Pseudo-random numbers/Splitmix64

Shiftmix64 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.

Shiftmix64 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" shiftmix64 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. */

    uint64 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 */
    }

    uint64 next-float() {
        return float 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 shiftmix64.

Show the first five integers generated using the seed 1234567.

    9086773575395155592
   12075168200337577354
    5360881288835356517
   10975871416297420776
    2494458855142162015

Show that for an initial seed of 987654321, the counts of 100_000 repetitions of floor next_float() * 5 is as follows:

   0: 19929, 1: 19817, 2: 20085, 3: 20122, 4: 20047

Show your output here, on this page.

See also

Java docs for splitmix64 Public domain C code used in many PRNG implementations; by Sebastiano Vigna

Related tasks

Pseudo-random numbers/Combined recursive generator MRG32k3a‎‎ Pseudo-random numbers/PCG32‎‎ Pseudo-random_numbers/Xorshift_star

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 += 0x9e3779b97f4a7c15;
       $next  +^= ($next +> 30) * 0xbf58476d1ce4e5b9;
       $next  +^= ($next +> 27) * 0x94d049bb133111eb;
       ($next +^  ($next +> 31)) +& (2⁶⁴ - 1);
   }

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

}

Test next-int

say 'Seed: 1234567; first five Int values'; my $rng = splitmix64.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"; $rng = splitmix64.new( :seed(987654321) ); say ( ($rng.next-rat * 5).floor xx 100_000 ).Bag;</lang>

Output:

Seed: 1234567; first five Int values
9086773575395155592
12075168200337577354
5360881288835356517
10975871416297420776
2494458855142162015

Seed: 987654321; first 1e5 Rat values histogram
Bag(0(19929) 1(19817) 2(20085) 3(20122) 4(20047)