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# Pseudo-random numbers/Combined recursive generator MRG32k3a

Pseudo-random numbers/Combined recursive generator MRG32k3a
You are encouraged to solve this task according to the task description, using any language you may know.
MRG32k3a Combined recursive generator (pseudo-code)
/* Constants */
/* First generator */
a1 = [0, 1403580, -810728]
m1 = 2**32 - 209
/* Second Generator */
a2 = [527612, 0, -1370589]
m2 = 2**32 - 22853

d = m1 + 1

class MRG32k3a
x1 = [0, 0, 0]  /* list of three last values of gen #1 */
x2 = [0, 0, 0]  /* list of three last values of gen #2 */

method seed(u64 seed_state)
assert seed_state in range >0 and < d
x1 = [seed_state, 0, 0]
x2 = [seed_state, 0, 0]
end method

method next_int()
x1i = (a1[0]*x1[0] + a1[1]*x1[1] + a1[2]*x1[2]) mod m1
x2i = (a2[0]*x2[0] + a2[1]*x2[1] + a2[2]*x2[2]) mod m2
x1 = [x1i, x1[0], x1[1]]    /* Keep last three */
x2 = [x2i, x2[0], x2[1]]    /* Keep last three */
z = (x1i - x2i) % m1

end method

method next_float():
return float next_int() / d
end method

end class

MRG32k3a Use:
random_gen = instance MRG32k3a
random_gen.seed(1234567)
print(random_gen.next_int())   /* 1459213977 */
print(random_gen.next_int())   /* 2827710106 */
print(random_gen.next_int())   /* 4245671317 */
print(random_gen.next_int())   /* 3877608661 */
print(random_gen.next_int())   /* 2595287583 */

• Generate a class/set of functions that generates pseudo-random

numbers as shown above.

• Show that the first five integers generated with the seed `1234567`

are as shown above

• Show that for an initial seed of '987654321' the counts of 100_000

repetitions of

floor(random_gen.next_float() * 5)

Is as follows:

0: 20002, 1: 20060, 2: 19948, 3: 20059, 4: 19931

## 11l

Translation of: Python
V a1 = [Int64(0), 1403580, -810728]
V m1 = Int64(2) ^ 32 - 209
V a2 = [Int64(527612), 0, -1370589]
V m2 = Int64(2) ^ 32 - 22853
V d = m1 + 1

T MRG32k3a
[Int64] x1, x2

F (seed_state = 123)
.seed(seed_state)

F seed(Int64 seed_state)
assert(seed_state C Int64(0) <.< :d, ‘Out of Range 0 x < #.’.format(:d))
.x1 = [Int64(seed_state), 0, 0]
.x2 = [Int64(seed_state), 0, 0]

F next_int()
‘return random int in range 0..d’
V x1i = (sum(zip(:a1, .x1).map((aa, xx) -> aa * xx)) % :m1 + :m1) % :m1
V x2i = (sum(zip(:a2, .x2).map((aa, xx) -> aa * xx)) % :m2 + :m2) % :m2
.x1 = [x1i] [+] .x1[0.<2]
.x2 = [x2i] [+] .x2[0.<2]
V z = ((x1i - x2i) % :m1 + :m1) % :m1
R z + 1

F next_float()
‘return random float between 0 and 1’
R Float(.next_int()) / :d

V random_gen = MRG32k3a()
random_gen.seed(1234567)
L 5
print(random_gen.next_int())

random_gen.seed(987654321)
V hist = Dict(0.<5, i -> (i, 0))
L 100'000
hist[Int(random_gen.next_float() * 5)]++
print(hist)
Output:
1459213977
2827710106
4245671317
3877608661
2595287583
[0 = 20002, 1 = 20060, 2 = 19948, 3 = 20059, 4 = 19931]

package MRG32KA is
type I64 is range -2**63..2**63 - 1;
m1 : constant I64 := 2**32 - 209;
m2 : constant I64 := 2**32 - 22853;

subtype state_value is I64 range 1..m1;

procedure Seed (seed_state : state_value);
function Next_Int return I64;
function Next_Float return Long_Float;
end MRG32KA;

package body MRG32KA is

type Data_Array is array (0..2) of I64;

d : constant I64 := m1 + 1;
----------------
-- Generators --
----------------

a1 : Data_Array := (0, 1403580, -810728);
a2 : Data_Array := (527612, 0, -1370589);

x1 : Data_Array := (0, 0, 0);
x2 : Data_Array := (0, 0, 0);
----------
-- Seed --
----------

procedure Seed (seed_state : state_value) is
begin
x1 := (seed_state, 0, 0);
x2 := (seed_state, 0, 0);
end Seed;

--------------
-- Next_Int --
--------------

function Next_Int return I64 is
x1i : i64;
x2i : I64;
z  : I64;
begin
x1i := (a1(0) * x1(0) + a1(1) * x1(1) + a1(2) * x1(2)) mod m1;
x2i := (a2(0) * x2(0) + a2(1) * x2(1) + a2(2) * x2(2)) mod m2;
x1  := (x1i, x1(0), x1(1));
x2  := (x2i, x2(0), x2(1));
z := (x1i - x2i) mod m1;
end Next_Int;

----------------
-- Next_Float --
----------------

function Next_Float return Long_Float is
begin
return Long_float(Next_Int) / Long_Float(d);
end Next_Float;

end MRG32KA;

with mrg32ka; use mrg32ka;

procedure Main is
counts : array(0..4) of Natural := (Others => 0);
J : Natural;
begin

seed(1234567);
for I in 1..5 loop
Put_Line(I64'Image(Next_Int));
end loop;
New_Line;
seed(987654321);

for I in 1..100_000 loop
J := Natural(Long_Float'Floor(Next_Float * 5.0));
Counts(J) := Counts(J) + 1;
end loop;

for I in Counts'Range loop
Put(I'Image & " :" & Counts(I)'Image);
end loop;

end Main;

Output:
1459213977
2827710106
4245671317
3877608661
2595287583

0 : 20002 1 : 20060 2 : 19948 3 : 20059 4 : 19931

## C

#include <math.h>
#include <stdio.h>
#include <stdint.h>

int64_t mod(int64_t x, int64_t y) {
int64_t m = x % y;
if (m < 0) {
if (y < 0) {
return m - y;
} else {
return m + y;
}
}
return m;
}

// Constants
// First generator
const static int64_t a1[3] = { 0, 1403580, -810728 };
const static int64_t m1 = (1LL << 32) - 209;
// Second generator
const static int64_t a2[3] = { 527612, 0, -1370589 };
const static int64_t m2 = (1LL << 32) - 22853;

const static int64_t d = (1LL << 32) - 209 + 1; // m1 + 1

// the last three values of the first generator
static int64_t x1[3];
// the last three values of the second generator
static int64_t x2[3];

void seed(int64_t seed_state) {
x1[0] = seed_state;
x1[1] = 0;
x1[2] = 0;

x2[0] = seed_state;
x2[1] = 0;
x2[2] = 0;
}

int64_t next_int() {
int64_t x1i = mod((a1[0] * x1[0] + a1[1] * x1[1] + a1[2] * x1[2]), m1);
int64_t x2i = mod((a2[0] * x2[0] + a2[1] * x2[1] + a2[2] * x2[2]), m2);
int64_t z = mod(x1i - x2i, m1);

// keep last three values of the first generator
x1[2] = x1[1];
x1[1] = x1[0];
x1[0] = x1i;

// keep last three values of the second generator
x2[2] = x2[1];
x2[1] = x2[0];
x2[0] = x2i;

return z + 1;
}

double next_float() {
return (double)next_int() / d;
}

int main() {
int counts[5] = { 0, 0, 0, 0, 0 };
int i;

seed(1234567);
printf("%lld\n", next_int());
printf("%lld\n", next_int());
printf("%lld\n", next_int());
printf("%lld\n", next_int());
printf("%lld\n", next_int());
printf("\n");

seed(987654321);
for (i = 0; i < 100000; i++) {
int64_t value = floor(next_float() * 5);
counts[value]++;
}
for (i = 0; i < 5; i++) {
printf("%d: %d\n", i, counts[i]);
}

return 0;
}
Output:
1459213977
2827710106
4245671317
3877608661
2595287583

0: 20002
1: 20060
2: 19948
3: 20059
4: 19931

## C++

Translation of: C
#include <array>
#include <iostream>

int64_t mod(int64_t x, int64_t y) {
int64_t m = x % y;
if (m < 0) {
if (y < 0) {
return m - y;
} else {
return m + y;
}
}
return m;
}

class RNG {
private:
// First generator
const std::array<int64_t, 3> a1{ 0, 1403580, -810728 };
const int64_t m1 = (1LL << 32) - 209;
std::array<int64_t, 3> x1;
// Second generator
const std::array<int64_t, 3> a2{ 527612, 0, -1370589 };
const int64_t m2 = (1LL << 32) - 22853;
std::array<int64_t, 3> x2;
// other
const int64_t d = (1LL << 32) - 209 + 1; // m1 + 1

public:
void seed(int64_t state) {
x1 = { state, 0, 0 };
x2 = { state, 0, 0 };
}

int64_t next_int() {
int64_t x1i = mod((a1[0] * x1[0] + a1[1] * x1[1] + a1[2] * x1[2]), m1);
int64_t x2i = mod((a2[0] * x2[0] + a2[1] * x2[1] + a2[2] * x2[2]), m2);
int64_t z = mod(x1i - x2i, m1);

// keep last three values of the first generator
x1 = { x1i, x1[0], x1[1] };
// keep last three values of the second generator
x2 = { x2i, x2[0], x2[1] };

return z + 1;
}

double next_float() {
return static_cast<double>(next_int()) / d;
}
};

int main() {
RNG rng;

rng.seed(1234567);
std::cout << rng.next_int() << '\n';
std::cout << rng.next_int() << '\n';
std::cout << rng.next_int() << '\n';
std::cout << rng.next_int() << '\n';
std::cout << rng.next_int() << '\n';
std::cout << '\n';

std::array<int, 5> counts{ 0, 0, 0, 0, 0 };
rng.seed(987654321);
for (size_t i = 0; i < 100000; i++) {
auto value = floor(rng.next_float() * 5.0);
counts[value]++;
}
for (size_t i = 0; i < counts.size(); i++) {
std::cout << i << ": " << counts[i] << '\n';
}

return 0;
}
Output:
1459213977
2827710106
4245671317
3877608661
2595287583

0: 20002
1: 20060
2: 19948
3: 20059
4: 19931

## D

Translation of: C++
import std.math;
import std.stdio;

long mod(long x, long y) {
long m = x % y;
if (m < 0) {
if (y < 0) {
return m - y;
} else {
return m + y;
}
}
return m;
}

class RNG {
private:
// First generator
immutable(long []) a1 = [0, 1403580, -810728];
immutable long m1 = (1L << 32) - 209;
long[3] x1;
// Second generator
immutable(long []) a2 = [527612, 0, -1370589];
immutable long m2 = (1L << 32) - 22853;
long[3] x2;
// other
immutable long d = m1 + 1;

public:
void seed(long state) {
x1 = [state, 0, 0];
x2 = [state, 0, 0];
}

long next_int() {
long x1i = mod((a1[0] * x1[0] + a1[1] * x1[1] + a1[2] * x1[2]), m1);
long x2i = mod((a2[0] * x2[0] + a2[1] * x2[1] + a2[2] * x2[2]), m2);
long z = mod(x1i - x2i, m1);

// keep the last three values of the first generator
x1 = [x1i, x1[0], x1[1]];
// keep the last three values of the second generator
x2 = [x2i, x2[0], x2[1]];

return z + 1;
}

double next_float() {
return cast(double) next_int() / d;
}
}

void main() {
auto rng = new RNG();

rng.seed(1234567);
writeln(rng.next_int);
writeln(rng.next_int);
writeln(rng.next_int);
writeln(rng.next_int);
writeln(rng.next_int);
writeln;

int[5] counts;
rng.seed(987654321);
foreach (i; 0 .. 100_000) {
auto value = cast(int) floor(rng.next_float * 5.0);
counts[value]++;
}
foreach (i,v; counts) {
writeln(i, ": ", v);
}
}
Output:
1459213977
2827710106
4245671317
3877608661
2595287583

0: 20002
1: 20060
2: 19948
3: 20059
4: 19931

## Factor

USING: arrays kernel math math.order math.statistics
math.vectors prettyprint sequences ;

CONSTANT: m1 4294967087
CONSTANT: m2 4294944443

: seed ( n -- seq1 seq2 )
dup 1 m1 between? t assert= 0 0 3array dup ;

: new-state ( seq1 seq2 n -- new-seq )
[ dup ] [ vdot ] [ rem prefix but-last ] tri* ;

: next-state ( a b -- a' b' )
[ { 0 1403580 -810728 } m1 new-state ]
[ { 527612 0 -1370589 } m2 new-state ] bi* ;

: next-int ( a b -- a' b' n )
next-state 2dup [ first ] [email protected] - m1 rem 1 + ;

: next-float ( a b -- a' b' x ) next-int m1 1 + /f ;

1234567 seed 5 [ next-int . ] times 2drop

987654321 seed 100,000 [ next-float 5 * >integer ] replicate
2nip histogram .
Output:
1459213977
2827710106
4245671317
3877608661
2595287583
H{ { 0 20002 } { 1 20060 } { 2 19948 } { 3 20059 } { 4 19931 } }

## Forth

Translation of: uBasic/4tH
Works with: 4tH v3.64
6 array (seed)                         \ holds the seed
6 array (gens) \ holds the generators
\ set up constants
0 (gens) 0 th ! \ 1st generator
1403580 (gens) 1 th !
-810728 (gens) 2 th !
527612 (gens) 3 th ! \ 2nd generator
0 (gens) 4 th !
-1370589 (gens) 5 th !

1 32 lshift 209 - value (m) \ 1st generator constant
1 32 lshift 22853 - value (n) \ 2nd generator constant
( n1 n2 -- n3)
: (mod) tuck mod tuck 0< if abs + ;then drop ;
: (generate) do (seed) i th @ (gens) i th @ * + loop swap (mod) ;
: (reseed) ?do (seed) i th ! loop ; ( n1 n2 n3 limit index --)
: randomize 6 0 do dup i 3 mod if >zero then (seed) i th ! loop drop ;
( n --)
: random ( -- n)
(m) 0 3 0 (generate) (n) 0 6 3 (generate) over over
(seed) 4 th @ (seed) 3 th @ rot 6 3 (reseed)
(seed) 1 th @ (seed) 0 th @ rot 3 0 (reseed) - (m) (mod) 1+
;

include lib/fp1.4th \ simple floating point support
include lib/zenfloor.4th \ for FLOOR

5 array (count) \ setup an array of 5 elements

: test
1234567 randomize
random . cr random . cr random . cr
random . cr random . cr cr \ perform the first test

987654321 randomize (m) 1+ s>f \ set up denominator

100000 0 ?do \ do this 100,000 times
random s>f fover f/ 5 s>f f* floor f>s cells (count) + 1 swap +!
loop fdrop
\ show the results
5 0 ?do i . ." : " (count) i th ? cr loop
;

test
Output:
1459213977
2827710106
4245671317
3877608661
2595287583

0 : 20002
1 : 20060
2 : 19948
3 : 20059
4 : 19931

## Go

Translation of: Python
package main

import (
"fmt"
"log"
"math"
)

var a1 = []int64{0, 1403580, -810728}
var a2 = []int64{527612, 0, -1370589}

const m1 = int64((1 << 32) - 209)
const m2 = int64((1 << 32) - 22853)
const d = m1 + 1

// Python style modulus
func mod(x, y int64) int64 {
m := x % y
if m < 0 {
if y < 0 {
return m - y
} else {
return m + y
}
}
return m
}

type MRG32k3a struct{ x1, x2 [3]int64 }

func MRG32k3aNew() *MRG32k3a { return &MRG32k3a{} }

func (mrg *MRG32k3a) seed(seedState int64) {
if seedState <= 0 || seedState >= d {
log.Fatalf("Argument must be in the range [0, %d].\n", d)
}
mrg.x1 = [3]int64{seedState, 0, 0}
mrg.x2 = [3]int64{seedState, 0, 0}
}

func (mrg *MRG32k3a) nextInt() int64 {
x1i := mod(a1[0]*mrg.x1[0]+a1[1]*mrg.x1[1]+a1[2]*mrg.x1[2], m1)
x2i := mod(a2[0]*mrg.x2[0]+a2[1]*mrg.x2[1]+a2[2]*mrg.x2[2], m2)
mrg.x1 = [3]int64{x1i, mrg.x1[0], mrg.x1[1]} /* keep last three */
mrg.x2 = [3]int64{x2i, mrg.x2[0], mrg.x2[1]} /* keep last three */
return mod(x1i-x2i, m1) + 1
}

func (mrg *MRG32k3a) nextFloat() float64 { return float64(mrg.nextInt()) / float64(d) }

func main() {
randomGen := MRG32k3aNew()
randomGen.seed(1234567)
for i := 0; i < 5; i++ {
fmt.Println(randomGen.nextInt())
}

var counts [5]int
randomGen.seed(987654321)
for i := 0; i < 1e5; i++ {
j := int(math.Floor(randomGen.nextFloat() * 5))
counts[j]++
}
fmt.Println("\nThe counts for 100,000 repetitions are:")
for i := 0; i < 5; i++ {
fmt.Printf("  %d : %d\n", i, counts[i])
}
}
Output:
1459213977
2827710106
4245671317
3877608661
2595287583

The counts for 100,000 repetitions are:
0 : 20002
1 : 20060
2 : 19948
3 : 20059
4 : 19931

import Data.List

randoms :: Int -> [Int]
randoms seed = unfoldr go ([seed,0,0],[seed,0,0])
where
go (x1,x2) =
let x1i = sum (zipWith (*) x1 a1) `mod` m1
x2i = sum (zipWith (*) x2 a2) `mod` m2
in Just \$ ((x1i - x2i) `mod` m1, (x1i:init x1, x2i:init x2))

a1 = [0, 1403580, -810728]
m1 = 2^32 - 209
a2 = [527612, 0, -1370589]
m2 = 2^32 - 22853

randomsFloat = map ((/ (2^32 - 208)) . fromIntegral) . randoms
*Main> take 5 \$ randoms 1234567
[1459213976,2827710105,4245671316,3877608660,2595287582]

*Main> let hist = map length . group . sort
*Main> hist . take 100000 \$ (floor . (*5)) <\$> randomsFloat 987654321
[20002,20060,19948,20059,19931]

### As a RandomGen instanse

import System.Random

newtype MRG32k3a = MRG32k3a ([Int],[Int])

mkMRG32k3a s = MRG32k3a ([s,0,0],[s,0,0])

instance RandomGen MRG32k3a where
next (MRG32k3a (x1,x2)) =
let x1i = sum (zipWith (*) x1 a1) `mod` m1
x2i = sum (zipWith (*) x2 a2) `mod` m2
in ((x1i - x2i) `mod` m1, MRG32k3a (x1i:init x1, x2i:init x2))
where
a1 = [0, 1403580, -810728]
m1 = 2^32 - 209
a2 = [527612, 0, -1370589]
m2 = 2^32 - 22853

split _ = error "MRG32k3a is not splittable"

In this case the sequence or numbers differs from direct unfolding, due to internal uniform shuffling.

*Main> take 5 \$ randoms (mkMRG32k3a 1234567)
[2827710105,3877608660,3642754129,1259674122,3002249941]

*Main> let hist = map length . group . sort
*Main> hist . take 100000 \$ (floor . (*5)) <\$> (randoms (mkMRG32k3a 987654321) :: [Float])
[20015,19789,20024,20133,20039]

## Java

Translation of: C++
public class App {
private static long mod(long x, long y) {
long m = x % y;
if (m < 0) {
if (y < 0) {
return m - y;
} else {
return m + y;
}
}
return m;
}

public static class RNG {
// first generator
private final long[] a1 = {0, 1403580, -810728};
private static final long m1 = (1L << 32) - 209;
private long[] x1;
// second generator
private final long[] a2 = {527612, 0, -1370589};
private static final long m2 = (1L << 32) - 22853;
private long[] x2;
// other
private static final long d = m1 + 1;

public void seed(long state) {
x1 = new long[]{state, 0, 0};
x2 = new long[]{state, 0, 0};
}

public long nextInt() {
long x1i = mod(a1[0] * x1[0] + a1[1] * x1[1] + a1[2] * x1[2], m1);
long x2i = mod(a2[0] * x2[0] + a2[1] * x2[1] + a2[2] * x2[2], m2);
long z = mod(x1i - x2i, m1);

// keep the last three values of the first generator
x1 = new long[]{x1i, x1[0], x1[1]};
// keep the last three values of the second generator
x2 = new long[]{x2i, x2[0], x2[1]};

return z + 1;
}

public double nextFloat() {
return 1.0 * nextInt() / d;
}
}

public static void main(String[] args) {
RNG rng = new RNG();

rng.seed(1234567);
System.out.println(rng.nextInt());
System.out.println(rng.nextInt());
System.out.println(rng.nextInt());
System.out.println(rng.nextInt());
System.out.println(rng.nextInt());
System.out.println();

int[] counts = {0, 0, 0, 0, 0};
rng.seed(987654321);
for (int i = 0; i < 100_000; i++) {
int value = (int) Math.floor(rng.nextFloat() * 5.0);
counts[value]++;
}
for (int i = 0; i < counts.length; i++) {
System.out.printf("%d: %d%n", i, counts[i]);
}
}
}
Output:
1459213977
2827710106
4245671317
3877608661
2595287583

0: 20002
1: 20060
2: 19948
3: 20059
4: 19931

## Julia

const a1 = [0, 1403580, -810728]
const m1 = 2^32 - 209
const a2 = [527612, 0, -1370589]
const m2 = 2^32 - 22853
const d = m1 + 1

mutable struct MRG32k3a
x1::Tuple{Int64, Int64, Int64}
x2::Tuple{Int64, Int64, Int64}
MRG32k3a() = new((0, 0, 0), (0, 0, 0))
MRG32k3a(seed_state) = new((seed_state, 0, 0), (seed_state, 0, 0))
end
seed(sd) = begin @assert(0 < sd < d); MRG32k3a(sd) end

function next_int(x::MRG32k3a)
x1i = mod1(a1[1] * x.x1[1] + a1[2] * x.x1[2] + a1[3] * x.x1[3], m1)
x2i = mod1(a2[1] * x.x2[1] + a2[2] * x.x2[2] + a2[3] * x.x2[3], m2)
x.x1 = (x1i, x.x1[1], x.x1[2])
x.x2 = (x2i, x.x2[1], x.x2[2])
return mod1(x1i - x2i, m1) + 1
end

next_float(x::MRG32k3a) = next_int(x) / d

const g1 = seed(1234567)
for _ in 1:5
println(next_int(g1))
end
const g2 = seed(987654321)
hist = fill(0, 5)
for _ in 1:100_000
hist[Int(floor(next_float(g2) * 5)) + 1] += 1
end
foreach(p -> print(p[1], ": ", p[2], " "), enumerate(hist))

Output:
1459213977
2827710106
4245671317
3877608661
2595287583
1: 20002  2: 20060  3: 19948  4: 20059  5: 19931

## Kotlin

Translation of: C++
import kotlin.math.floor

fun mod(x: Long, y: Long): Long {
val m = x % y
return if (m < 0) {
if (y < 0) {
m - y
} else {
m + y
}
} else m
}

class RNG {
// first generator
private val a1 = arrayOf(0L, 1403580L, -810728L)
private val m1 = (1L shl 32) - 209
private var x1 = arrayOf(0L, 0L, 0L)

// second generator
private val a2 = arrayOf(527612L, 0L, -1370589L)
private val m2 = (1L shl 32) - 22853
private var x2 = arrayOf(0L, 0L, 0L)

private val d = m1 + 1

fun seed(state: Long) {
x1 = arrayOf(state, 0, 0)
x2 = arrayOf(state, 0, 0)
}

fun nextInt(): Long {
val x1i = mod(a1[0] * x1[0] + a1[1] * x1[1] + a1[2] * x1[2], m1)
val x2i = mod(a2[0] * x2[0] + a2[1] * x2[1] + a2[2] * x2[2], m2)
val z = mod(x1i - x2i, m1)

// keep last three values of the first generator
x1 = arrayOf(x1i, x1[0], x1[1])
// keep last three values of the second generator
x2 = arrayOf(x2i, x2[0], x2[1])

return z + 1
}

fun nextFloat(): Double {
return nextInt().toDouble() / d
}
}

fun main() {
val rng = RNG()

rng.seed(1234567)
println(rng.nextInt())
println(rng.nextInt())
println(rng.nextInt())
println(rng.nextInt())
println(rng.nextInt())
println()

val counts = IntArray(5)
rng.seed(987654321)
for (i in 0 until 100_000) {
val v = floor((rng.nextFloat() * 5.0)).toInt()
counts[v]++
}
for (iv in counts.withIndex()) {
println("\${iv.index}: \${iv.value}")
}
}
Output:
1459213977
2827710106
4245671317
3877608661
2595287583

0: 20002
1: 20060
2: 19948
3: 20059
4: 19931

## Nim

import algorithm, math, sequtils, strutils, tables

const
# First generator.
a1 = [int64 0, 1403580, -810728]
m1: int64 = 2^32 - 209
# Second generator.
a2 = [int64 527612, 0, -1370589]
m2: int64 = 2^32 - 22853

d = m1 + 1

type MRG32k3a = object
x1: array[3, int64] # List of three last values of gen #1.
x2: array[3, int64] # List of three last values of gen #2.

func seed(gen: var MRG32k3a; seedState: int64) =
assert seedState in 1..<d
gen.x1 = [seedState, 0, 0]
gen.x2 = [seedState, 0, 0]

func nextInt(gen: var MRG32k3a): int64 =
let x1i = floormod(a1[0] * gen.x1[0] + a1[1] * gen.x1[1] + a1[2] * gen.x1[2], m1)
let x2i = floormod(a2[0] * gen.x2[0] + a2[1] * gen.x2[1] + a2[2] * gen.x2[2], m2)
# In version 1.4, the following two lines doesn't work.
# gen.x1 = [x1i, gen.x1[0], gen.x1[1]] # Keep last three.
# gen.x2 = [x2i, gen.x2[0], gen.x2[1]] # Keep last three.
gen.x1[2] = gen.x1[1]; gen.x1[1] = gen.x1[0]; gen.x1[0] = x1i
gen.x2[2] = gen.x2[1]; gen.x2[1] = gen.x2[0]; gen.x2[0] = x2i
result = floormod(x1i - x2i, m1) + 1

func nextFloat(gen: var MRG32k3a): float =
gen.nextInt().float / d.float

when isMainModule:
var gen: MRG32k3a

gen.seed(1234567)
for _ in 1..5:
echo gen.nextInt()

echo ""
gen.seed(987654321)
var counts: CountTable[int]
for _ in 1..100_000:
counts.inc int(gen.nextFloat() * 5)
echo sorted(toSeq(counts.pairs)).mapIt(\$it[0] & ": " & \$it[1]).join(", ")
Output:
1459213977
2827710106
4245671317
3877608661
2595287583

0: 20002, 1: 20060, 2: 19948, 3: 20059, 4: 19931

## Pari/GP

Pretty straightforward translation from the directions. Used column/vector multiplication (essentially he dot product) instead of the more tedious form given in the definition of x1i and x2i; rationals (t_FRAC) used in place of floating-point since GP lacks floating-point.

a1 = [0, 1403580, -810728];
m1 = 2^32-209;
a2 = [527612, 0, -1370589];
m2 = 2^32-22853;
d = m1+1;
seed(s)=x1=x2=[s,0,0];
next_int()=
{
my(x1i=a1*x1~%m1, x2i=a2*x2~%m2);
x1 = [x1i, x1[1], x1[2]];
x2 = [x2i, x2[1], x2[2]];
(x1i-x2i)%m1 + 1;
}
next_float()=next_int()/d;

seed(1234567);
vector(5,i,next_int())
seed(987654321);
v=vector(5); for(i=1,1e5, v[next_float()*5\1+1]++); v
Output:
%1 = [1459213977, 2827710106, 4245671317, 3877608661, 2595287583]
%2 = [20002, 20060, 19948, 20059, 19931]

## Perl

use strict;
use warnings;
use feature 'say';

package MRG32k3a {

use constant {
m1 => 2**32 - 209,
m2 => 2**32 - 22853
};

use Const::Fast;
const my @a1 => < 0 1403580 -810728>;
const my @a2 => <527612 0 -1370589>;

sub new {
my (\$class,undef,\$seed) = @_;
my @x1 = my @x2 = (\$seed, 0, 0);
bless {x1 => \@x1, x2 => \@x2}, \$class;
}

sub next_int {
my (\$self) = @_;
unshift @{\$\$self{x1}}, (\$a1[0] * \$\$self{x1}[0] + \$a1[1] * \$\$self{x1}[1] + \$a1[2] * \$\$self{x1}[2]) % m1; pop @{\$\$self{x1}};
unshift @{\$\$self{x2}}, (\$a2[0] * \$\$self{x2}[0] + \$a2[1] * \$\$self{x2}[1] + \$a2[2] * \$\$self{x2}[2]) % m2; pop @{\$\$self{x2}};
(\$\$self{x1}[0] - \$\$self{x2}[0]) % (m1 + 1)
}

sub next_float { \$_[0]->next_int / (m1 + 1) }
}

say 'Seed: 1234567, first 5 values:';
my \$rng = MRG32k3a->new( seed => 1234567 );
say \$rng->next_int for 1..5;

my %h;
say "\nSeed: 987654321, values histogram:";
\$rng = MRG32k3a->new( seed => 987654321 );
\$h{int 5 * \$rng->next_float}++ for 1..100_000;
say "\$_ \$h{\$_}" for sort keys %h;
Output:
Seed: 1234567, first 5 values:
1459213977
2827710106
4245671317
3877608661
2595287583

Seed: 987654321, values histogram:
0 20002
1 20060
2 19948
3 20059
4 19931

## Phix

with javascript_semantics
constant
-- First generator
a1 = {0, 1403580, -810728},
m1 = power(2,32) - 209,
-- Second Generator
a2 = {527612, 0, -1370589},
m2 = power(2,32) - 22853,
d = m1 + 1

sequence x1 = {0, 0, 0},  /* list of three last values of gen #1 */
x2 = {0, 0, 0}   /* list of three last values of gen #2 */

procedure seed(integer seed_state)
assert(seed_state>0 and seed_state<d)
x1 = {seed_state, 0, 0}
x2 = {seed_state, 0, 0}
end procedure

function next_int()
atom x1i = mod(a1[1]*x1[1] + a1[2]*x1[2] + a1[3]*x1[3],m1),
x2i = mod(a2[1]*x2[1] + a2[2]*x2[2] + a2[3]*x2[3],m2)
x1 = {x1i, x1[1], x1[2]}    /* Keep last three */
x2 = {x2i, x2[1], x2[2]}    /* Keep last three */
atom z = mod(x1i-x2i,m1),
end function

function next_float()
return next_int() / d
end function

seed(1234567)
for i=1 to 5 do
printf(1,"%d\n",next_int())
end for
seed(987654321)
sequence r = repeat(0,5)
for i=1 to 100_000 do
integer rdx = floor(next_float()*5)+1
r[rdx] += 1
end for
?r
Output:
1459213977
2827710106
4245671317
3877608661
2595287583
{20002,20060,19948,20059,19931}

## Python

# Constants
a1 = [0, 1403580, -810728]
m1 = 2**32 - 209
#
a2 = [527612, 0, -1370589]
m2 = 2**32 - 22853
#
d = m1 + 1

class MRG32k3a():

def __init__(self, seed_state=123):
self.seed(seed_state)

def seed(self, seed_state):
assert 0 <seed_state < d, f"Out of Range 0 x < {d}"
self.x1 = [seed_state, 0, 0]
self.x2 = [seed_state, 0, 0]

def next_int(self):
"return random int in range 0..d"
x1i = sum(aa * xx for aa, xx in zip(a1, self.x1)) % m1
x2i = sum(aa * xx for aa, xx in zip(a2, self.x2)) % m2
self.x1 = [x1i] + self.x1[:2]
self.x2 = [x2i] + self.x2[:2]

z = (x1i - x2i) % m1

def next_float(self):
"return random float between 0 and 1"
return self.next_int() / d

if __name__ == '__main__':
random_gen = MRG32k3a()
random_gen.seed(1234567)
for i in range(5):
print(random_gen.next_int())

random_gen.seed(987654321)
hist = {i:0 for i in range(5)}
for i in range(100_000):
hist[int(random_gen.next_float() *5)] += 1
print(hist)
Output:
1459213977
2827710106
4245671317
3877608661
2595287583
{0: 20002, 1: 20060, 2: 19948, 3: 20059, 4: 19931}

## Raku

Works with: Rakudo version 2020.07
Translation of: Python

All constants are encapsulated within the class.

class MRG32k3a {
has @!x1;
has @!x2;

constant a1 = 0, 1403580, -810728;
constant a2 = 527612, 0, -1370589;
constant m1 = 2**32 - 209;
constant m2 = 2**32 - 22853;

submethod BUILD ( Int :\$seed where 0 < * <= m1 = 1 ) { @!x1 = @!x2 = \$seed, 0, 0 }

method next-int {
@!x1.unshift: (a1[0] * @!x1[0] + a1[1] * @!x1[1] + a1[2] * @!x1[2]) % m1; @!x1.pop;
@!x2.unshift: (a2[0] * @!x2[0] + a2[1] * @!x2[1] + a2[2] * @!x2[2]) % m2; @!x2.pop;
(@!x1[0] - @!x2[0]) % (m1 + 1)
}

method next-rat { self.next-int / (m1 + 1) }
}

# Test next-int with custom seed
say 'Seed: 1234567; first five Int values:';
my \$rng = MRG32k3a.new :seed(1234567);
.say for \$rng.next-int xx 5;

# Test next-rat (since these are rational numbers by default)
say "\nSeed: 987654321; first 1e5 Rat values histogram:";
\$rng = MRG32k3a.new :seed(987654321);
say ( (\$rng.next-rat * 5).floor xx 100_000 ).Bag;

# Test next-int with default seed
say "\nSeed: default; first five Int values:";
\$rng = MRG32k3a.new;
.say for \$rng.next-int xx 5;
Output:
Seed: 1234567; first five Int values:
1459213977
2827710106
4245671317
3877608661
2595287583

Seed: 987654321; first 1e5 Rat values histogram:
Bag(0(20002) 1(20060) 2(19948) 3(20059) 4(19931))

Seed: default; first five Int values:
4294439476
798392476
1012402088
1268414424
3353586348

## Ruby

Translation of: C
def mod(x, y)
m = x % y
if m < 0 then
if y < 0 then
return m - y
else
return m + y
end
end
return m
end

# Constants
# First generator
A1 = [0, 1403580, -810728]
A1.freeze
M1 = (1 << 32) - 209
# Second generator
A2 = [527612, 0, -1370589]
A2.freeze
M2 = (1 << 32) - 22853

D = M1 + 1

# the last three values of the first generator
\$x1 = [0, 0, 0]
# the last three values of the second generator
\$x2 = [0, 0, 0]

def seed(seed_state)
\$x1 = [seed_state, 0, 0]
\$x2 = [seed_state, 0, 0]
end

def next_int()
x1i = mod((A1[0] * \$x1[0] + A1[1] * \$x1[1] + A1[2] * \$x1[2]), M1)
x2i = mod((A2[0] * \$x2[0] + A2[1] * \$x2[1] + A2[2] * \$x2[2]), M2)
z = mod(x1i - x2i, M1)

\$x1 = [x1i, \$x1[0], \$x1[1]]
\$x2 = [x2i, \$x2[0], \$x2[1]]

return z + 1
end

def next_float()
return 1.0 * next_int() / D
end

########################################

seed(1234567)
print next_int(), "\n"
print next_int(), "\n"
print next_int(), "\n"
print next_int(), "\n"
print next_int(), "\n"
print "\n"

counts = [0, 0, 0, 0, 0]
seed(987654321)
for i in 1 .. 100000
value = (next_float() * 5.0).floor
counts[value] = counts[value] + 1
end
counts.each_with_index { |v,i|
print i, ": ", v, "\n"
}
Output:
1459213977
2827710106
4245671317
3877608661
2595287583

0: 20002
1: 20060
2: 19948
3: 20059
4: 19931

### Mimicking the Pseudo-code

# Constants
# First generator
A1 = [0, 1403580, -810728]
M1 = 2**32 - 209
# Second Generator
A2 = [527612, 0, -1370589]
M2 = 2**32 - 22853

D = M1 + 1

class MRG32k3a

def seed(seed_state)
raise ArgumentError unless seed_state.between?(0, D)
@x1 = [seed_state, 0, 0]
@x2 = [seed_state, 0, 0]
end

def next_int
x1i = (A1[0]*@x1[0] + A1[1]*@x1[1] + A1[2]*@x1[2]).modulo M1
x2i = (A2[0]*@x2[0] + A2[1]*@x2[1] + A2[2]*@x2[2]).modulo M2
@x1 = [x1i, @x1[0], @x1[1]] # Keep last three
@x2 = [x2i, @x2[0], @x2[1]] # Keep last three
z = (x1i - x2i) % M1
return z + 1
end

def next_float
next_int.to_f / D
end

end

random_gen = MRG32k3a.new
random_gen.seed(1234567)
5.times{ puts random_gen.next_int}

random_gen = MRG32k3a.new
random_gen.seed(987654321)
p 100_000.times.map{(random_gen.next_float() * 5).floor}.tally.sort.to_h

## Sidef

Translation of: Perl
class MRG32k3a(seed) {

define(
m1 = (2**32 - 209)
m2 = (2**32 - 22853)
)

define(
a1 = %n< 0 1403580 -810728>
a2 = %n<527612 0 -1370589>
)

has x1 = [seed, 0, 0]
has x2 = x1.clone

method next_int {
x1.unshift(a1.map_kv {|k,v| v * x1[k] }.sum % m1); x1.pop
x2.unshift(a2.map_kv {|k,v| v * x2[k] }.sum % m2); x2.pop
(x1[0] - x2[0]) % (m1 + 1)
}

method next_float { self.next_int / (m1 + 1) -> float }
}

say "Seed: 1234567, first 5 values:"
var rng = MRG32k3a(seed: 1234567)
5.of { rng.next_int }.each { .say }

say "\nSeed: 987654321, values histogram:";
var rng = MRG32k3a(seed: 987654321)
var freq = 100_000.of { rng.next_float * 5 -> int }.freq
freq.sort.each_2d {|k,v| say "#{k} #{v}" }
Output:
Seed: 1234567, first 5 values:
1459213977
2827710106
4245671317
3877608661
2595287583

Seed: 987654321, values histogram:
0 20002
1 20060
2 19948
3 20059
4 19931

## uBasic/4tH

Works with: v3.64
Translation of: C

Since uBasic/4tH has no floating point support, only the integer part of the task can be implemented.

@(0) = 0                               ' First generator
@(1) = 1403580
@(2) = -810728
m = SHL(1, 32) - 209

@(3) = 527612 ' Second generator
@(4) = 0
@(5) = -1370589
n = SHL(1, 32) - 22853

d = SHL(1, 32) - 209 + 1 ' m + 1

Proc _Seed(1234567)
Print FUNC(_NextInt)
Print FUNC(_NextInt)
Print FUNC(_NextInt)
Print FUNC(_NextInt)
Print FUNC(_NextInt)
Print
End

_Mod Param(2)
Local(1)
[email protected] = [email protected] % [email protected]
If [email protected] < 0 Then
If [email protected] < 0 Then
Return ([email protected]@)
Else
Return ([email protected][email protected])
Endif
EndIf
Return ([email protected])

_Seed Param(1) ' seed the PRNG
@(6) = [email protected]
@(7) = 0
@(8) = 0

@(9) = [email protected]
@(10) = 0
@(11) = 0
Return

_NextInt ' get the next random integer value
Local(3)

[email protected] = FUNC(_Mod((@(0) * @(6) + @(1) * @(7) + @(2) * @(8)), m))
[email protected] = FUNC(_Mod((@(3) * @(9) + @(4) * @(10) + @(5) * @(11)), n))
[email protected] = FUNC(_Mod([email protected] - [email protected], m))

' keep last three values of the first generator
@(8) = @(7)
@(7) = @(6)
@(6) = [email protected]

' keep last three values of the second generator
@(11) = @(10)
@(10) = @(9)
@(9) = [email protected]

Return ([email protected] + 1)
Output:
1459213977
2827710106
4245671317
3877608661
2595287583

0 OK, 0:398

## Wren

Translation of: Python
// constants
var A1 = [0, 1403580, -810728]
var M1 = 2.pow(32) - 209
var A2 = [527612, 0, -1370589]
var M2 = 2.pow(32) - 22853
var D = M1 + 1

// Python style modulus
var Mod = Fn.new { |x, y|
var m = x % y
return (m < 0) ? m + y.abs : m
}

class MRG32k3a {
construct new() {
_x1 = [0, 0, 0]
_x2 = [0, 0, 0]
}

seed(seedState) {
if (seedState <= 0 || seedState >= D) {
Fiber.abort("Argument must be in the range [0, %(D)].")
}
_x1 = [seedState, 0, 0]
_x2 = [seedState, 0, 0]
}

nextInt {
var x1i = Mod.call(A1[0]*_x1[0] + A1[1]*_x1[1] + A1[2]*_x1[2], M1)
var x2i = Mod.call(A2[0]*_x2[0] + A2[1]*_x2[1] + A2[2]*_x2[2], M2)
_x1 = [x1i, _x1[0], _x1[1]] /* keep last three */
_x2 = [x2i, _x2[0], _x2[1]] /* keep last three */
return Mod.call(x1i - x2i, M1) + 1
}

nextFloat { nextInt / D }
}

var randomGen = MRG32k3a.new()
randomGen.seed(1234567)
for (i in 0..4) System.print(randomGen.nextInt)

var counts = List.filled(5, 0)
randomGen.seed(987654321)
for (i in 1..1e5) {
var i = (randomGen.nextFloat * 5).floor
counts[i] = counts[i] + 1
}
System.print("\nThe counts for 100,000 repetitions are:")
for (i in 0..4) System.print("  %(i) : %(counts[i])")
Output:
1459213977
2827710106
4245671317
3877608661
2595287583

The counts for 100,000 repetitions are:
0 : 20002
1 : 20060
2 : 19948
3 : 20059
4 : 19931