drSquares is based upon the original version of Squares which has three rounds. Widynski wrote: "With an extra round of squaring it may be more likely to pass some (as of yet unknown) statistical test. This version is slower than the three round version, but still faster than Philox." He gives timings for both and the four round version is about 28% slower than the three round version.
What I have learned this last few years is that other people's timings do not give us a clue as to what FB's C-emitter plus gcc will behave like. With the yellow/blue pixel test and the 20 second test the difference between the Squares three round version and the four round version is negligible.
What I now need to do is subject the four round version to a PractRand analysis. If that is successful then PCG32II may well be looking at a replacement.
Here is the four round version of Squares which I have called drSquares4.bas.
drSquares4.bas
Code: Select all
'#Console On
#include "keys.bi"
#macro Engine
x = this.key * (this.ctr+1)
y = x
z = y + this.key
x = x * x + y
x = ( x shr 32 ) or ( x shl 32 )
x = x * x + z
x = ( x shr 32 ) or ( x shl 32 )
x = x * x + y
x = ( x shr 32 ) or ( x shl 32 )
this.ctr += 1
#endmacro
type Squares
Public:
declare Constructor
Declare Sub MyRandomize( Byval counter As Ulongint = 0, Byval keyno As Ulongint = 0 )
declare function rand() as ulong
declare function randse() as double
Declare Function randd() As Double
Declare Function range Overload ( First As Long, Last As Long ) As Long
Declare Function range Overload ( First As Double, Last As Double ) As Double
Declare Function Getctr() as ulongint
Declare Sub Setctr( Counter As Ulongint )
Declare Function Getkeynumber As Ushort
Declare Sub Setkeynumber( keyno As Ushort )
Declare Function Getkey() As Ulongint
Declare Sub GetSnapshot()
Declare Sub SetSnapshot()
Private:
ctr as ulongint
keynumber As Ushort
key as ulongint
' The following are used by GetSnapshot/SetSnapshot
ctrSnapshot As ULongInt
keySnapshot As ulongint
end type
Function RandomKey() as Ushort
Dim dummy As Ushort
Asm
rdtsc ' Get a fast changing number from the processor
mov word Ptr [dummy], ax
End Asm
Return dummy\4 ' 0 to 16383
End Function
Private Sub Squares.MyRandomize( byval counter As Ulongint = 0, byval keyno As Ulongint = 0 )
Dim As Ushort dummy
If counter = 0 Then
Randomize , 5 ' Cryptographic
this.ctr = ( Cast( Ulongint, Rnd*(2^32) ) Shl 32) Or Cast( Ulongint, Rnd*(2^32) )
Else
this.ctr = counter
End If
If keyno = 0 Then
dummy = RandomKey ' 0 to 16383
this.key = __SQRNG_KEY__( dummy )
this.keynumber = dummy
Else
this.key = __SQRNG_KEY__( keyno )
this.keynumber = keyno
End If
' Warm up generator - may not be needed but playing it safe
For i As Ulong = 1 To 500
this.rand()
Next
End Sub
private function Squares.rand() as ulong
Dim As Ulongint x, y, z
Engine
return (x * x + z) shr 32
end function
private function Squares.randse() as double ' 32-bit granularity
Dim As Ulongint x, y, z
Engine
return ((x * x + z) shr 32)/2^32
end function
Private Function mkulongint(n1 as ulong,n2 as ulong) as ulongint ' Courtesy MrSwiss
Dim As Ulongint res
Cast(Ulong Ptr,@res)[0]=n1
Cast(Ulong ptr,@res)[1]=n2
Return res
End Function
Private Function Squares.randd() As Double ' 53-bit granularity
Dim As Ulongint x, y, z
Dim As Ulong TempVar1, TempVar2
Engine
TempVar1 = (x * x + z) shr 32
Engine
TempVar2 = (x * x + z) shr 32
x = mkulongint( TempVar1, TempVar2 )
return x/2^64
End Function
Function Squares.range(First As Long, Last As Long) As Long
return clng(this.rand Mod (Last-First+1)) + First ' Mod method by dodicat
End Function
function Squares.range( First as double, Last as double ) as double
Return this.rand/2^32 * ( Last - First ) + First
end function
Private Function Squares.Getctr() As Ulongint
Return This.ctr
End Function
Private Sub Squares.Setctr( Counter As Ulongint )
This.ctr = Counter
End Sub
Private Function Squares.Getkeynumber() As Ushort
Return This.keynumber
End Function
Private Sub Squares.Setkeynumber( keyno As UShort )
This.keynumber = keyno
this.key = __SQRNG_KEY__( keyno )
End Sub
Private Function Squares.Getkey() As Ulongint
Return This.key
End Function
Private Sub Squares.GetSnapshot()
This.ctrSnapshot = This.ctr
This.keySnapshot = This.key
End Sub
Private Sub Squares.SetSnapshot()
This.ctr = This.ctrSnapshot
This.key = This.keySnapshot
End Sub
Constructor Squares
This.MyRandomize
This.GetSnapShot
End Constructor
Dim Shared As Squares Sq
#undef Rnd
#define Rnd Sq.randse
