C# implementation of UnityEngine.Random with (almost) 1-to-1 parity

Unity-XORShift.md

This is a partial C# implementation of UnityEngine.Random with (almost) 1-to-1 parity.

Unity uses Xorshift for psuedorandom number generation. In particular Xorshift128, which uses a state consisting of four unsigned 32-bit integer values. The state is initialized in UnityEngine.Random.InitState using a signed 32-bit integer seed, which is shuffled around with a technique similar to the way a Mersenne Twister is initialized.

This has been tested as far back as Unity 4.7.0f1, and as recent as Unity 2020.1.17f1.

Notes

• Huge thanks to MoatShrimp for figuring out how Unity initializes the Xorshift state parameters in InitState, and floating point generation.
• C# - As below. Values may differ in .NET 5.0, but thankfully Unity doesn't yet support that.
• JavaScript - Check out MoatShrimp's JS implemention (and neat Undermine loot lookup tool) here:
  • http://moatshrimp.com/
• Lua - I've translated this into Lua for use on MediaWiki wikis with the Scribunto extension installed. Note that this only works if Lua was compiled with LUA_NUMBER = double, which should be the case for most wikis. In my case the initial goal was to evaluate random loot lists in Pillars of Eternity, for use on the wiki.
  • Module:Lootlist (might have to scroll down a bit)
• If you translate this into other languages, or have any improvements/insights, feel free to comment below!
• If you do translate this, be mindful of:
  • How your language handles numbers. Most programming languages that only define one type for numbers will use a double-precision floating point value to represent all numbers.
  • Integer overflow, and casting behaviours (particularly from uint to int)
  • Differences in the % operator (modulo vs remainder)

Unknowns

• How Unity initializes UnityEngine.Random when a seed is not provided. Probably seeded based on time, perhaps hourly? Need to do further testiong.
• Floating point RPG is slightly inaccurate. Unity's implementation is likely done differently, though their exact method is unknown.

Tests

The following tests were performed using the C# implementation in Unity, initialized with: UnityEngine.Random.InitState(1234) and XORShift128.InitSeed(1234), generated sequentially (the state isn't reset between runs).

UnityEngine.Random.State.s3 and XORShift128.w are the last state parameter in Xorshift, the actual number that was generated in Xorshift. This value is a uint and is used as a basis for all other Random functions.

Integer

Uses UnityEngine.Random.Range(min, max) and XORShift128.NextIntRange(min, max)

0 to int.MaxValue

s3 / w	Unity	XORShift
3463400838	1315917191	1315917191
3496203776	1348720129	1348720129
3452947669	1305464022	1305464022
1278673611	1278673611	1278673611
4169168310	2021684663	2021684663

0 to int.MinValue (-2,147,483,648)

s3 / w	Unity	XORShift
916287344	-916287344	-916287344
2240259090	-92775442	-92775442
1901252403	-1901252403	-1901252403
2323917162	-176433514	-176433514
1472147877	-1472147877	-1472147877

int.MinValue to int.MaxValue

s3 / w	Unity	XORShift
4020283508	1872799860	1872799860
141347300	-2006136348	-2006136348
2735243002	587759354	587759354
227819815	-1919663833	-1919663833
3885870057	1738386409	1738386409

int.MaxValue to int.MinValue

s3 / w	Unity	XORShift
2312142103	-164658456	-164658456
1775189369	372294278	372294278
3338523678	-1191040031	-1191040031
3426086347	-1278602700	-1278602700
3322349983	-1174866336	-1174866336

int.MinValue to int.MinValue (error is caught and a suitable value is returned before a value is even generated, hence the non-changing state value)

s3 / w	Unity	XORShift
3322349983	-2147483648	-2147483648
3322349983	-2147483648	-2147483648
3322349983	-2147483648	-2147483648
3322349983	-2147483648	-2147483648
3322349983	-2147483648	-2147483648

Floating point

Uses UnityEngine.Random.value and XORShift128.NextFloat()

s3 / w	Unity	XORShift
3593715923	0.4043221	0.404322
4266042159	0.551855	0.551855
2642301593	0.9868958	0.9868957
1674312536	0.593608	0.5936079
733387434	0.426595	0.426595

Uses UnityEngine.Random.Range(min, max) and XORShift128.NextFloatRange(min, max) 0.0 to 100.0

s3 / w	Unity	XORShift
3760331560	73.35463	73.35463
2410116911	69.16753	69.16753
3012185272	91.95337	91.95337
745993129	7.068896	7.068908
3699201620	2.080286	2.080297

0.0 to 100000.0

s3 / w	Unity	XORShift
1758944507	31747.49	31747.5
2312712917	30313.62	30313.62
313095164	67614.8	67614.8
609241099	37280.14	37280.14
4138924286	60177.63	60177.64

0.0 to float.MaxValue (3.402823E+38)

s3 / w	Unity	XORShift
3065852775	1.775827E+38	1.775827E+38
4023550175	1.209507E+38	1.209507E+38
1231330622	7.280383E+37	7.280387E+37
678488548	4.010639E+37	4.010643E+37
1997128070	3.143466E+38	3.143466E+38

0.0 to float.MinValue (-3.402823E+38)

s3 / w	Unity	XORShift
212231104	-2.382252E+38	-2.382252E+38
1632010759	-1.528401E+38	-1.528402E+38
3470161922	-1.104089E+38	-1.104089E+38
4159346095	-5.693158E+37	-5.693162E+37
3362607345	-4.967007E+37	-4.967012E+37

float.MinValue to float.MaxValue

s3 / w	Unity	XORShift
2641274177	-2.480102E+38	-2.480101E+38
3758475398	3.095331E+38	3.095331E+38
1138851524	-1.78091E+38	-1.780909E+38
3785966737	1.208649E+38	1.208649E+38
151368008	3.100158E+38	3.100158E+38

float.MaxValue to float.MinValue

s3 / w	Unity	XORShift
3347712278	-2.869245E+38	-2.869245E+38
2413123709	1.13493E+38	1.13493E+38
619907290	2.713464E+38	2.713463E+38
5796605	1.299941E+38	1.299941E+38
2534213977	-2.709683E+38	-2.709683E+38

float.MinValue to float.MinValue

s3 / w	Unity	XORShift
2990456181	-3.402823E+38	-3.402823E+38
238536240	-3.402823E+38	-3.402823E+38
3443233425	-3.402823E+38	-3.402823E+38
847449518	-3.402823E+38	-3.402823E+38
1964100510	-3.402823E+38	-3.402823E+38

XORShift128.cs

public static class XORShift128
{
    public static uint x = 0, y = 0, z = 0, w = 0;

    const uint MT19937 = 1812433253;

    // Initialize Xorshift using a signed integer seed, calculating the state values using the initialization method from Mersenne Twister (MT19937)
    // https://en.wikipedia.org/wiki/Mersenne_Twister#Initialization
    public static void InitSeed(int seed)
    {
        x = (uint)seed;
        y = (uint)(MT19937 * x + 1);
        z = (uint)(MT19937 * y + 1);
        w = (uint)(MT19937 * z + 1);
    }

    // Explicitly set the state parameters
    public static void InitState(uint x, uint y, uint z, uint w)
    {
        XORShift128.x = x;
        XORShift128.y = y;
        XORShift128.z = z;
        XORShift128.w = w;
    }

    // XORShift, returns an unsigned 32-bit integer
    public static uint XORShift()
    {
        uint t = x ^ (x << 11);
        x = y; y = z; z = w;
        return w = w ^ (w >> 19) ^ t ^ (t >> 8);
    }

    // UInt32 / uint

    // UnityEngine.Random doesn't have any uint functions so these functions behave exactly like int Random.Range

    // Alias of base Next/XORShift
    public static uint NextUInt()
    {
        return XORShift();
    }

    // Generate a random unsigned 32-bit integer value in the range 0 (inclusive) to max (exclusive)
    public static uint NextUIntMax(uint max)
    {
        if (max == 0) return 0;
        return XORShift() % max;
    }

    // Generate random unsigned 32-bit integer value in the range min (inclusive) to max (exclusive)
    public static uint NextUIntRange(uint min, uint max)
    {
        if (max - min == 0) return min;

        if (max < min)
            return min - XORShift() % (max + min);
        else
            return min + XORShift() % (max - min);
    }

    // Int32 / int

    // Generate a random signed 32-bit integer value in the range -2,147,483,648 (inclusive) to 2,147,483,647 (inclusive)
    public static int NextInt()
    {
        return (int)(XORShift() % int.MaxValue);
    }

    public static int NextIntMax(int max)
    {
        return NextInt() % max;
    }

    // Generate a random signed 32-bit integer value in the range min (inclusive) to max (exclusive)
    // If you only need to generate positive integers, use NextUIntRange instead
    public static int NextIntRange(int min, int max)
    {
        // If max and min are the same, just return min since it will result in a DivideByZeroException
        if (max - min == 0) return min;

        // Do operations in Int64 to prevent overflow that might be caused by any of the following operations
        // I'm sure there's a faster/better way to do this and avoid casting, but we prefer equivalence to Unity over performance
        long minLong = (long)min;
        long maxLong = (long)max;
        long r = XORShift();

        // Flip the first operator if the max is lower than the min,
        if (max < min)
            return (int)(minLong - r % (maxLong - minLong));
        else
            return (int)(minLong + r % (maxLong - minLong));
    }

    // Single / float

    // Generate a random floating point between 0.0 and 1.0 (inclusive?)
    public static float NextFloat()
    {
        return 1.0f - NextFloatRange(0.0f, 1.0f);
    }

    // Generate a random floating point between min (inclusive) and max (exclusive) 
    public static float NextFloatRange(float min, float max)
    {
        return (min - max) * ((float)(XORShift() << 9) / 0xFFFFFFFF) + max;
    }
}

~Tests.cs

using UnityEngine;
using System.Runtime.InteropServices;
using Random = UnityEngine.Random;

public class Tests : MonoBehaviour
{
    System.Text.StringBuilder sb = new System.Text.StringBuilder();

    // Start is called before the first frame update
    void Start()
    {
        UnityEngine.Random.InitState(1234);
        XORShift128.InitSeed(1234);

        // Print some ranged integers
        // 0 to max
        IntegerTests(0, int.MaxValue);
        // 0 to min
        IntegerTests(0, int.MinValue);
        // Min to max
        IntegerTests(int.MinValue, int.MaxValue);
        // Max to min
        IntegerTests(int.MaxValue, int.MinValue);
        // Min to min (error)
        IntegerTests(int.MinValue, int.MinValue);

        // Print some floating points
        for (int i = 0; i < 5; i++) AppendTestFloat(Random.value, XORShift128.NextFloat());

        // Print some ranged floating points
        // 0 to 100
        FloatingPointTests(0f, 100f);
        // 0 to 100000
        FloatingPointTests(0f, 100000f);
        // 0 to max (not accurate)
        FloatingPointTests(0f, float.MaxValue);
        // 0 to min (not accurate)
        FloatingPointTests(0f, float.MinValue);
        // Min to max
        FloatingPointTests(float.MinValue, float.MaxValue);
        // Max to min
        FloatingPointTests(float.MaxValue, float.MinValue);
        // Min to min
        FloatingPointTests(float.MinValue, float.MinValue);

        Debug.Log(sb.ToString());
    }

    void IntegerTests(int min, int max)
    {
        sb.AppendLine("--- " + min + " to " + max + " ---");

        for (int i = 0; i < 5; i++)
        {
            int ur = UnityEngine.Random.Range(min, max);
            int xr = XORShift128.NextIntRange(min, max);
            AppendTestInt(ur, xr);
        }
    }

    void FloatingPointTests(float min, float max)
    {
        sb.AppendLine("--- " + min + " to " + max + " ---");
        for (int i = 0; i < 5; i++)
        {
            float ur = UnityEngine.Random.Range(min, max);
            float xr = XORShift128.NextFloatRange(min, max);
            AppendTestFloat(ur, xr);
        }
    }

    void AppendTest(string a, string b)
    {
        var state = (RandomStateWrapper)UnityEngine.Random.state;
        sb.AppendLine(state.v3.ToString().PadRight(15) + XORShift128.w.ToString().PadRight(15) + a.PadRight(15) + b.PadRight(15));
    }

    void AppendTestInt(int a, int b)
    {
        AppendTest(a.ToString(), b.ToString());
    }

    void AppendTestFloat(float a, float b)
    {
        AppendTest(a.ToString(), b.ToString());
    }
}

[StructLayout(LayoutKind.Explicit)]
public struct RandomStateWrapper
{
    [FieldOffset(0)] public Random.State state;
    [FieldOffset(0)] public uint v0;
    [FieldOffset(4)] public uint v1;
    [FieldOffset(8)] public uint v2;
    [FieldOffset(12)] public uint v3;

    public static implicit operator RandomStateWrapper(Random.State aState)
    {
        return new RandomStateWrapper { state = aState };
    }
    public static implicit operator Random.State(RandomStateWrapper aState)
    {
        return aState.state;
    }

    public override string ToString()
    {
        return v0 + ", " + v1 + ", " + v2 + ", " + v3;
    }
}

Thank you very much for that information! As i made this using your information, i thought i might share this version of it i made in Rust:

use std::num::Wrapping;

const MT19937: Wrapping<u32> = Wrapping(1812433253);

pub struct XORShift128 {
    x: Wrapping<u32>,
    y: Wrapping<u32>,
    z: Wrapping<u32>,
    w: Wrapping<u32>
}

impl XORShift128 {
    pub fn from_seed(seed: i32) -> Self {
        let x = Wrapping(seed as u32);
        let y = MT19937 * x + Wrapping(1);
        let z = MT19937 * y + Wrapping(1);
        let w = MT19937 * z + Wrapping(1);
        return XORShift128 { x, y, z, w }
    }

    fn xorshift(&mut self) -> u32 {
        let t = self.x ^ (self.x << 11);
        self.x = self.y;
        self.y = self.z;
        self.z = self.w;
        self.w = self.w ^ (self.w >> 19) ^ t ^ (t >> 8);
        return self.w.0;
    }

    pub fn range(&mut self, min: i32, max: i32) -> i32 {
        if max - min == 0 {
            return min;
        }

        let min_long = min as i64;
        let max_long = max as i64;
        let r = self.xorshift() as i64;

        return if max < min {
            (min_long - r % (max_long - min_long)) as i32
        } else {
            (min_long + r % (max_long - min_long)) as i32
        }
    }
}

It's missing most of the calls, but since this is all i needed, i didn't spend more time. As Rust does not allow integer overflow, i had to use the std::num::Wrapping.

JFYI

NextInt() and NextIntMax() are bugged.

This line:

return (int)(XORShift() % int.MaxValue);

coerces signedness in such a way that you will never get a negative number. if you cast XORShift() to int, alone, then mod, you can get negative numbers. but as is, NextInt() never produces negative numbers (nor NextIntMax, since it depends on NextInt). NextIntRange does not use NextInt(), and tests only cover NextIntRange so that's probably how this was missed.