[RESOLVED] Random

[dbasnett]

Just for the heck of it I am buying this true random generator.

https://www.amazon.com/TrueRNG-V3-Ha.../dp/B01KR2JHTA

The device sends bytes over the comport that are random.

To get a head start I thought I would try and mimic what the Random class does. At the core of Random is the .Sample method. And right from go I am confused.

How do you create a Double greater than or equal to 0 and less than one from 8 random bytes? I have some code that appears to work but is slow, 6 seconds to produce 1,000,000 Doubles.

            '   Significand or mantissa 	0-51
            '   Exponent 52 - 62
            '   Sign (0 = Positive, 1 = Negative) 	63
            '                     8000000000000
            Me._methodLock.WaitOne() 'for thread safety
            Dim rv As Double = Double.NaN
            Const MantMsk As Long = &HFFFFFFFFFFFFFL
            Const ExpMsk As Long = &H7FF0000000000000L
            Const Mask As Long = MantMsk Or ExpMsk 'negative numbers not possible with this mask
            Dim L As Long = Long.MinValue
            If Me.WaitForBytes(8) Then 'wait for there to be at least 8 bytes in the com buffer
                Dim byteVal As New List(Of Byte)
                Do While byteVal.Count < 8 'get eight bytes from the com buffer
                    Dim b As Byte
                    If Me.buf.TryDequeue(b) Then
                        byteVal.Add(b)
                    End If
                Loop
                ' L is a long
                L = Mask And BitConverter.ToInt64(byteVal.ToArray, 0)
                Do
                    Dim ct As Integer = 0
                    rv = BitConverter.ToDouble(BitConverter.GetBytes(L), 0)
                    '1.#QNAN
                    If Double.IsInfinity(rv) OrElse
                            Double.IsNaN(rv) OrElse
                            Double.IsNegativeInfinity(rv) OrElse
                            Double.IsPositiveInfinity(rv) Then
                        L = L Xor Long.MinValue
                    ElseIf rv >= 0.0R AndAlso rv < 1.0R Then '
                        Exit Do 'success
                    End If
                    ct += 1
                    Dim foo As Long = L
                    Dim exp As Long = (foo And ExpMsk) >> 52
                    exp = (exp << 51) And ExpMsk
                    foo = (foo And MantMsk)
                    foo = foo Or exp
                    L = foo
                Loop
            Else
                'todo
                Stop
            End If

Until I get the device I am filling the comport buffer with random bytes using the Random class.

[dday9]

For what its worth, here is the source code for Random: https://referencesource.microsoft.co...stem/random.cs

It is using the Linear Congruential Generator algorithm to initialize the seed. That's about as far down the rabbit hole I got.

Random is a topic similar to infinity for me. It's really cool but gets way over my head way too quickly.

[jmcilhinney]

Note that the Random class only produces pseudorandom numbers. They appear random to the casual observer but the sequence is predictable if you know the initial conditions. The RandomNumberGenerator class provides numbers that are sufficiently random for cryptographic use.

[digitalShaman]

x = BitConverter.Touint32(byteVal.ToArray, 0)
y = BitConverter.Touint32(byteVal.ToArray, 4)
rv = x / y

add code to care about the edge cases (y=0 and x=y if you do not want 1 as possible result)

edit: of course you need to exchange x and y if x > y so that y is always bigger or equal x. But i guess you get the point.

[dbasnett]

x = BitConverter.Touint32(byteVal.ToArray, 0)
y = BitConverter.Touint32(byteVal.ToArray, 4)
rv = x / y

add code to care about the edge cases (y=0 and x=y if you do not want 1 as possible result)

edit: of course you need to exchange x and y if x > y so that y is always bigger or equal x. But i guess you get the point.

Thought about something like this. I'll give it a try tomorrow. The device should be here Wednesday. Thanks!

[dbasnett]

This is where I am so far, still waiting on the actual device. I have ran some test for verification, see end.

Here is a question, could I use Int16 instead of Int32? Or should I use Int64?

        ''' <summary>
        ''' returns a double greater than or equal to 0 and less than 1
        ''' </summary>
        ''' <returns>Double</returns>
        ''' <remarks></remarks>
        Private Function Sample() As Double
            Dim rv As Double = Double.NaN
            Dim int1 As Integer
            Dim int2 As Integer
            Dim byts() As Byte
            int1 = 0
            int2 = 0
            'create two integers
            Do While int1 = int2
                byts = Me.GetBytes(4) 'get 4 bytes from com buffer
                'use loop because .GetBytes might not return 4 bytes
                For idx As Integer = 0 To byts.Length - 1
                    int1 = int1 << 8
                    int1 = int1 Or byts(idx)
                Next
                byts = Me.GetBytes(4) 'get bytes from com buffer
                For idx As Integer = 0 To byts.Length - 1
                    int2 = int2 << 8
                    int2 = int2 Or byts(idx)
                Next
                'turn off sign
                int1 = int1 And Integer.MaxValue
                int2 = int2 And Integer.MaxValue
                If int1 = int2 Then
                    int1 = int1 Xor Integer.MaxValue
                End If
            Loop

            If int1 > 0 OrElse int2 > 0 Then
                If int1 > int2 Then
                    rv = int2 / int1
                Else
                    rv = int1 / int2
                End If
            Else
                Stop 'todo ??????
            End If
            'does this happen?????
            If Double.IsInfinity(rv) OrElse
                    Double.IsNaN(rv) OrElse
                    Double.IsNegativeInfinity(rv) OrElse
                    Double.IsPositiveInfinity(rv) Then

                Stop 'todo
            End If

            Return rv
        End Function

I ran 5,000,000 iterations of:

Heads / Tails and it was 50 / 50
Two dice and it matched the total distribution
Created integers and counted digits in the answer
-- ran the same thing against the System.Random and matched

As you can see there are some questions in the code that I will resolve when I get the device.

Is anyone interested about the device?


Results of significant digit count

System.Random

1 0.0000 %
2 0.0000 %
3 0.0000 %
4 0.0004 %
5 0.0045 %
6 0.0412 %
7 0.4186 %
8 4.1937 %
9 41.8918 %
10 53.4497 %

TRNG

1 0.0000 %
2 0.0000 %
3 0.0000 %
4 0.0004 %
5 0.0038 %
6 0.0428 %
7 0.4186 %
8 4.1972 %
9 41.8843 %
10 53.4530 %

[digitalShaman]

A warning: I am not so sure anymore that this approach will generate evenly distributed numbers.
For example the result of Int.max-1 / int.max will only be possible with these exact two numbers while a result of 0.5 is generated by multiple number combinations such as 1/2, 2/4, etc.

[dbasnett]

A warning: I am not so sure anymore that this approach will generate evenly distributed numbers.
For example the result of Int.max-1 / int.max will only be possible with these exact two numbers while a result of 0.5 is generated by multiple number combinations such as 1/2, 2/4, etc.

I was going to try to figure out the distribution but realized I didn't understand a lot of the code I looked at.

I did let the device run overnight turning on two pixels per second in a blank image.

Result:

[dbasnett]

A warning: I am not so sure anymore that this approach will generate evenly distributed numbers.
For example the result of Int.max-1 / int.max will only be possible with these exact two numbers while a result of 0.5 is generated by multiple number combinations such as 1/2, 2/4, etc.

Haven't tested with the TRNG hardware but this works with Random.

    Private prng As New Random
    Private gtONE As ULong = 0UL
    Private Function Sample() As Double
        Dim rv As Double = 0.0#
        'Bytes
        '7   Mantissa	0-51 
        '2   Exponent	52-62  0 - 1022
        Dim byts(8) As Byte '9 bytes
        prng.NextBytes(byts) ' <<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<<REPLACE with TRNG get
        Dim exp As Long = 0L
        If byts.Length > 1 Then
            'create Exponent
            exp = byts(0)
            exp = exp << 8
            exp = exp Or byts(1)
            ' keep 10 bits only
            exp = exp And &H3FFL ''this mask &H1FFL  stops >= 1.0 '  
        End If
        If exp >= 1023 Then exp -= 1L
        '  If exp >= 1000 Then exp -= 23L ' but some exp >= 1000 are good
        '  e.g. 0.46678963503161  exp = 1021

        exp = exp << 52 'position Exponent
        Dim L As Long = 0L
        For x As Integer = 2 To byts.Length - 1 'create Mantissa
            L = L << 8
            L = L Or byts(x)
        Next
        L = L And SignificandMSK '52 bits only
        L = L Or exp 'add Exponent
        rv = BitConverter.Int64BitsToDouble(L)
        If rv >= 1.0# Then
            rv = rv / Math.PI
            Me.gtONE += 1UL
        End If
        If rv >= 1.0# Then
            'todo
            Stop
        End If
        Return rv
    End Function

[dbasnett]

Great, just great. So I have been looking at the source of .Random. In it I find this.

    public virtual int Next(int maxValue) {
          if (maxValue<0) {
              throw new ArgumentOutOfRangeException("maxValue", Environment.GetResourceString("ArgumentOutOfRange_MustBePositive", "maxValue"));
          }
          Contract.EndContractBlock();
          return (int)(Sample()*maxValue);
      }

So my new .Sample apparently does a broader range.

8.7253577634378e-280
5.10351429655486e-168
7.66905992703698e-225
1.63228078929909e-137
4.81252807881766e-185
1.0806761131728e-158
6.00381557186564e-135
8.91585051435279e-183
6.63151599550507e-162
1.81935382013397e-138
2.28408466952934e-71
2.78949524958343e-283
2.43364313225461e-265
3.82096161246175e-165
4.3831210318899e-140
9.54907848369536e-123

4.76116207454203e-45
0.00277009731881507
6.20504061442252e-205
2.4889082471918e-20
8.67933824628034e-253
6.59549839909513e-49
8.6448449726707e-288
7.30206483116989e-111
3.26052204441488e-102
3.3667687899405e-128
1.70358091448857e-77
3.67136132927937e-269
3.41397071621818e-15
3.43220382872364e-155
2.58852200039163e-64
3.55377161269553e-68

3.16103698589824e-189
1.34132824028634e-196
4.7029016099803e-18
1.3649258957631e-292
8.71277705385738e-183
5.49958265719597e-29
4.36150273910638e-175
7.54537044298667e-15
6.01228626236831e-65
6.82407168351128e-05
2.00518986766811e-122
2.00214876288474e-104
6.97052809694117e-110
1.07402982506738e-62
1.75113941553553e-190
8.01532381965969e-278

5.87034189846368e-30
4.39118219624152e-193
1.12863560347159e-72
4.07807280569997e-183
1.33797727986362e-152
8.77861478648681e-271
6.52053556928832e-197
1.17493728755003e-116
6.11487766561578e-74
1.12273389231186e-176
3.58183377297382e-181
2.02060585288374e-236
3.29833187060158e-233
4.51661450924151e-149
3.40411805343502e-15
1.31057074649206e-126

Too broad to do this,

        Dim rv As Double = Me.Sample() * maxValue
        rv = CInt(Math.Truncate(smpl))
        Return rv

Damn, damn, ....

[dbasnett]

I have resolved this with code based on System.Random. Left the original as a conditional.

    Const MBIG As Double = 1.0# / Integer.MaxValue
    Private Function ISample() As Double
        Dim rv As Double = 0
#Const Methd = "1" ' "2"
        Dim I1 As Integer = Me.Next 'get random integer between 0 and Integer.MaxValue
#If Methd = "1" Then
        rv = I1 * MBIG
#ElseIf Methd = "2" Then
        Dim I2 As Integer = Me.Next
        If I1 > I2 Then
            rv = I2 / I1
        ElseIf I2 > I1 Then
            rv = I1 / I2
        ElseIf I1 <> Integer.MaxValue Then
            rv = I2 / (I1 + 1)
        Else
            rv = (I2 - 1) / I1
        End If
#End If
        Return rv
    End Function