Pseudo-random numbers/Splitmix64: Difference between revisions

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λ> hist . take 100000 $ (floor . (*5) . toFloat) <$> (randoms 987654321)
λ> hist . take 100000 $ (floor . (*5) . toFloat) <$> (randoms 987654321)
[20027,19892,20073,19978,20030]</pre>
[20027,19892,20073,19978,20030]</pre>

=={{header|Jasmin}}==

<lang>u64 c1 = 0x9e3779b97f4a7c15;
u64 c2 = 0xbf58476d1ce4e5b9;
u64 c3 = 0x94d049bb133111eb;

inline
fn next_int(reg u64 state) -> reg u64 {
reg u64 z a;
z = [state];
z += c1;
[state] = z;
a = z;
a >>= 30;
z ^= a;
z *= c2;
a = z;
a >>= 27;
z ^= a;
z *= c3;
a = z;
a >>= 31;
z ^= a;
return z;
}

inline
fn test() -> reg u64[5] {
reg u64 seed;
seed = 0x1000;
[seed] = 1234567;
inline int i;
reg u64[5] result;
for i = 0 to 5 {
result[i] = next_int(seed);
}
return result;
}
exec test(0x1000:8)</lang>


=={{header|Julia}}==
=={{header|Julia}}==

Revision as of 13:14, 24 July 2022

Task
Pseudo-random numbers/Splitmix64
You are encouraged to solve this task according to the task description, using any language you may know.

Splitmix64 is the default pseudo-random number generator algorithm in Java and is included / available in many other languages. It uses a fairly simple algorithm that, though it is considered to be poor for cryptographic purposes, is very fast to calculate, and is "good enough" for many random number needs. It passes several fairly rigorous PRNG "fitness" tests that some more complex algorithms fail.

Splitmix64 is not recommended for demanding random number requirements, but is often used to calculate initial states for other more complex pseudo-random number generators.

The "standard" splitmix64 maintains one 64 bit state variable and returns 64 bits of random data with each call.

Basic pseudocode algorithm: 

    uint64 state                                  /* The state can be seeded with any (upto) 64 bit integer value. */

    next_int() {
        state += 0x9e3779b97f4a7c15               /* increment the state variable */
        uint64 z = state                          /* copy the state to a working variable */
        z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9  /* xor the variable with the variable right bit shifted 30 then multiply by a constant */
        z = (z ^ (z >> 27)) * 0x94d049bb133111eb  /* xor the variable with the variable right bit shifted 27 then multiply by a constant */
        return z ^ (z >> 31)                      /* return the variable xored with itself right bit shifted 31 */
    }

    next_float() {
        return next_int() / (1 << 64)             /* divide by 2^64 to return a value between 0 and 1 */
    }

The returned value should hold 64 bits of numeric data. If your language does not support unsigned 64 bit integers directly you may need to apply appropriate bitmasks during bitwise operations.

In keeping with the general layout of several recent pseudo-random number tasks:


Task
  • Write a class or set of functions that generates pseudo-random numbers using splitmix64.
  • Show the first five integers generated using the seed 1234567.
    6457827717110365317
    3203168211198807973
    9817491932198370423
    4593380528125082431
   16408922859458223821
  • Show that for an initial seed of 987654321, the counts of 100_000 repetitions of floor next_float() * 5 is as follows:
   0: 20027, 1: 19892, 2: 20073, 3: 19978, 4: 20030
  • Show your output here, on this page.


See also


Related tasks


11l

Translation of: Python

<lang 11l>T Splitmix64 

  UInt64 state

  F seed(seed_state)
     .state = seed_state

  F next_int()
     .state += 9E37'79B9'7F4A'7C15
     V z = .state
     z = (z (+) (z >> 30)) * BF58'476D'1CE4'E5B9
     z = (z (+) (z >> 27)) * 94D0'49BB'1331'11EB
     R z (+) (z >> 31)

  F next_float()
     R Float(.next_int()) / 2.0^64

V random_gen = Splitmix64() 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)</lang>

Output:
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821
[0 = 20027, 1 = 19892, 2 = 20073, 3 = 19978, 4 = 20030]

Ada

The random number functions are written in a stand-alone package. The package is split into a package specification defining the interfaces to the public subprograms and a body containing the implementation of the random number generator.

package specification: <lang Ada>with Interfaces; use Interfaces;

package Random_Splitmix64 is 

  function next_Int return Unsigned_64;
  function next_float return Float;
  procedure Set_State (Seed : in Unsigned_64);

end Random_Splitmix64;</lang> package body: <lang Ada>package body Random_Splitmix64 is 

  Internal : Unsigned_64 := 1234567;

  --------------
  -- next_Int --
  --------------

  function next_Int return Unsigned_64 is
     Z : Unsigned_64;
  begin
     Internal := Internal + 16#9e3779b97f4a7c15#;
     Z := Internal;
     Z := (Z xor Shift_Right(Z, 30)) * 16#bf58476d1ce4e5b9#;
     Z := (Z xor Shift_Right(Z, 27)) * 16#94d049bb133111eb#;
     return Z xor Shift_Right(Z, 31);
  end next_Int;

  ----------------
  -- next_float --
  ----------------

  function next_float return Float is
  begin
     return float(next_int) / (2.0 ** 64);
  end next_float;

  ---------------
  -- Set_State --
  ---------------

  procedure Set_State (Seed : in Unsigned_64) is
  begin
     Internal := Seed;
  end Set_State;

end Random_Splitmix64;</lang> Main procedure: <lang Ada>with Interfaces; use Interfaces; with Random_Splitmix64; use Random_Splitmix64; with Ada.Text_IO; use Ada.Text_IO;

procedure Main is 

  subtype idx is Integer range 0 .. 4;
  type answer_arr is array (idx) of Natural;
  Vec : answer_arr := (others => 0);
  J   : Integer;
  fj  : Float;

begin 

  Set_State (1_234_567);
  for I in 1 .. 5 loop
     Put (Unsigned_64'Image (next_Int));
     New_Line;
  end loop;

  Set_State (987_654_321);

  for I in 1 .. 100_000 loop
     fj      := Float'Truncation (next_float * 5.0);
     J       := Integer (fj);
     Vec (J) := Vec (J) + 1;
  end loop;

  for I in Vec'Range loop
     Put_Line (I'Image & ":" & Integer'Image (Vec (I)));
  end loop;

end Main; </lang>

Output:
 6457827717110365317
 3203168211198807973
 9817491932198370423
 4593380528125082431
 16408922859458223821
 0: 20027
 1: 19892
 2: 20073
 3: 19978
 4: 20030

ALGOL 68

Works with: ALGOL 68G version Any Tested with release 2.8.3.win32

<lang algol68>BEGIN # generate some pseudo random numbers using Splitmix64 # 

   # note that although LONG INT is 64 bits in Algol 68G, LONG BITS is longer than 64 bits #
   LONG BITS mask 64    = LONG 16rffffffffffffffff;
   LONG BITS state     := 16r1234567;
   LONG INT  one shl 64 = ABS ( LONG 16r1 SHL 64 );
   # sets the state to the specified seed value #
   PROC seed = ( LONG INT num )VOID: state := BIN num;
   # XOR and assign convenience operator #
   PRIO XORAB = 1;
   OP   XORAB = ( REF LONG BITS x, LONG BITS v )REF LONG BITS:
        x := ( x XOR v ) AND mask 64;
   # add a LONG BITS value to a LONG BITS #
   OP   +:= = ( REF LONG BITS r, LONG BITS v )REF LONG BITS:
        r := SHORTEN ( BIN ( LENG ABS r + LENG ABS v ) AND mask 64 );
   # multiplies a LONG BITS value by a LONG BITS value #
   OP   *:= = ( REF LONG BITS r, LONG BITS v )REF LONG BITS:
        r := SHORTEN ( BIN ( ABS LENG r * LENG ABS v ) AND mask 64 );
   # gets the next pseudo random integer #
   PROC next int = LONG INT:
        BEGIN
           state +:= LONG 16r9e3779b97f4a7c15;
           LONG BITS z := state;
           z XORAB ( z SHR 30 );
           z *:= LONG 16rbf58476d1ce4e5b9;
           z XORAB ( z SHR 27 );
           z *:= LONG 16r94d049bb133111eb;
           z XORAB ( z SHR 31 );
           ABS z
        END # next int # ;
   # gets the next pseudo random real #
   PROC next float = LONG REAL: next int / one shl 64;
   BEGIN # task test cases #
       seed( 1234567 );
       print( ( whole( next int, 0 ), newline ) ); #  6457827717110365317 #
       print( ( whole( next int, 0 ), newline ) ); #  3203168211198807973 #
       print( ( whole( next int, 0 ), newline ) ); #  9817491932198370423 #
       print( ( whole( next int, 0 ), newline ) ); #  4593380528125082431 #
       print( ( whole( next int, 0 ), newline ) ); # 16408922859458223821 #
       # count the number of occurances of 0..4 in a sequence of pseudo random reals scaled to be in [0..5) #
       seed( 987654321 );
       [ 0 : 4 ]INT counts; FOR i FROM LWB counts TO UPB counts DO counts[ i ] := 0 OD;
       TO 100 000 DO counts[ SHORTEN ENTIER ( next float * 5 ) ] +:= 1 OD;
       FOR i FROM LWB counts TO UPB counts DO
           print( ( whole( i, -2 ), ": ", whole( counts[ i ], -6 ) ) )
       OD;
       print( ( newline ) )
   END

END</lang>

Output:
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821
 0:  20027 1:  19892 2:  20073 3:  19978 4:  20030

C

Code copied from the reference C implementation used by Java, and using GNU GCC v7.1.1. <lang c>/* Written in 2015 by Sebastiano Vigna (vigna@acm.org)

To the extent possible under law, the author has dedicated all copyright and related and neighboring rights to this software to the public domain worldwide. This software is distributed without any warranty.

See <http://creativecommons.org/publicdomain/zero/1.0/>. */

  1. include <stdint.h>
  2. include <stdio.h>
  3. include <math.h>

/* This is a fixed-increment version of Java 8's SplittableRandom generator 

  See http://dx.doi.org/10.1145/2714064.2660195 and 
  http://docs.oracle.com/javase/8/docs/api/java/util/SplittableRandom.html

  It is a very fast generator passing BigCrush, and it can be useful if
  for some reason you absolutely want 64 bits of state. */

static uint64_t x; /* The state can be seeded with any value. */

uint64_t next() { uint64_t z = (x += 0x9e3779b97f4a7c15); z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9; z = (z ^ (z >> 27)) * 0x94d049bb133111eb; return z ^ (z >> 31); }

double next_float() { 

   return next() / pow(2.0, 64);

}

int main() { 

   int i, j;
   x = 1234567;
   for(i = 0; i < 5; ++i)
       printf("%llu\n", next()); /* needed to use %lu verb for GCC 7.5.0-3 */
   x = 987654321;
   int vec5[5] = {0, 0, 0, 0, 0};
   for(i = 0; i < 100000; ++i) {
       j = next_float() * 5.0;
       vec5[j] += 1;
   }
   for(i = 0; i < 5; ++i)
       printf("%d: %d  ", i, vec5[i]);

}

</lang>

Output:
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821
0: 20027  1: 19892  2: 20073  3: 19978  4: 20030

Factor

<lang factor>USING: io kernel math math.bitwise math.functions math.statistics namespaces prettyprint sequences ;

SYMBOL: state

seed ( n -- ) 64 bits state set ;
next-int ( -- n )
   0x9e3779b97f4a7c15 state [ + 64 bits ] change
   state get -30 0xbf58476d1ce4e5b9 -27 0x94d049bb133111eb -31 1
   [ [ dupd shift bitxor ] dip * 64 bits ] 2tri@ ;
next-float ( -- x ) next-int 64 2^ /f ;

! Test next-int "Seed: 1234567; first five integer values" print 1234567 seed 5 [ next-int . ] times nl

! Test next-float "Seed: 987654321; first 100,000 float values histogram" print 987654321 seed 100,000 [ next-float 5 * >integer ] replicate histogram .</lang>

Output:
Seed: 1234567; first five integer values
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821

Seed: 987654321; first 100,000 float values histogram
H{ { 0 20027 } { 1 19892 } { 2 20073 } { 3 19978 } { 4 20030 } }


Forth

Works with: gforth version 0.7.3

<lang forth>variable rnd-state

rnd-base-op ( z factor shift -- u ) 2 pick swap rshift rot xor * ;
rnd-next ( -- u )
 $9e3779b97f4a7c15 rnd-state +!
 rnd-state @
 $bf58476d1ce4e5b9 #30 rnd-base-op
 $94d049bb133111eb #27 rnd-base-op
 #1 #31 rnd-base-op
  1. 1234567 rnd-state !

cr rnd-next u. cr rnd-next u. cr rnd-next u. cr rnd-next u. cr rnd-next u. cr


rnd-next-float ( -- f )
 rnd-next 0 d>f 0 1 d>f f/

create counts 0 , 0 , 0 , 0 , 0 ,

counts-fill
 #987654321 rnd-state !
 100000 0 do
   rnd-next-float 5.0e0 f* f>d drop cells counts + dup @ 1+ swap !
 loop
counts-disp
 5 0 do
   cr i . ': emit bl emit
   counts i cells + @ .
 loop cr

counts-fill counts-disp</lang>

Output:
6457827717110365317 
3203168211198807973 
9817491932198370423 
4593380528125082431 
16408922859458223821 

0 : 20027 
1 : 19892 
2 : 20073 
3 : 19978 
4 : 20030 
 ok

F#

<lang fsharp>// Pure F# Implementation of SplitMix64 let a: uint64 = 0x9e3779b97f4a7c15UL

let nextInt (state: uint64) = 

   let newstate = state + (0x9e3779b97f4a7c15UL)
   let rand = newstate
   let rand = (rand ^^^ (rand >>> 30)) * 0xbf58476d1ce4e5b9UL
   let rand = (rand ^^^ (rand >>> 27)) * 0x94d049bb133111ebUL
   let rand = rand ^^^ (rand >>> 31)
   (rand, newstate)

let nextFloat (state: uint64) = 

   let (rand, newState) = nextInt state
   let randf = (rand / (1UL <<< 64)) |> float
   (randf, newState)

[<EntryPoint>] let main argv = 

   let state = 1234567UL
   let (first, state) = nextInt state
   let (second, state) = nextInt state
   let (third, state) = nextInt state
   let (fourth, state) = nextInt state
   let (fifth, state) = nextInt state
   printfn "%i" first
   printfn "%i" second
   printfn "%i" third
   printfn "%i" fourth
   printfn "%i" fifth
   0</lang>
Output:
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821

Go

<lang Go>package main

import ( 

   "fmt"
   "math"

)

type Splitmix64 struct{ state uint64 }

func Splitmix64New(state uint64) *Splitmix64 { return &Splitmix64{state} }

func (sm64 *Splitmix64) nextInt() uint64 { 

   sm64.state += 0x9e3779b97f4a7c15
   z := sm64.state
   z = (z ^ (z >> 30)) * 0xbf58476d1ce4e5b9
   z = (z ^ (z >> 27)) * 0x94d049bb133111eb
   return z ^ (z >> 31)

}

func (sm64 *Splitmix64) nextFloat() float64 { 

   return float64(sm64.nextInt()) / (1 << 64)

}

func main() { 

   randomGen := Splitmix64New(1234567)
   for i := 0; i < 5; i++ {
       fmt.Println(randomGen.nextInt())
   }

   var counts [5]int
   randomGen = Splitmix64New(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])
   }

}</lang>

Output:
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821

The counts for 100,000 repetitions are:
  0 : 20027
  1 : 19892
  2 : 20073
  3 : 19978
  4 : 20030

Haskell

<lang haskell>import Data.Bits import Data.Word import Data.List

next :: Word64 -> (Word64, Word64) next state = f4 $ state + 0x9e3779b97f4a7c15 

 where
   f1 z = (z `xor` (z `shiftR` 30)) * 0xbf58476d1ce4e5b9
   f2 z = (z `xor` (z `shiftR` 27)) * 0x94d049bb133111eb
   f3 z = z `xor` (z `shiftR` 31)
   f4 s = ((f3 . f2 . f1) s, s)

randoms = unfoldr (pure . next)

toFloat n = fromIntegral n / (2^64 - 1)</lang> 

λ> mapM_ print $ take 5 $ randoms 1234567
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821

λ> let hist = map length . group . sort
λ> hist . take 100000 $ (floor . (*5) . toFloat) <$> (randoms 987654321)
[20027,19892,20073,19978,20030]

Jasmin

<lang>u64 c1 = 0x9e3779b97f4a7c15; u64 c2 = 0xbf58476d1ce4e5b9; u64 c3 = 0x94d049bb133111eb;

inline fn next_int(reg u64 state) -> reg u64 { 

  reg u64 z a;
  z = [state];
  z += c1;
  [state] = z;
  a = z;
  a >>= 30;
  z ^= a;
  z *= c2;
  a = z;
  a >>= 27;
  z ^= a;
  z *= c3;
  a = z;
  a >>= 31;
  z ^= a;
  return z;

}

inline fn test() -> reg u64[5] { 

 reg u64 seed;
 seed = 0x1000;
 [seed] = 1234567;
 inline int i;
 reg u64[5] result;
 for i = 0 to 5 {
   result[i] = next_int(seed);
 }
 return result;

} exec test(0x1000:8)</lang>

Julia

Translation of: Python

<lang julia>const C1 = 0x9e3779b97f4a7c15 const C2 = 0xbf58476d1ce4e5b9 const C3 = 0x94d049bb133111eb

mutable struct Splitmix64 

   state::UInt

end

""" return random int between 0 and 2**64 """ function next_int(smx::Splitmix64) 

   z = smx.state = smx.state + C1
   z = (z ⊻ (z >> 30)) * C2
   z = (z ⊻ (z >> 27)) * C3
   return z ⊻ (z >> 31)

end

""" return random float between 0 and 1 """ next_float(smx::Splitmix64) = next_int(smx) / one(Int128) << 64

function testSplitmix64() 

   random_gen = Splitmix64(1234567)
   for i in 1:5
       println(next_int(random_gen))
   end

   random_gen = Splitmix64(987654321)
   hist = fill(0, 5)
   for _ in 1:100_000
       hist[Int(floor(next_float(random_gen) * 5)) + 1] += 1
   end
   foreach(n -> print(n - 1, ": ", hist[n], "  "), 1:5)

end

testSplitmix64()

</lang>

Output:
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821
0: 20027  1: 19892  2: 20073  3: 19978  4: 20030

Mathematica/Wolfram Language

<lang Mathematica>ClearAll[BitShiftLevelUint, MultiplyUint, GenerateRandomNumbers] BitShiftLevelUint[z_, n_] := BitShiftRight[z, n] MultiplyUint[z_, n_] := Mod[z n, 2^64] GenerateRandomNumbers[st_, n_] := Module[{state = st}, 

 Table[
  state += 16^^9e3779b97f4a7c15;
  state = Mod[state, 2^64];
  z = state;
  z = MultiplyUint[BitXor[z, BitShiftLevelUint[z, 30]], 16^^bf58476d1ce4e5b9];
  z = MultiplyUint[BitXor[z, BitShiftLevelUint[z, 27]], 16^^94d049bb133111eb];
  Mod[BitXor[z, BitShiftLevelUint[z, 31]], 2^64]
  ,
  {n}
  ]
 ]

GenerateRandomNumbers[1234567, 5] nums = GenerateRandomNumbers[987654321, 10^5]; KeySort[Counts[Floor[5 nums/N[2^64]]]]</lang>

Output:
{6457827717110365317, 3203168211198807973, 9817491932198370423, 4593380528125082431, 16408922859458223821}
<|0->20027, 1->19892, 2->20073, 3->19978, 4->20030|>

Nim

<lang Nim>import math, sequtils, strutils

const Two64 = 2.0^64

type Splitmix64 = object 

 state: uint64

func initSplitmix64(seed: uint64): Splitmix64 = 

 ## Initialize a Splitmiax64 PRNG.
 Splitmix64(state: seed)

func nextInt(r: var Splitmix64): uint64 = 

 ## Return the next pseudorandom integer (actually a uint64 value).
 r.state += 0x9e3779b97f4a7c15u
 var z = r.state
 z = (z xor z shr 30) * 0xbf58476d1ce4e5b9u
 z = (z xor z shr 27) * 0x94d049bb133111ebu
 result = z xor z shr 31

func nextFloat(r: var Splitmix64): float = 

 ## Retunr the next pseudorandom float (between 0.0 and 1.0 excluded).
 r.nextInt().float / Two64


when isMainModule: 

 echo "Seed = 1234567:"
 var prng = initSplitmix64(1234567)
 for i in 1..5:
   echo i, ": ", ($prng.nextInt).align(20)

 echo "\nSeed = 987654321:"
 var counts: array[0..4, int]
 prng = initSplitmix64(987654321)
 for _ in 1..100_000:
   inc counts[int(prng.nextFloat * 5)]
 echo toSeq(counts.pairs).mapIt(($it[0]) & ": " & ($it[1])).join(", "</lang>
Output:
Seed = 1234567:
1:  6457827717110365317
2:  3203168211198807973
3:  9817491932198370423
4:  4593380528125082431
5: 16408922859458223821

Seed = 987654321:
0: 20027, 1: 19892, 2: 20073, 3: 19978, 4: 20030

Perl

<lang perl>use strict; use warnings; no warnings 'portable'; use feature 'say'; use Math::AnyNum qw(:overload);

package splitmix64 { 

   sub new {
       my ($class, %opt) = @_;
       bless {state => $opt{seed}}, $class;
   }

   sub next_int {
       my ($self) = @_;
       my $next = $self->{state} = ($self->{state} + 0x9e3779b97f4a7c15) & (2**64 - 1);
       $next = ($next ^ ($next >> 30)) * 0xbf58476d1ce4e5b9 & (2**64 - 1);
       $next = ($next ^ ($next >> 27)) * 0x94d049bb133111eb & (2**64 - 1);
       ($next ^ ($next >> 31)) & (2**64 - 1);
   }

   sub next_float {
       my ($self) = @_;
       $self->next_int / 2**64;
   }

}

say 'Seed: 1234567, first 5 values:'; my $rng = splitmix64->new(seed => 1234567); say $rng->next_int for 1 .. 5;

my %h; say "\nSeed: 987654321, values histogram:"; $rng = splitmix64->new(seed => 987654321); $h{int 5 * $rng->next_float}++ for 1 .. 100_000; say "$_ $h{$_}" for sort keys %h;</lang>

Output:
Seed: 1234567, first 5 values:
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821

Seed: 987654321, values histogram:
0 20027
1 19892
2 20073
3 19978
4 20030

Phix

As per Pseudo-random_numbers/PCG32#Phix, resorting to mpfr/gmp 

with javascript_semantics
include mpfr.e
mpz state = mpz_init(),
    shift = mpz_init("0x9e3779b97f4a7c15"),
    mult1 = mpz_init("0xbf58476d1ce4e5b9"),
    mult2 = mpz_init("0x94d049bb133111eb"),
      b64 = mpz_init("0x10000000000000000"),  -- (truncate to 64 bits)
      tmp = mpz_init(),
        z = mpz_init()
 
procedure seed(integer num)
    mpz_set_si(state,num)
end procedure
 
procedure next_int()
    mpz_add(state, state, shift)    -- state += shift
    mpz_fdiv_r(state, state, b64)   -- state := remainder(z,b64) 
    mpz_set(z, state)               -- z := state
    mpz_tdiv_q_2exp(tmp, z, 30)     -- tmp := trunc(z/2^30)
    mpz_xor(z, z, tmp)              -- z := xor_bits(z,tmp)
    mpz_mul(z, z, mult1)            -- z *= mult1
    mpz_fdiv_r(z, z, b64)           -- z := remainder(z,b64) 
    mpz_tdiv_q_2exp(tmp, z, 27)     -- tmp := trunc(z/2^27)
    mpz_xor(z, z, tmp)              -- z := xor_bits(z,tmp)
    mpz_mul(z, z, mult2)            -- z *= mult2
    mpz_fdiv_r(z, z, b64)           -- z := remainder(z,b64) 
    mpz_tdiv_q_2exp(tmp, z, 31)     -- tmp := trunc(z/2^31)
    mpz_xor(z, z, tmp)              -- z := xor_bits(z,tmp)
    -- (result left in z)
end procedure
 
function next_float()
    next_int()
    mpfr f = mpfr_init_set_z(z)
    mpfr_div_z(f, f, b64)
    return mpfr_get_d(f)
end function
 
seed(1234567)
for i=1 to 5 do
    next_int()
    printf(1,"%s\n",mpz_get_str(z))
end for
seed(987654321)
sequence r = repeat(0,5)
for i=1 to 100000 do
    integer rdx = floor(next_float()*5)+1
    r[rdx] += 1
end for
?r
Output:
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821
{20027,19892,20073,19978,20030}

Object Pascal

<lang Pascal> program splitmix64;

{$IF Defined(FPC)}{$MODE Delphi}{$ENDIF} {$INLINE ON} {$Q-}{$R-}

{ 

 Written in 2015 by Sebastiano Vigna (vigna@acm.org)
 http://prng.di.unimi.it/splitmix64.c

 Onject Pascal port written in 2020 by I. Kakoulidis

 To the extent possible under law, the author has dedicated all copyright
 and related and neighboring rights to this software to the public domain
 worldwide. This software is distributed without any warranty.

 See <http://creativecommons.org/publicdomain/zero/1.0/>.

}

{ 

 This is a fixed-increment version of Java 8's SplittableRandom generator
 See http://dx.doi.org/10.1145/2714064.2660195 and
 http://docs.oracle.com/javase/8/docs/api/java/util/SplittableRandom.html

 It is a very fast generator passing BigCrush, and it can be useful if
 for some reason you absolutely want 64 bits of state.

} uses Math;

type 

 TSplitMix64 = record
   state: UInt64;
   procedure Init(seed: UInt64); inline;
   function Next(): UInt64; inline;
   function NextFloat(): double; inline;
 end;

procedure TSplitMix64.Init(seed: UInt64); begin 

 state := seed;

end;

function TSplitMix64.Next(): UInt64; begin 

 state := state + UInt64($9e3779b97f4a7c15);
 Result := state;
 Result := (Result xor (Result shr 30)) * UInt64($bf58476d1ce4e5b9);
 Result := (Result xor (Result shr 27)) * UInt64($94d049bb133111eb);
 Result := Result xor (Result shr 31);

end;

function TSplitMix64.NextFloat(): Double; begin 

 Result := Next() / 18446744073709551616.0;

end;

var 

 r: TSplitMix64;
 i, j: Integer;
 vec: array[0..4] of Integer;

begin 

 j := 0;
 r.Init(1234567);
 for i := 0 to 4 do
   WriteLn(r.Next());

 r.Init(987654321); 
 for i := 0 to 99999 do
 begin
   j := Trunc(r.NextFloat() * 5.0);
   Inc(vec[j]);
 end;

 for i := 0 to 4 do
   Write(i, ': ', vec[i], '  ');

end.

</lang>

Output:
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821
0: 20027  1: 19892  2: 20073  3: 19978  4: 20030

PicoLisp

<lang PicoLisp>(zero *Split) # global state

(de mod64 (N) 

  (& N `(hex "FFFFFFFFFFFFFFFF")) )

(de mod64+ (A B) 

  (mod64 (+ A B)) )

(de mod64* (A B) 

  (mod64 (* A B)) )

(de roundf (N) # rounds down 

  (/ N (** 10 *Scl)) )

(de nextSplit () 

  (setq *Split (mod64+ *Split `(hex "9e3779b97f4a7c15")))
  (let Z *Split
     (setq
        Z (mod64* `(hex "bf58476d1ce4e5b9") (x| Z (>> 30 Z)))
        Z (mod64* `(hex "94d049bb133111eb") (x| Z (>> 27 Z))) )
     (x| Z (>> 31 Z)) ) )

(prinl "First 5 numbers:") (setq *Split 1234567) (do 5 

  (println (nextSplit)) )

(prinl "The counts for 100,000 repetitions are:") (scl 12) (off R) (setq *Split 987654321) (do 100000 

  (accu
     'R
     (roundf (* 5 (*/ (nextSplit) 1.0 18446744073709551616)))
     1 ) )

(mapc println (sort R))</lang>

Output:
First 5 numbers:
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821
The counts for 100,000 repetitions are:
(0 . 20027)
(1 . 19892)
(2 . 20073)
(3 . 19978)
(4 . 20030)

Python

<lang python>MASK64 = (1 << 64) - 1 C1 = 0x9e3779b97f4a7c15 C2 = 0xbf58476d1ce4e5b9 C3 = 0x94d049bb133111eb


class Splitmix64(): 

   def __init__(self, seed=0):
       self.state = seed & MASK64

   def seed(self, num):
       self.state =  num & MASK64
   
   def next_int(self):
       "return random int between 0 and 2**64"
       z = self.state = (self.state + C1) & MASK64
       z = ((z ^ (z >> 30)) * C2) & MASK64
       z = ((z ^ (z >> 27)) * C3) & MASK64
       answer = (z ^ (z >> 31)) & MASK64

       return answer
   
   def  next_float(self):
       "return random float between 0 and 1"
       return self.next_int() / (1 << 64)

if __name__ == '__main__': 

   random_gen = Splitmix64()
   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)</lang>
Output:
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821
{0: 20027, 1: 19892, 2: 20073, 3: 19978, 4: 20030}

Raku

Works with: Rakudo version 2020.07

<lang perl6>class splitmix64 { 

   has $!state;

   submethod BUILD ( Int :$seed where * >= 0 = 1 ) { $!state = $seed }

   method next-int {
       my $next = $!state = ($!state + 0x9e3779b97f4a7c15) +& (2⁶⁴ - 1);
       $next = ($next +^ ($next +> 30)) * 0xbf58476d1ce4e5b9 +& (2⁶⁴ - 1);
       $next = ($next +^ ($next +> 27)) * 0x94d049bb133111eb +& (2⁶⁴ - 1);
       ($next +^ ($next +> 31)) +& (2⁶⁴ - 1);
   }

   method next-rat { self.next-int / 2⁶⁴ }

}

  1. Test next-int

say 'Seed: 1234567; first five Int values'; my $rng = splitmix64.new( :seed(1234567) ); .say for $rng.next-int xx 5;


  1. Test next-rat (since these are rational numbers by default)

say "\nSeed: 987654321; first 1e5 Rat values histogram"; $rng = splitmix64.new( :seed(987654321) ); say ( ($rng.next-rat * 5).floor xx 100_000 ).Bag;</lang>

Output:
Seed: 1234567; first five Int values
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821

Seed: 987654321; first 1e5 Rat values histogram
Bag(0(20027) 1(19892) 2(20073) 3(19978) 4(20030))

REXX

<lang rexx>/*REXX program generates pseudo─random numbers using the split mix 64 bit method.*/ numeric digits 200 /*ensure enough decimal digs for mult. */ parse arg n reps pick seed1 seed2 . /*obtain optional arguments from the CL*/ if n== | n=="," then n= 5 /*Not specified? Then use the default.*/ if reps== | reps=="," then reps= 100000 /* " " " " " " */ if pick== | pick=="," then pick= 5 /* " " " " " " */ if seed1== | seed1=="," then seed1= 1234567 /* " " " " " " */ if seed2== | seed2=="," then seed2= 987654321 /* " " " " " " */ const.1= x2d( 9e3779b97f4a7c15 ) /*initialize 1st constant to be used. */ const.2= x2d('bf58476d1ce4e5b9') /* " 2nd " " " " */ const.3= x2d( 94d049bb133111eb ) /* " 3rd " " " " */ o.30= copies(0, 30) /*construct 30 bits of zeros. */ o.27= copies(0, 27) /* " 27 " " " */ o.31= copies(0, 31) /* " 31 " " " */ w= max(3, length(n) ) /*for aligning the left side of output.*/ state= seed1 /* " the state to seed #1. */ 

            do j=1  for n
            if j==1  then do;   say center('n', w)     "     pseudo─random number   "
                                say copies('═', w)     " ════════════════════════════"
                          end
            say right(j':', w)" "  right(commas(next()), 27)  /*display a random number*/
            end   /*j*/

say if reps==0 then exit 0 /*stick a fork in it, we're all done. */ say center('#', w) " count of pseudo─random #" say copies('═', w) " ════════════════════════════" state= seed2 /* " the state to seed #2. */ @.= 0; div= pick / 2**64 /*convert division to inverse multiply.*/ 

            do k=1  for reps
            parse value next()*div  with  _ '.' /*get random #, floor of a "division". */
            @._= @._ + 1                        /*bump the counter for this random num.*/
            end   /*k*/

            do #=0  for pick
            say right(#':', w)" "  right(commas(@.#), 15) /*show count of a random num.*/
            end   /*#*/

exit 0 /*stick a fork in it, we're all done. */ /*──────────────────────────────────────────────────────────────────────────────────────*/ commas: parse arg _; do ?=length(_)-3 to 1 by -3; _= insert(',', _, ?); end; return _ b2d: parse arg ?; return x2d( b2x(?) ) /*convert bin──►decimal. */ d2b: parse arg ?; return right( x2b( d2x(?) ), 64, 0) /*convert dec──►64 bit bin.*/ /*──────────────────────────────────────────────────────────────────────────────────────*/ next: procedure expose state const. o. 

     state= state + const.1        ; z= d2b(state)          /*add const1──►STATE; conv.*/
     z= xor(z, left(o.30 || z, 64)); z= d2b(b2d(z)*const.2) /*shiftR 30 bits & XOR;  " */
     z= xor(z, left(o.27 || z, 64)); z= d2b(b2d(z)*const.3) /*   "   27  "   "  "    " */
     z= xor(z, left(o.31 || z, 64));        return b2d(z)   /*   "   31  "   "  "    " */

/*──────────────────────────────────────────────────────────────────────────────────────*/ xor: parse arg a, b; $= /*perform a bit─wise XOR. */ 

               do !=1  for length(a);   $= $  ||  (substr(a,!,1)  &&  substr(b,!,1) )
               end   /*!*/;      return $</lang>
output   when using the default inputs:
 n       pseudo─random number
═══  ════════════════════════════
 1:    6,457,827,717,110,365,317
 2:    3,203,168,211,198,807,973
 3:    9,817,491,932,198,370,423
 4:    4,593,380,528,125,082,431
 5:   16,408,922,859,458,223,821

 #     count of pseudo─random #
═══  ════════════════════════════
 0:           20,027
 1:           19,892
 2:           20,073
 3:           19,978
 4:           20,030

Ruby

<lang ruby>class Splitmix64 

 MASK64 = (1 << 64) - 1
 C1, C2, C3 = 0x9e3779b97f4a7c15, 0xbf58476d1ce4e5b9, 0x94d049bb133111eb
 
 def initialize(seed = 0) =  @state = seed & MASK64
   
 def rand_i
   z = @state = (@state + C1) & MASK64
   z = ((z ^ (z >> 30)) * C2) & MASK64
   z = ((z ^ (z >> 27)) * C3) & MASK64
   (z ^ (z >> 31)) & MASK64
 end
 
 def rand_f = rand_i.fdiv(1<<64)

end

rand_gen = Splitmix64.new(1234567) 5.times{ puts rand_gen.rand_i }

rand_gen = Splitmix64.new(987654321) p 100_000.times.lazy.map{(rand_gen.rand_f * 5).floor}.tally.sort.to_h </lang>

Output:
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821
{0=>20027, 1=>19892, 2=>20073, 3=>19978, 4=>20030}

Sidef

Translation of: Perl

<lang ruby>class Splitmix64(state) { 

   define (
       mask64 = (2**64 - 1)
   )

   method next_int {
       var n = (state = ((state + 0x9e3779b97f4a7c15) & mask64))
       n = ((n ^ (n >> 30)) * 0xbf58476d1ce4e5b9 & mask64)
       n = ((n ^ (n >> 27)) * 0x94d049bb133111eb & mask64)
       (n ^ (n >> 31)) & mask64
   }

   method next_float {
       self.next_int / (mask64+1)
   }

}

say 'Seed: 1234567, first 5 values:' var rng = Splitmix64(1234567) 5.of { rng.next_int.say }

say "\nSeed: 987654321, values histogram:" var rng = Splitmix64(987654321) var histogram = Bag(1e5.of { floor(5*rng.next_float) }...) histogram.pairs.sort.each { .join(": ").say }</lang>

Output:
Seed: 1234567, first 5 values:
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821

Seed: 987654321, values histogram:
0: 20027
1: 19892
2: 20073
3: 19978
4: 20030

Wren

Library: Wren-big

No 64 bit integers so we use BigInt with a mask. <lang ecmascript>import "/big" for BigInt

var Const1 = BigInt.fromBaseString("9e3779b97f4a7c15", 16) var Const2 = BigInt.fromBaseString("bf58476d1ce4e5b9", 16) var Const3 = BigInt.fromBaseString("94d049bb133111eb", 16) var Mask64 = (BigInt.one << 64) - BigInt.one

class Splitmix64 { 

   construct new(state) {
       _state  = state
   }

   nextInt {
       _state = (_state + Const1) & Mask64
       var z = _state
       z = ((z ^ (z >> 30)) * Const2) & Mask64
       z = ((z ^ (z >> 27)) * Const3) & Mask64
       return (z ^ (z >> 31)) & Mask64
   }

   nextFloat { nextInt.toNum / 2.pow(64) }

}

var randomGen = Splitmix64.new(BigInt.new(1234567)) for (i in 0..4) System.print(randomGen.nextInt)

var counts = List.filled(5, 0) randomGen = Splitmix64.new(BigInt.new(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])")</lang>

Output:
6457827717110365317
3203168211198807973
9817491932198370423
4593380528125082431
16408922859458223821

The counts for 100,000 repetitions are:
  0 : 20027
  1 : 19892
  2 : 20073
  3 : 19978
  4 : 20030
Retrieved from "https://rosettacode.org/wiki/Pseudo-random_numbers/Splitmix64?oldid=302117"