Pseudo-random numbers/Combined recursive generator MRG32k3a

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
           answer = (z + 1)
           
           return answer
       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 */

Task

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

Show your output here, on this page.

Factor[edit]

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 ;
 
! Task
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 } }

Go[edit]

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

Julia[edit]

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

Phix[edit]

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),
    answer = (z + 1)
    return answer
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
    r[floor(next_float()*5)+1] += 1
end for
?r

Output:

1459213977
2827710106
4245671317
3877608661
2595287583
{20002,20060,19948,20059,19931}

Python[edit]

# 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
        answer = (z + 1)
 
        return answer
 
    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[edit]

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

Wren[edit]

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

Pseudo-random numbers/Combined recursive generator MRG32k3a

Contents

Factor[edit]

Go[edit]

Julia[edit]

Phix[edit]

Python[edit]

Raku[edit]

Wren[edit]