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Full Version: Random Number Generation Challenge (sort of)
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Hi All,

I am trying to write a random number generator on my HP41CX such that I use the built-in time module to generate either an initial seed for a sequence of random numbers, or generate random numbers outright. Using the values for the current time (and also date) has the potential of generating unique initial seed values.

I think the solution involves the values of time, date, and possibly some sort of a counter.

The simpler the solution the better. So let's put our math thinking caps, shall we!

Namir

PS: I am also trying to solve the same problem with Excel. Of course using VBA code I have a lot of options for more complex/elaborate solutions and more speed.

Edited: 13 Feb 2010, 9:16 a.m.

```01  LBL "RNG4"
02  DATE
03  TIME
04  +
05   E49
06  *
07  PI
08  MOD
09  LN1+X
10  R-D
11  FRC
12  END
```

That's what I use.

This one will always make a new random number, it does not have the capability of regenerating a given sequence. It is a good starting point for both functions, though, since the routine can be used as a seed, then plugged into another RNG from the same URL that just uses a given seed.

Edited: 13 Feb 2010, 9:57 a.m.

Namir

Here is the VBA code for a class (which I call CVirtTime) that performs random number generation using a "virtual clock" that is not affected by the speed of the computer running the code. This virtual clock will advance the virtual time each time you call method NextRand() which generates uniform random numbers between 0 and 1. You must initialize the instance of the class using either InitMyTime or InitTime. The first method allows you to specify any time and date you want (and therefore you can duplicate the sequence of numbers generated). The method InitTime initializes the class instance using the current system date and time. Using this method you cannot replicate the sequence of random numbers. Once you initialize the class instance the virtual clock "ticks" as fast as the number of calls to method NextRand().

```Option Explicit
Private m_nSec As Integer
Private m_nMin As Integer
Private m_nHour As Integer
Private m_nDay As Integer
Private m_nMonth As Integer
Private m_nYear As Integer
Private m_fCounter As Double
Private PI As Double
Private Function Log10(ByVal X As Double) As Double
Log10 = Log(X) / Log(10)
End Function
Private Function AbSin(ByVal X As Double) As Double
AbSin = Abs(Sin(X)) + 1
End Function
Private Function AbCos(ByVal X As Double) As Double
AbCos = Abs(Cos(X)) + 1
End Function
Private Sub INC(ByRef N As Integer)
N = N + 1
End Sub
Public Sub InitMyTime(ByVal nSec As Integer, ByVal nMin As Integer, ByVal nHour As Integer, _
ByVal nDay As Integer, ByVal nMonth As Integer, ByVal nYear As Integer)
m_nSec = Abs(nSec)
If m_nSec > 59 Then m_nSec = 0
m_nHour = Abs(nHour)
If m_nHour > 23 Then m_nHour = 0
m_nMin = Abs(nMin)
If m_nMin > 59 Then m_nHour = 0
m_nDay = Abs(nDay)
If m_nDay > 30 Or m_nDay = 0 Then m_nDay = 1
m_nMonth = Abs(nMonth)
If m_nMonth > 12 Or m_nMonth = 0 Then m_nMonth = 1
m_nYear = Abs(nYear)
If m_nYear < 1900 Then m_nYear = 1900
m_fCounter = 0
PI = 4 * Atn(1)
End Sub
Public Sub InitTime()
Dim t As Date
t = Now
m_nSec = Second(t)
m_nHour = Hour(t)
m_nMin = Minute(t)
m_nDay = Day(t)
m_nMonth = Month(t)
m_nYear = Year(t)
m_fCounter = 0
PI = 4 * Atn(1)
End Sub
Public Function NextRand() As Double
Dim X As Double
' manage the virtual time and date
If m_nSec = 60 Then
m_nSec = 0
INC m_nMin
If m_nMin = 60 Then
m_nMin = 0
INC m_nHour
If m_nHour = 24 Then
m_nHour = 0
INC m_nDay
If m_nDay = 30 Then
m_nDay = 1
INC m_nMonth
If m_nMonth = 12 Then
m_nMonth = 1
INC m_nYear
Else
INC m_nMonth
End If
Else
INC m_nDay
End If
Else
INC m_nHour
End If
Else
INC m_nMin
End If
Else
INC m_nSec
End If

X = (5773 * AbSin(137 * m_nSec) * AbCos(173 * m_nMin) * AbSin(137 * m_nHour)) + _
(2377 * AbSin(237 * m_nDay) * AbCos(117 * m_nMonth) * AbCos(m_nYear))
m_fCounter = m_fCounter + 1
If m_fCounter > 1E+99 Then m_fCounter = 0
X = X + Abs(Sin(m_fCounter) + Log(1 + m_fCounter))
NextRand = X - Int(X)
End Function
```

Calculating the value for variable X is more of an art than a science (at least in my humble opinion). You can develop so many different kinds of expression to calculate X--some better than others. I tried using the modulo operator in a "creative" way, but found that using sin and cos function works rather well.

Namir

Edited: 15 Feb 2010, 8:52 a.m. after one or more responses were posted

```Hi everyone.
Here is an M-Code function that I wrote to get random numbers.
-"RAND" uses the timer to produce pseudo-random numbers r between 0 and 1 ( 0 < r < 1 ). I don't know if r = 0 may happen.
-The content of register X is saved in L-register

084   "D"
00E   "N"
001   "A"
012   "R"
128   WRIT 4(L)
130   LDI S&X
010   010                The user memory must be deselected by selecting
270   RAM SLCT           a non-existent RAM ( at 010h )
130   LDI S&X            then the Timer
0FB   0FB                is
3F0   PRPH SLCT          selected
3E8   WRIT 15(e)         Set the A/B pointer to A
1BC   RCR 11             Rotates C-register 11 digits right
046   C=0 S&X            The user memory
270   RAM SLCT           is selected again
05E   C=0 MS
130   LDI S&X
041   041
2A0   SETDEC
10E   A=C ALL
04E   C=0 ALL
35C   PT=12
1D0   LD@PT- 7
210   LD@PT- 8
110   LD@PT- 4
050   LD@PT- 1
090   LD@PT- 2
250   LD@PT- 9
190   LD@PT- 6
1D0   LD@PT- 7
210   LD@PT- 8
1D0   LD@PT- 7
044   CLRF 4                  C
070   N=C ALL                 =
171   ?NCXQ                   A
064   195C                  mod C
10E   A=C ALL
0B0   C=N ALL
261   ?NCXQ                   C =
060   1898                    A/C
0E8   WRIT 3(X)
3E0   RTN
Best Regards,
Jean-Marc.
```

Cool ........ but it looks Greek to me!!!

:-)

Namir

Namir, having read Donald Knuth I have the feeling that you are on the wrong track. From the top of my head, he states that having a complicated function does not make the pseudo random sequence any better. As a result: There are simple workable solutions like the Linear Congruential Method:

(from the pages cited below.)

(I'll have to check the pages for myself but they look promising.)

Beautiful example Jean-Marc, thanks for sharing it.

There is another implementation on the SandMath module, functions SEEDT and RAND written by Håkan Thörngren "a few years ago" - and published on PPCJ back then. I like it because it uses a memory buffer to store the seed(s). Also the time module is used to obtain an initial seed if the input is zero.

Cheers,
ÁM.

Edited: 15 Feb 2010, 4:30 a.m.

Marcus,

Sure the equation you mentioned is very popular and I used it to write typical pseudo-random number generators. My basic approach in this thread is to use the computer's system date and time as an automatic initial seed OR as a way to generate uniform random numbers outright. Since PC's run fast, a system date/time based algorithm risks of generating large arrays of the same random number. This problem prompted me to think of a using a counter to avoid generating the same numbers. Then, I thought of creating a class for a virtual clock that can be initialized by the actual system clock and then run at it's own pace and totally independent of the actual CPU speed. Thus, my virtual clock ticks each time you generate a random number.

The equation I am using uses all of the components of date and time.

Namir

Quote:
PS: I am also trying to solve the same problem with Excel. Of course using VBA code I have a lot of options for more complex/elaborate solutions and more speed.

I found that many random number generating routines performed poorly with regards to having too much repitition when I required 100's of 1000's of numbers. A very good one I found for Excel was Mersenne-Twister. On the site there are links to several implementations and also an Excel add-in.