D_PARAM x0).
*/
@safe
this(UIntType x0)
{
seed(x0);
}
/**
* (Re)seeds the generator.
*/
@safe
nothrow void seed(UIntType x0)
{
// Initialization routine from MersenneTwisterEngine.
foreach (i, e; seeds_)
seeds_[i] = x0 = cast(UIntType)(1812433253U * (x0 ^ (x0 >> 30)) + i + 1);
// All seeds must not be 0.
sanitizeSeeds(seeds_);
popFront();
}
/**
* Returns the current number in the random sequence.
*/
@property @safe
nothrow UIntType front()
{
static if (bits == 192) {
return value_;
} else {
return seeds_[Size - 1];
}
}
/**
* Advances the random sequence.
*/
@safe
nothrow void popFront()
{
UIntType temp;
static if (bits == 32) {
temp = seeds_[0] ^ (seeds_[0] << a);
temp = temp >> b;
seeds_[0] = temp ^ (temp << c);
} else static if (bits == 64) {
temp = seeds_[0] ^ (seeds_[0] << a);
seeds_[0] = seeds_[1];
seeds_[1] = seeds_[1] ^ (seeds_[1] >> c) ^ temp ^ (temp >> b);
} else static if (bits == 96) {
temp = seeds_[0] ^ (seeds_[0] << a);
seeds_[0] = seeds_[1];
seeds_[1] = seeds_[2];
seeds_[2] = seeds_[2] ^ (seeds_[2] >> c) ^ temp ^ (temp >> b);
} else static if (bits == 128){
temp = seeds_[0] ^ (seeds_[0] << a);
seeds_[0] = seeds_[1];
seeds_[1] = seeds_[2];
seeds_[2] = seeds_[3];
seeds_[3] = seeds_[3] ^ (seeds_[3] >> c) ^ temp ^ (temp >> b);
} else static if (bits == 160){
temp = seeds_[0] ^ (seeds_[0] >> a);
seeds_[0] = seeds_[1];
seeds_[1] = seeds_[2];
seeds_[2] = seeds_[3];
seeds_[3] = seeds_[4];
seeds_[4] = seeds_[4] ^ (seeds_[4] >> c) ^ temp ^ (temp >> b);
} else { // 192bits
temp = seeds_[0] ^ (seeds_[0] >> a);
seeds_[0] = seeds_[1];
seeds_[1] = seeds_[2];
seeds_[2] = seeds_[3];
seeds_[3] = seeds_[4];
seeds_[4] = seeds_[4] ^ (seeds_[4] << c) ^ temp ^ (temp << b);
value_ = seeds_[4] + (seeds_[5] += 362437);
}
}
/**
* Captures a range state.
*/
@property
typeof(this) save()
{
return this;
}
/**
* Compares against $(D_PARAM rhs) for equality.
*/
@safe
nothrow bool opEquals(ref const XorshiftEngine rhs) const
{
return seeds_ == rhs.seeds_;
}
private:
@safe
static nothrow void sanitizeSeeds(ref UIntType[Size] seeds)
{
for (uint i; i < seeds.length; i++) {
if (seeds[i] == 0)
seeds[i] = i + 1;
}
}
unittest
{
static if (Size == 4) // Other bits too
{
UIntType[Size] seeds = [1, 0, 0, 4];
sanitizeSeeds(seeds);
assert(seeds == [1, 2, 3, 4]);
}
}
}
/**
* Define $(D XorshiftEngine) generators with well-chosen parameters. See each bits examples of "Xorshift RNGs".
* $(D Xorshift) is a Xorshift128's alias because 128bits implementation is mostly used.
*
* Example:
* -----
* // 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
* -----
*/
alias XorshiftEngine!(uint, 32, 13, 17, 5) Xorshift32;
alias XorshiftEngine!(uint, 64, 10, 13, 10) Xorshift64; /// ditto
alias XorshiftEngine!(uint, 96, 10, 5, 26) Xorshift96; /// ditto
alias XorshiftEngine!(uint, 128, 11, 8, 19) Xorshift128; /// ditto
alias XorshiftEngine!(uint, 160, 2, 1, 4) Xorshift160; /// ditto
alias XorshiftEngine!(uint, 192, 2, 1, 4) Xorshift192; /// ditto
alias Xorshift128 Xorshift; /// ditto
unittest
{
assert(isForwardRange!Xorshift);
assert(isUniformRNG!Xorshift);
assert(isUniformRNG!(Xorshift, uint));
assert(isSeedable!Xorshift);
assert(isSeedable!(Xorshift, uint));
// Result from reference implementation.
auto checking = [
[2463534242UL, 267649, 551450, 53765, 108832, 215250, 435468, 860211, 660133, 263375],
[362436069UL, 2113136921, 19051112, 3010520417, 951284840, 1213972223, 3173832558, 2611145638, 2515869689, 2245824891],
[521288629UL, 1950277231, 185954712, 1582725458, 3580567609, 2303633688, 2394948066, 4108622809, 1116800180, 3357585673],
[88675123UL, 3701687786, 458299110, 2500872618, 3633119408, 516391518, 2377269574, 2599949379, 717229868, 137866584],
[5783321UL, 93724048, 491642011, 136638118, 246438988, 238186808, 140181925, 533680092, 285770921, 462053907],
[0UL, 246875399, 3690007200, 1264581005, 3906711041, 1866187943, 2481925219, 2464530826, 1604040631, 3653403911]
];
foreach (I, Type; TypeTuple!(Xorshift32, Xorshift64, Xorshift96, Xorshift128, Xorshift160, Xorshift192)) {
Type rnd;
foreach (e; checking[I]) {
assert(rnd.front == e);
rnd.popFront();
}
}
}
/**
A "good" seed for initializing random number engines. Initializing
with $(D_PARAM unpredictableSeed) makes engines generate different
random number sequences every run.
Example:
----
auto rnd = Random(unpredictableSeed);
auto n = rnd.front;
...
----
*/
@property uint unpredictableSeed()
{
static bool seeded;
static MinstdRand0 rand;
if (!seeded) {
uint threadID = cast(uint) cast(void*) Thread.getThis();
rand.seed((getpid() + threadID) ^ cast(uint) TickDuration.currSystemTick().length);
seeded = true;
}
rand.popFront();
return cast(uint) (TickDuration.currSystemTick().length ^ rand.front);
}
unittest
{
// not much to test here
auto a = unpredictableSeed;
static assert(is(typeof(a) == uint));
}
/**
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.
*/
alias Mt19937 Random;
unittest
{
assert(isUniformRNG!Random);
assert(isUniformRNG!(Random, uint));
assert(isSeedable!Random);
assert(isSeedable!(Random, uint));
}
/**
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.
*/
@property ref Random rndGen()
{
static Random result;
static bool initialized;
if (!initialized)
{
result = Random(unpredictableSeed);
initialized = true;
}
return result;
}
/**
Generates a number between $(D a) and $(D b). The $(D boundaries)
parameter controls the shape of the interval (open vs. closed on
either side). Valid values for $(D boundaries) are $(D "[]"), $(D
"$(LPAREN)]"), $(D "[$(RPAREN)"), and $(D "()"). The default interval
is closed to the left and open to the right. The version that does not
take $(D urng) uses the default generator $(D rndGen).
Example:
----
Random gen(unpredictableSeed);
// Generate an integer in [0, 1023]
auto a = uniform(0, 1024, gen);
// Generate a float in [0, 1$(RPAREN)
auto a = uniform(0.0f, 1.0f, gen);
----
*/
auto uniform(string boundaries = "[)", T1, T2)
(T1 a, T2 b) if (!is(CommonType!(T1, T2) == void))
{
return uniform!(boundaries, T1, T2, Random)(a, b, rndGen);
}
unittest
{
MinstdRand0 gen;
foreach (i; 0 .. 20)
{
auto x = uniform(0., 15., gen);
assert(0 <= x && x < 15);
}
foreach (i; 0 .. 20)
{
auto x = uniform!"[]"('a', 'z', gen);
assert('a' <= x && x <= 'z');
}
foreach (i; 0 .. 20)
{
auto x = uniform('a', 'z', gen);
assert('a' <= x && x < 'z');
}
foreach(i; 0 .. 20) {
immutable ubyte a = 0;
immutable ubyte b = 15;
auto x = uniform(a, b, gen);
assert(a <= x && x < b);
}
}
// Implementation of uniform for floating-point types
/// ditto
auto uniform(string boundaries = "[)",
T1, T2, UniformRandomNumberGenerator)
(T1 a, T2 b, ref UniformRandomNumberGenerator urng)
if (isFloatingPoint!(CommonType!(T1, T2)))
{
alias Unqual!(CommonType!(T1, T2)) NumberType;
static if (boundaries[0] == '(')
{
NumberType _a = nextafter(cast(NumberType) a, NumberType.infinity);
}
else
{
NumberType _a = a;
}
static if (boundaries[1] == ')')
{
NumberType _b = nextafter(cast(NumberType) b, -NumberType.infinity);
}
else
{
NumberType _b = b;
}
enforce(_a <= _b,
text("std.random.uniform(): invalid bounding interval ",
boundaries[0], a, ", ", b, boundaries[1]));
NumberType result =
_a + (_b - _a) * cast(NumberType) (urng.front - urng.min)
/ (urng.max - urng.min);
urng.popFront();
return result;
}
// Implementation of uniform for integral types
auto uniform(string boundaries = "[)",
T1, T2, UniformRandomNumberGenerator)
(T1 a, T2 b, ref UniformRandomNumberGenerator urng)
if (isIntegral!(CommonType!(T1, T2)) || isSomeChar!(CommonType!(T1, T2)))
{
alias Unqual!(CommonType!(T1, T2)) ResultType;
// We handle the case "[)' as the common case, and we adjust all
// other cases to fit it.
static if (boundaries[0] == '(')
{
enforce(cast(ResultType) a < ResultType.max,
text("std.random.uniform(): invalid left bound ", a));
ResultType min = cast(ResultType) a + 1;
}
else
{
ResultType min = a;
}
static if (boundaries[1] == ']')
{
enforce(min <= cast(ResultType) b,
text("std.random.uniform(): invalid bounding interval ",
boundaries[0], a, ", ", b, boundaries[1]));
if (b == ResultType.max && min == ResultType.min)
{
// Special case - all bits are occupied
return .uniform!ResultType(urng);
}
auto count = unsigned(b - min) + 1u;
static assert(count.min == 0);
}
else
{
enforce(min < cast(ResultType) b,
text("std.random.uniform(): invalid bounding interval ",
boundaries[0], a, ", ", b, boundaries[1]));
auto count = unsigned(b - min);
static assert(count.min == 0);
}
assert(count != 0);
if (count == 1) return min;
alias typeof(count) CountType;
static assert(CountType.min == 0);
auto bucketSize = 1u + (CountType.max - count + 1) / count;
CountType r;
do
{
r = cast(CountType) (uniform!CountType(urng) / bucketSize);
}
while (r >= count);
return cast(typeof(return)) (min + r);
}
unittest
{
auto gen = Mt19937(unpredictableSeed);
static assert(isForwardRange!(typeof(gen)));
auto a = uniform(0, 1024, gen);
assert(0 <= a && a <= 1024);
auto b = uniform(0.0f, 1.0f, gen);
assert(0 <= b && b < 1, to!string(b));
auto c = uniform(0.0, 1.0);
assert(0 <= c && c < 1);
foreach(T; TypeTuple!(char, wchar, dchar, byte, ubyte, short, ushort,
int, uint, long, ulong, float, double, real))
{
T lo = 0, hi = 100;
T init = uniform(lo, hi);
size_t i = 50;
while (--i && uniform(lo, hi) == init) {}
assert(i > 0);
}
}
/**
Generates a uniformly-distributed number in the range $(D [T.min,
T.max]) for any integral type $(D T). If no random number generator is
passed, uses the default $(D rndGen).
*/
auto uniform(T, UniformRandomNumberGenerator)
(ref UniformRandomNumberGenerator urng)
if (isIntegral!T || isSomeChar!T)
{
auto r = urng.front;
urng.popFront();
static if (T.sizeof <= r.sizeof)
{
return cast(T) r;
}
else
{
static assert(T.sizeof == 8 && r.sizeof == 4);
T r1 = urng.front | (cast(T)r << 32);
urng.popFront();
return r1;
}
}
/// Ditto
auto uniform(T)()
if (isIntegral!T || isSomeChar!T)
{
return uniform!T(rndGen);
}
unittest
{
foreach(T; TypeTuple!(char, wchar, dchar, byte, ubyte, short, ushort,
int, uint, long, ulong))
{
T init = uniform!T();
size_t i = 50;
while (--i && uniform!T() == init) {}
assert(i > 0);
}
}
/**
Generates a uniform probability distribution of size $(D n), i.e., an
array of size $(D n) of positive numbers of type $(D F) that sum to
$(D 1). If $(D useThis) is provided, it is used as storage.
*/
F[] uniformDistribution(F = double)(size_t n, F[] useThis = null)
{
useThis.length = n;
foreach (ref e; useThis)
{
e = uniform(0.0, 1);
}
normalize(useThis);
return useThis;
}
unittest
{
static assert(is(CommonType!(double, int) == double));
auto a = uniformDistribution(5);
enforce(a.length == 5);
enforce(approxEqual(reduce!"a + b"(a), 1));
a = uniformDistribution(10, a);
enforce(a.length == 10);
enforce(approxEqual(reduce!"a + b"(a), 1));
}
/**
Shuffles elements of $(D r) using $(D gen) as a shuffler. $(D r) must be
a random-access range with length.
*/
void randomShuffle(Range, RandomGen = Random)(Range r,
ref RandomGen gen = rndGen)
{
foreach (i; 0 .. r.length)
{
swapAt(r, i, i + uniform(0, r.length - i, gen));
}
}
unittest
{
auto a = ([ 1, 2, 3, 4, 5, 6, 7, 8, 9 ]).dup;
auto b = a.dup;
Mt19937 gen;
randomShuffle(a, gen);
assert(a.sort == b.sort);
randomShuffle(a);
assert(a.sort == b.sort);
}
/**
Rolls a dice with relative probabilities stored in $(D
proportions). Returns the index in $(D proportions) that was chosen.
Example:
----
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
----
*/
size_t dice(Rng, Num)(ref Rng rnd, Num[] proportions...)
if (isNumeric!Num && isForwardRange!Rng)
{
return diceImpl(rnd, proportions);
}
/// Ditto
size_t dice(R, Range)(ref R rnd, Range proportions)
if (isForwardRange!Range && isNumeric!(ElementType!Range) && !isArray!Range)
{
return diceImpl(rnd, proportions);
}
/// Ditto
size_t dice(Range)(Range proportions)
if (isForwardRange!Range && isNumeric!(ElementType!Range) && !isArray!Range)
{
return diceImpl(rndGen, proportions);
}
/// Ditto
size_t dice(Num)(Num[] proportions...)
if (isNumeric!Num)
{
return diceImpl(rndGen, proportions);
}
private size_t diceImpl(Rng, Range)(ref Rng rng, Range proportions)
if (isForwardRange!Range && isNumeric!(ElementType!Range) && isForwardRange!Rng)
{
double sum = reduce!("(assert(b >= 0), a + b)")(0.0, proportions.save);
enforce(sum > 0, "Proportions in a dice cannot sum to zero");
immutable point = uniform(0.0, sum, rng);
assert(point < sum);
auto mass = 0.0;
size_t i = 0;
foreach (e; proportions) {
mass += e;
if (point < mass) return i;
i++;
}
// this point should not be reached
assert(false);
}
unittest {
auto rnd = Random(unpredictableSeed);
auto i = dice(rnd, 0.0, 100.0);
assert(i == 1);
i = dice(rnd, 100.0, 0.0);
assert(i == 0);
i = dice(100U, 0U);
assert(i == 0);
}
/**
Covers a given range $(D r) in a random manner, i.e. goes through each
element of $(D r) once and only once, just in a random order. $(D r)
must be a random-access range with length.
Example:
----
int[] a = [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ];
auto rnd = Random(unpredictableSeed);
foreach (e; randomCover(a, rnd))
{
writeln(e);
}
----
*/
struct RandomCover(Range, Random) if (isUniformRNG!Random)
{
private Range _input;
private Random _rnd;
private bool[] _chosen;
private uint _current;
private uint _alreadyChosen;
this(Range input, Random rnd)
{
_input = input;
_rnd = rnd;
_chosen.length = _input.length;
popFront();
}
static if (hasLength!Range)
@property size_t length()
{
return (1 + _input.length) - _alreadyChosen;
}
@property auto ref front()
{
return _input[_current];
}
void popFront()
{
if (_alreadyChosen >= _input.length)
{
// No more elements
++_alreadyChosen; // means we're done
return;
}
size_t k = _input.length - _alreadyChosen;
uint i;
foreach (e; _input)
{
if (_chosen[i]) { ++i; continue; }
// Roll a dice with k faces
auto chooseMe = uniform(0, k, _rnd) == 0;
assert(k > 1 || chooseMe);
if (chooseMe)
{
_chosen[i] = true;
_current = i;
++_alreadyChosen;
return;
}
--k;
++i;
}
assert(false);
}
@property typeof(this) save()
{
auto ret = this;
ret._input = _input.save;
ret._rnd = _rnd.save;
return ret;
}
@property bool empty() { return _alreadyChosen > _input.length; }
}
/// Ditto
RandomCover!(Range, Random) randomCover(Range, Random)(Range r, Random rnd)
if(isUniformRNG!Random)
{
return typeof(return)(r, rnd);
}
unittest
{
int[] a = [ 0, 1, 2, 3, 4, 5, 6, 7, 8 ];
auto rnd = Random(unpredictableSeed);
RandomCover!(int[], Random) rc = randomCover(a, rnd);
static assert(isForwardRange!(typeof(rc)));
int[] b = new int[9];
uint i;
foreach (e; rc)
{
//writeln(e);
b[i++] = e;
}
sort(b);
assert(a == b, text(b));
}
// RandomSample
/**
Selects a random subsample out of $(D r), containing exactly $(D n)
elements. The order of elements is the same as in the original
range. The total length of $(D r) must be known. If $(D total) is
passed in, the total number of sample is considered to be $(D
total). Otherwise, $(D RandomSample) uses $(D r.length).
If the number of elements is not exactly $(D total), $(D
RandomSample) throws an exception. This is because $(D total) is
essential to computing the probability of selecting elements in the
range.
Example:
----
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);
}
----
*/
struct RandomSample(R, Random = void)
if(isUniformRNG!Random || is(Random == void))
{
private size_t _available, _toSelect;
private R _input;
private size_t _index;
// If we're using the default thread-local random number generator then
// we shouldn't store a copy of it here. Random == void is a sentinel
// for this. If we're using a user-specified generator then we have no
// choice but to store a copy.
static if(!is(Random == void))
{
Random gen;
}
/**
Constructor.
*/
static if (hasLength!R)
this(R input, size_t howMany)
{
this(input, howMany, input.length);
}
this(R input, size_t howMany, size_t total)
{
_input = input;
_available = total;
_toSelect = howMany;
enforce(_toSelect <= _available);
// we should skip some elements initially so we don't always
// start with the first
prime();
}
/**
Range primitives.
*/
@property bool empty() const
{
return _toSelect == 0;
}
@property auto ref front()
{
assert(!empty);
return _input.front;
}
/// Ditto
void popFront()
{
_input.popFront();
--_available;
--_toSelect;
++_index;
prime();
}
/// Ditto
@property typeof(this) save()
{
auto ret = this;
ret._input = _input.save;
return ret;
}
/// Ditto
@property size_t length()
{
return _toSelect;
}
/**
Returns the index of the visited record.
*/
size_t index()
{
return _index;
}
private void prime()
{
if (empty) return;
assert(_available && _available >= _toSelect);
for (;;)
{
static if(is(Random == void))
{
auto r = uniform(0, _available);
}
else
{
auto r = uniform(0, _available, gen);
}
if (r < _toSelect)
{
// chosen!
return;
}
// not chosen, retry
assert(!_input.empty);
_input.popFront();
++_index;
--_available;
assert(_available > 0);
}
}
}
/// Ditto
auto randomSample(R)(R r, size_t n, size_t total)
if(isInputRange!R)
{
return RandomSample!(R, void)(r, n, total);
}
/// Ditto
auto randomSample(R)(R r, size_t n) if (hasLength!R)
{
return RandomSample!(R, void)(r, n, r.length);
}
/// Ditto
auto randomSample(R, Random)(R r, size_t n, size_t total, Random gen)
if(isInputRange!R && isUniformRNG!Random)
{
auto ret = RandomSample!(R, Random)(r, n, total);
ret.gen = gen;
return ret;
}
/// Ditto
auto randomSample(R, Random)(R r, size_t n, Random gen)
if (isInputRange!R && hasLength!R && isUniformRNG!Random)
{
auto ret = RandomSample!(R, Random)(r, n, r.length);
ret.gen = gen;
return ret;
}
unittest
{
Random gen;
int[] a = [ 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 ];
static assert(isForwardRange!(typeof(randomSample(a, 5))));
static assert(isForwardRange!(typeof(randomSample(a, 5, gen))));
//int[] a = [ 0, 1, 2 ];
assert(randomSample(a, 5).length == 5);
assert(randomSample(a, 5, 10).length == 5);
assert(randomSample(a, 5, gen).length == 5);
uint i;
foreach (e; randomSample(randomCover(a, rndGen), 5))
{
++i;
//writeln(e);
}
assert(i == 5);
}
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