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randomdude



Joined: 01 Jun 2012
Posts: 83
randomdude
i have extracted these functions from a program:

Code:
proc my_getfastrand32,min,max

        locals
                tmpvalue dd ?
        endl

        mov     eax,dword[min]
        cmp     eax,dword[max]
        je      .end
        stdcall my_fastrand32
        mov     dword[tmpvalue],eax
        fild    dword[tmpvalue]
        fdiv    qword[dbl_2147483648] ;dq 2147483648.0
        mov     eax,dword[max]
        sub     eax,dword[min]
        add     eax,1
        mov     dword[tmpvalue],eax
        fild    dword[tmpvalue]
        fmulp   st1,st
        fiadd   dword[min]
        cinvoke _ftol2
        .end:
        ret
endp    


Code:
proc my_fastrand32

        mov     eax,dword[sfastrand32] ;seed
        imul    eax,343FDh
        add     eax,269EC3h
        mov     dword[sfastrand32],eax
        ;remove sign
        shr     eax,20h
        and     eax,7FFFFFFFh
        ret
endp    


my_fastrand32 returns a dword with a random value between 0 and 2147483647, and my_getfastrand32 uses it to return a value between 'min' and 'max'

however i would like to to enable negative values (eg. : min -50, max 50) but it returns sometimes values lower than 'min'. what can i do?
Post 27 Oct 2013, 19:16
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HaHaAnonymous



Joined: 02 Dec 2012
Posts: 1180
Location: Unknown
HaHaAnonymous
[ Post removed by author. ]


Last edited by HaHaAnonymous on 28 Feb 2015, 19:16; edited 1 time in total
Post 27 Oct 2013, 20:06
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AsmGuru62



Joined: 28 Jan 2004
Posts: 1419
Location: Toronto, Canada
AsmGuru62
You can generate a value in range [0..100] and then subtract 50.
Post 27 Oct 2013, 22:22
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hopcode



Joined: 04 Mar 2008
Posts: 563
Location: Germany
hopcode
randomdude wrote:
i have extracted these functions from a program:
Code:
proc my_fastrand32
...
    ;remove sign
    shr   eax,20h
    and  eax,7FFFFFFFh 
...
    ret
endp    
it seems a sloppy version of the Park-Miller generator.
anyway it's not safe choosing bits that way (SHR/AND) without a theory.
it may corrupt entirely the pseudo-randmoness Very Happy genuinity of the algo,if any.
this may help http://board.x64lab.net/viewtopic.php?f=2&t=35.
then open Park'pdf there and follow instructions for the minimal standard
to get back -+50 as ret value.

Cheers,
Very Happy

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Post 28 Oct 2013, 12:04
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randomdude



Joined: 01 Jun 2012
Posts: 83
randomdude
AsmGuru62 wrote:
You can generate a value in range [0..100] and then subtract 50.


yeah, but thats not very practical

hopcode wrote:
it seems a sloppy version of the Park-Miller generator.
anyway it's not safe choosing bits that way (SHR/AND) without a theory.
it may corrupt entirely the pseudo-randmoness Very Happy genuinity of the algo,if any.
this may help http://board.x64lab.net/viewtopic.php?f=2&t=35.
then open Park'pdf there and follow instructions for the minimal standard
to get back -+50 as ret value.

Cheers,
Very Happy


very interesting stuff indeed, hopcode!

however i dont see how can that help me tho

my_fastrand32 is actually the rand() function from msvcrt.dll, i just extended the two last instruction to increase the 32767 limit

Code:
proc rand

        mov     eax,dword[seed]
        imul    eax,343FDh
        add     eax,269EC3h
        mov     dword[seed],eax
        shr     eax,10h
        and     eax,7FFFh
        ret
endp    


by removing shr/and it will return negative values too from range -2147483648 to 2147483647, but for some reason if i do that my_getfastrand32 starts acting weird and returns negative values below the 'min' argument

this is my_getfastrand32 in c++:

Code:
int my_getfastrand32(int min, int max)
{
        if (min == max)
                return min;
        else
                return (int)(my_fastrand32() / (double)(2147483648.0 + 1.0) * (max - min + 1) + min);
}    


Description:
Download
Filename: rand.rar
Filesize: 2.54 KB
Downloaded: 163 Time(s)

Post 28 Oct 2013, 18:24
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cod3b453



Joined: 25 Aug 2004
Posts: 619
cod3b453
The my_fastrand32/2^31 term will be negative for negative my_fastrand32 and for suitably large magnitude round to -1 hence the product with the range is negative and the addition of min gives a value below min.
Post 28 Oct 2013, 18:38
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revolution
When all else fails, read the source


Joined: 24 Aug 2004
Posts: 17658
Location: In your JS exploiting you and your system
revolution
randomdude wrote:
by removing shr/and it will return negative values too from range -2147483648 to 2147483647 ...
Sure you can alter it like that but you will get some pretty crappy "random" numbers.

It might be better to use some LCG parameters that are designed for 32-bit, sequences rather than using your extended version that originally was designed for 16-bit sequences. Have you tested the period of it yet? I suspect it will be very short.

That is all assuming that an LCG is okay for your situation. For something like Monte-Carlo simulations LCGs are terrible generators to use.
Post 28 Oct 2013, 19:42
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AsmGuru62



Joined: 28 Jan 2004
Posts: 1419
Location: Toronto, Canada
AsmGuru62
I posted Mersenne Twister here some time ago:
http://board.flatassembler.net/topic.php?t=13741

Also, there is a good discussion about RNG on that thread.
Post 28 Oct 2013, 21:07
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Sasha



Joined: 17 Nov 2011
Posts: 93
Sasha
Quote:

my_fastrand32 is actually the rand() function from msvcrt.dll

This generator is the poorest one)
And the only thing you can NOT do with it is
Quote:

extended the two last instruction to increase the 32767 limit

In wikipedia there is a good explanation about the limits of LCG's.
Generally, what do you want from the generator?
If you want a good random numbers, then work on Mersenne Twister or xorshift.
If LCG is enough there are very simple LCG's with the maximum 32 bit period. Discussed here. I made many of them. It is very hard to find a good constants that will give you a good sequence. So you must chose from the tested ones or make all the required tests yourself. Some bits can be less random than others, so they are cut for this reason.
Then you need to cut the random number to the desired range.
Code:
if max>min
return min+((number*(max-min))/2^32)
    

or this, but I haven't used it. Correct me if I'm wrong.
Code:
if max>min
return min+(number mod (max-min))
    

Btw, can you explain what does this mean?
Quote:

Code:
shr     eax,20h
    


And why do you think, that subtracting is not practical if you are using one? And why do you need a fpu ?
Post 29 Oct 2013, 00:02
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HaHaAnonymous



Joined: 02 Dec 2012
Posts: 1180
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HaHaAnonymous
[ Post removed by author. ]


Last edited by HaHaAnonymous on 28 Feb 2015, 19:15; edited 1 time in total
Post 29 Oct 2013, 00:14
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hopcode



Joined: 04 Mar 2008
Posts: 563
Location: Germany
hopcode
Hallo randomdude,
i cannot resist, you set me in such a good and agreeable mood... Very Happy
i ehmmm have urgence to quote it again
randomdude wrote:
...from msvcrt.dll, i just extended the two last instruction to increase the 32767 limit...
Code:
...
    ;remove sign
    shr   eax,20h
    and  eax,7FFFFFFFh 
...    

ramdudu wrote:
AsmGuru62 wrote:
You can generate a value in range [0..100] and then subtract 50.
yeah, but thats not very practical

why not ? never understimate the solutions from AsmGuru62 Wink . try this untested implementation. it should ret in EAX the desired value
Code:
proc .rand
  sub esp,4
  mov  eax,dword[seed]
  imul eax,343FDh
  add  eax,269EC3h
  mov  dword[seed],eax
  shr  eax,10h
  and  eax,7FFFh
  mov [esp],eax
  fild dword[esp]
  fdiv dword[_const]
  fmul dword[_consta]
  fistp dword[esp]
  pop eax
  sub eax,50
  ret
align 4
  _const dd 32767.0
  _consta dd 100.0
endp
    

but seriously speaking now, from what i know the rand-algo there is crappy. AFAIK, from a 1 to 10 skala
it may stay level 1, where sushi-marsenne provided from AsmGuru level 6. i think it is of relevance to have a general vision of the
whole...firstly.

Cheers,
Very Happy

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Post 29 Oct 2013, 01:43
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Sasha



Joined: 17 Nov 2011
Posts: 93
Sasha
I thought, that shifting 32 times will zero the 32 bit register. Tested it...it's almost yes, but not) Shifting 31 times almost clears, but 32 restores all bits, then shr eax,33 is again like shr eax,1.
Post 29 Oct 2013, 01:54
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Sasha



Joined: 17 Nov 2011
Posts: 93
Sasha
hopcode, why fpu?
Why not this? This is like my first example.
Code:
    
proc my_getfastrand32,min,max

        locals
                tmpvalue dd ?
        endl

        mov     eax,dword[min]
        cmp     eax,dword[max]
        je      .end
        stdcall my_fastrand32
        mov edx,[max]
        sub edx,[min]
        mul edx
        mov eax,edx
        add eax,[min]        
        .end:
        ret
endp
    
Post 29 Oct 2013, 02:10
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hopcode



Joined: 04 Mar 2008
Posts: 563
Location: Germany
hopcode
Sasha wrote:
hopcode, why fpu?
i dont know, perhaps ramdudu has an hidden talent for FPU, and i decided automagically to stay instructionally with the code he posted above. who knows ? Very Happy
i have read just now the discussion there you linked above, and ehmm... i dont want to disappoint you but the algo-level is practically the same as here,imho.
that discussion is anyway important because you can find there some hints on how to get acquainted with the general vision about "randomness".
it is not simple...
Very Happy

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Post 29 Oct 2013, 02:37
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Sasha



Joined: 17 Nov 2011
Posts: 93
Sasha
By algo-level you mean the quality of random numbers or the optimisation of a code for speed? This is what I wanted, and randomdude called his proc fastrand. So after some benchmarks (not today, in the times of that thread) I've figure out, that the RNG that have only one mul is slower than xorshift, that have several xor's,shr's and mov's! At least on my comp and in my implementation.
Post 29 Oct 2013, 02:57
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hopcode



Joined: 04 Mar 2008
Posts: 563
Location: Germany
hopcode
yes. quality of numbers. i quote revolution from there
Quote:
Speed of generation is not the issue... LCGs are low quality and this must be considered when deciding which class of generator to use for the needed purpose.

one may think to improve some LCG acording a theory, but only when the purpose is worth. applying firstly a bit of mathe, before benchmarking can save lot of time, avoiding needing to test modifications.

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Post 29 Oct 2013, 03:18
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Sasha



Joined: 17 Nov 2011
Posts: 93
Sasha
So what I'm trying to say, that the LCG's worth is in its simplicity, but they give bad numbers and bad speed!
Post 29 Oct 2013, 11:55
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AsmGuru62



Joined: 28 Jan 2004
Posts: 1419
Location: Toronto, Canada
AsmGuru62
LCG speed should be very good actually, but numbers -- yes, they can be not suitable for some serious work, like simulations.
Post 29 Oct 2013, 17:51
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hopcode



Joined: 04 Mar 2008
Posts: 563
Location: Germany
hopcode
Hallo people,
just yesterday i was reading something about pi and i got suddenly Very Happy an idea how to implement an hypercube
(something alike from the sushi-marsene) from a stream of it.
here some results of my not-yet-tuned-theory, i have been implementing just 2 hours ago.

test on 16k data
Code:
flat assembler  version 1.71.15  (1048576 kilobytes memory)
3 passes, 2048 bytes.
        seconds...0.029206991195679
Value Char Occurrences Fraction
  0               80   0.004883
  1               59   0.003601
  2               61   0.003723
  3               72   0.004395
  4               59   0.003601
  5               58   0.003540
  6               75   0.004578
  7               65   0.003967
  8               68   0.004150
  9               61   0.003723
 10               64   0.003906
 11               66   0.004028
 12               61   0.003723
 13               64   0.003906
 14               71   0.004333
 15               56   0.003418
 16               75   0.004578
 17               64   0.003906
 18               67   0.004089
 19               70   0.004272
 20               68   0.004150
 21               62   0.003784
 22               69   0.004211
 23               66   0.004028
 24               65   0.003967
 25               58   0.003540
 26               80   0.004883
 27               72   0.004395
 28               70   0.004272
 29               52   0.003174
 30               66   0.004028
 31               78   0.004761
 32               59   0.003601
 33   !           65   0.003967
 34   "           61   0.003723
 35   #           63   0.003845
 36   $           62   0.003784
 37   %           76   0.004639
 38   &           50   0.003052
 39   '           59   0.003601
 40   (           68   0.004150
 41   )           75   0.004578
 42   *           82   0.005005
 43   +           58   0.003540
 44   ,           54   0.003296
 45   -           49   0.002991
 46   .           71   0.004333
 47   /           70   0.004272
 48   0           63   0.003845
 49   1           67   0.004089
 50   2           70   0.004272
 51   3           62   0.003784
 52   4           67   0.004089
 53   5           66   0.004028
 54   6           58   0.003540
 55   7           72   0.004395
 56   8           72   0.004395
 57   9           56   0.003418
 58   :           72   0.004395
 59   ;           65   0.003967
 60   <           63   0.003845
 61   =           62   0.003784
 62   >           57   0.003479
 63   ?           63   0.003845
 64   @           55   0.003357
 65   A           74   0.004517
 66   B           63   0.003845
 67   C           78   0.004761
 68   D           67   0.004089
 69   E           71   0.004333
 70   F           55   0.003357
 71   G           51   0.003113
 72   H           65   0.003967
 73   I           68   0.004150
 74   J           85   0.005188
 75   K           60   0.003662
 76   L           74   0.004517
 77   M           68   0.004150
 78   N           59   0.003601
 79   O           59   0.003601
 80   P           64   0.003906
 81   Q           82   0.005005
 82   R           83   0.005066
 83   S           48   0.002930
 84   T           60   0.003662
 85   U           64   0.003906
 86   V           65   0.003967
 87   W           56   0.003418
 88   X           66   0.004028
 89   Y           59   0.003601
 90   Z           51   0.003113
 91   [           73   0.004456
 92   \           65   0.003967
 93   ]           58   0.003540
 94   ^           61   0.003723
 95   _           57   0.003479
 96   `           70   0.004272
 97   a           57   0.003479
 98   b           58   0.003540
 99   c           63   0.003845
100   d           88   0.005371
101   e           73   0.004456
102   f           60   0.003662
103   g           70   0.004272
104   h           53   0.003235
105   i           63   0.003845
106   j           60   0.003662
107   k           61   0.003723
108   l           52   0.003174
109   m           77   0.004700
110   n           56   0.003418
111   o           66   0.004028
112   p           67   0.004089
113   q           60   0.003662
114   r           53   0.003235
115   s           64   0.003906
116   t           57   0.003479
117   u           67   0.004089
118   v           58   0.003540
119   w           62   0.003784
120   x           59   0.003601
121   y           64   0.003906
122   z           65   0.003967
123   {           67   0.004089
124   |           72   0.004395
125   }           70   0.004272
126   ~           50   0.003052
127               53   0.003235
128               45   0.002747
129               73   0.004456
130               68   0.004150
131               60   0.003662
132               83   0.005066
133               58   0.003540
134               61   0.003723
135               70   0.004272
136               63   0.003845
137               66   0.004028
138               59   0.003601
139               69   0.004211
140               63   0.003845
141               66   0.004028
142               71   0.004333
143               55   0.003357
144               56   0.003418
145               65   0.003967
146               63   0.003845
147               50   0.003052
148               71   0.004333
149               76   0.004639
150               60   0.003662
151               74   0.004517
152               62   0.003784
153               63   0.003845
154               58   0.003540
155               59   0.003601
156               68   0.004150
157               71   0.004333
158               72   0.004395
159               77   0.004700
160               55   0.003357
161   ¡           69   0.004211
162   ¢           76   0.004639
163   £           58   0.003540
164   ¤           67   0.004089
165   ¥           67   0.004089
166   ¦           74   0.004517
167   §           62   0.003784
168   ¨           53   0.003235
169   ©           67   0.004089
170   ª           61   0.003723
171   «           59   0.003601
172   ¬           59   0.003601
173   ­           71   0.004333
174   ®           66   0.004028
175   ¯           55   0.003357
176   °           73   0.004456
177   ±           59   0.003601
178   ²           63   0.003845
179   ³           62   0.003784
180   ´           63   0.003845
181   µ           55   0.003357
18253   0.003235
183   ·           71   0.004333
184   ¸           67   0.004089
185   ¹           58   0.003540
186   º           52   0.003174
187   »           63   0.003845
188   ¼           65   0.003967
189   ½           79   0.004822
190   ¾           53   0.003235
191   ¿           60   0.003662
192   À           61   0.003723
193   Á           61   0.003723
194   Â           60   0.003662
195   Ã           68   0.004150
196   Ä           55   0.003357
197   Å           54   0.003296
198   Æ           73   0.004456
199   Ç           70   0.004272
200   È           59   0.003601
201   É           61   0.003723
202   Ê           68   0.004150
203   Ë           56   0.003418
204   Ì           67   0.004089
205   Í           56   0.003418
206   Î           78   0.004761
207   Ï           64   0.003906
208   Ð           72   0.004395
209   Ñ           67   0.004089
210   Ò           75   0.004578
211   Ó           52   0.003174
212   Ô           66   0.004028
213   Õ           60   0.003662
214   Ö           75   0.004578
215   ×           68   0.004150
216   Ø           61   0.003723
217   Ù           67   0.004089
218   Ú           62   0.003784
219   Û           54   0.003296
220   Ü           68   0.004150
221   Ý           53   0.003235
222   Þ           85   0.005188
223   ß           67   0.004089
224   à           55   0.003357
225   á           78   0.004761
226   â           55   0.003357
227   ã           60   0.003662
228   ä           70   0.004272
229   å           42   0.002563
230   æ           62   0.003784
231   ç           62   0.003784
232   è           58   0.003540
233   é           54   0.003296
234   ê           56   0.003418
235   ë           68   0.004150
236   ì           75   0.004578
237   í           67   0.004089
238   î           54   0.003296
239   ï           62   0.003784
240   ð           71   0.004333
241   ñ           62   0.003784
242   ò           63   0.003845
243   ó           50   0.003052
244   ô           71   0.004333
245   õ           61   0.003723
246   ö           65   0.003967
247   ÷           53   0.003235
248   ø           76   0.004639
249   ù           60   0.003662
250   ú           61   0.003723
251   û           70   0.004272
252   ü           56   0.003418
253   ý           66   0.004028
254   þ           57   0.003479
255   ÿ           53   0.003235

Total:         16384   1.000000

Entropy = 7.989049 bits per byte.

Optimum compression would reduce the size
of this 16384 byte file by 0 percent.

Chi square distribution for 16384 samples is 249.81, and randomly
would exceed this value 57.99 percent of the times.

Arithmetic mean value of data bytes is 126.4144 (127.5 = random).
Monte Carlo value for Pi is 3.166300366 (error 0.79 percent).
Serial correlation coefficient is -0.005951 (totally uncorrelated = 0.0).
    

and as a confirmation theory is not that bad, look at the improved values
matching the general rules of what we know being called as "randomness".
on 32k * 32 data
Code:
flat assembler  version 1.71.15  (1048576 kilobytes memory)
3 passes, 0.1 seconds, 2048 bytes.
        seconds...7.4178831577301
Value Char Occurrences Fraction
  0            16296   0.003885
  1            16425   0.003916
  2            16456   0.003923
  3            16326   0.003892
  4            16257   0.003876
  5            16582   0.003953
  6            16338   0.003895
  7            16304   0.003887
  8            16578   0.003953
  9            16319   0.003891
 10            16396   0.003909
 11            16483   0.003930
 12            16733   0.003989
 13            16397   0.003909
 14            16376   0.003904
 15            16443   0.003920
 16            16482   0.003930
 17            16465   0.003926
 18            16515   0.003937
 19            16448   0.003922
 20            16234   0.003870
 21            16468   0.003926
 22            16555   0.003947
 23            16199   0.003862
 24            16239   0.003872
 25            16565   0.003949
 26            16410   0.003912
 27            16309   0.003888
 28            16542   0.003944
 29            16470   0.003927
 30            16345   0.003897
 31            16174   0.003856
 32            16464   0.003925
 33   !        16284   0.003882
 34   "        16147   0.003850
 35   #        16474   0.003928
 36   $        16468   0.003926
 37   %        16329   0.003893
 38   &        16428   0.003917
 39   '        16310   0.003889
 40   (        16441   0.003920
 41   )        16303   0.003887
 42   *        16506   0.003935
 43   +        16435   0.003918
 44   ,        16099   0.003838
 45   -        16382   0.003906
 46   .        16390   0.003908
 47   /        16315   0.003890
 48   0        16287   0.003883
 49   1        16535   0.003942
 50   2        16535   0.003942
 51   3        16473   0.003927
 52   4        16294   0.003885
 53   5        16365   0.003902
 54   6        16198   0.003862
 55   7        16244   0.003873
 56   8        16422   0.003915
 57   9        16351   0.003898
 58   :        16341   0.003896
 59   ;        16437   0.003919
 60   <        16601   0.003958
 61   =        16214   0.003866
 62   >        16274   0.003880
 63   ?        16354   0.003899
 64   @        16279   0.003881
 65   A        16135   0.003847
 66   B        16548   0.003945
 67   C        16482   0.003930
 68   D        16206   0.003864
 69   E        16441   0.003920
 70   F        16423   0.003916
 71   G        16168   0.003855
 72   H        16248   0.003874
 73   I        16488   0.003931
 74   J        16213   0.003865
 75   K        16353   0.003899
 76   L        16516   0.003938
 77   M        16379   0.003905
 78   N        16227   0.003869
 79   O        16229   0.003869
 80   P        16610   0.003960
 81   Q        16307   0.003888
 82   R        16527   0.003940
 83   S        16359   0.003900
 84   T        16448   0.003922
 85   U        16331   0.003894
 86   V        16261   0.003877
 87   W        16439   0.003919
 88   X        16394   0.003909
 89   Y        16297   0.003886
 90   Z        16389   0.003907
 91   [        16459   0.003924
 92   \        16288   0.003883
 93   ]        16709   0.003984
 94   ^        16236   0.003871
 95   _        16515   0.003937
 96   `        16148   0.003850
 97   a        16410   0.003912
 98   b        16295   0.003885
 99   c        16120   0.003843
100   d        16510   0.003936
101   e        16536   0.003942
102   f        16466   0.003926
103   g        16384   0.003906
104   h        16375   0.003904
105   i        16140   0.003848
106   j        16401   0.003910
107   k        16441   0.003920
108   l        16301   0.003886
109   m        16275   0.003880
110   n        16490   0.003932
111   o        16590   0.003955
112   p        16222   0.003868
113   q        16475   0.003928
114   r        16412   0.003913
115   s        16384   0.003906
116   t        16285   0.003883
117   u        16496   0.003933
118   v        16492   0.003932
119   w        16286   0.003883
120   x        16343   0.003896
121   y        16589   0.003955
122   z        16293   0.003885
123   {        16416   0.003914
124   |        16385   0.003906
125   }        16310   0.003889
126   ~        16385   0.003906
127            16388   0.003907
128            16456   0.003923
129            16377   0.003905
130            16463   0.003925
131            16578   0.003953
132            16428   0.003917
133            16401   0.003910
134            16384   0.003906
135            16388   0.003907
136            16389   0.003907
137            16393   0.003908
138            16411   0.003913
139            16334   0.003894
140            16505   0.003935
141            16214   0.003866
142            16690   0.003979
143            16247   0.003874
144            16412   0.003913
145            16544   0.003944
146            16476   0.003928
147            16251   0.003875
148            16416   0.003914
149            16489   0.003931
150            16294   0.003885
151            16435   0.003918
152            16502   0.003934
153            16234   0.003870
154            16154   0.003851
155            16293   0.003885
156            16232   0.003870
157            16341   0.003896
158            16517   0.003938
159            16559   0.003948
160            16220   0.003867
161   ¡        16324   0.003892
162   ¢        16619   0.003962
163   £        16093   0.003837
164   ¤        16268   0.003879
165   ¥        16691   0.003979
166   ¦        16505   0.003935
167   §        16161   0.003853
168   ¨        16421   0.003915
169   ©        16606   0.003959
170   ª        16140   0.003848
171   «        16405   0.003911
172   ¬        16388   0.003907
173   ­        16381   0.003906
174   ®        16305   0.003887
175   ¯        16395   0.003909
176   °        16583   0.003954
177   ±        16402   0.003911
178   ²        16267   0.003878
179   ³        16440   0.003920
180   ´        16346   0.003897
181   µ        16326   0.003892
18216501   0.003934
183   ·        16513   0.003937
184   ¸        16242   0.003872
185   ¹        16592   0.003956
186   º        16292   0.003884
187   »        16107   0.003840
188   ¼        16405   0.003911
189   ½        16359   0.003900
190   ¾        16407   0.003912
191   ¿        16507   0.003936
192   À        16415   0.003914
193   Á        16463   0.003925
194   Â        16457   0.003924
195   Ã        16264   0.003878
196   Ä        16366   0.003902
197   Å        16262   0.003877
198   Æ        16498   0.003933
199   Ç        16625   0.003964
200   È        16569   0.003950
201   É        16239   0.003872
202   Ê        16437   0.003919
203   Ë        16372   0.003903
204   Ì        16324   0.003892
205   Í        16117   0.003843
206   Î        16583   0.003954
207   Ï        16439   0.003919
208   Ð        16276   0.003881
209   Ñ        16468   0.003926
210   Ò        16563   0.003949
211   Ó        16125   0.003844
212   Ô        16461   0.003925
213   Õ        16241   0.003872
214   Ö        16314   0.003890
215   ×        16465   0.003926
216   Ø        16564   0.003949
217   Ù        16487   0.003931
218   Ú        16313   0.003889
219   Û        16448   0.003922
220   Ü        16564   0.003949
221   Ý        16212   0.003865
222   Þ        16439   0.003919
223   ß        16331   0.003894
224   à        16315   0.003890
225   á        16527   0.003940
226   â        16360   0.003901
227   ã        16419   0.003915
228   ä        16259   0.003876
229   å        16201   0.003863
230   æ        16401   0.003910
231   ç        16360   0.003901
232   è        16484   0.003930
233   é        16506   0.003935
234   ê        16486   0.003931
235   ë        16275   0.003880
236   ì        16412   0.003913
237   í        16454   0.003923
238   î        16205   0.003864
239   ï        16482   0.003930
240   ð        16409   0.003912
241   ñ        16199   0.003862
242   ò        16319   0.003891
243   ó        16520   0.003939
244   ô        16506   0.003935
245   õ        16266   0.003878
246   ö        16247   0.003874
247   ÷        16373   0.003904
248   ø        16392   0.003908
249   ù        16385   0.003906
250   ú        16382   0.003906
251   û        16197   0.003862
252   ü        16383   0.003906
253   ý        16180   0.003858
254   þ        16490   0.003932
255   ÿ        16415   0.003914

Total:       4194304   1.000000

Entropy = 7.999957 bits per byte.

Optimum compression would reduce the size
of this 4194304 byte file by 0 percent.

Chi square distribution for 4194304 samples is 250.61, and randomly
would exceed this value 56.59 percent of the times.

Arithmetic mean value of data bytes is 127.4910 (127.5 = random).
Monte Carlo value for Pi is 3.143437522 (error 0.06 percent).
Serial correlation coefficient is -0.000431 (totally uncorrelated = 0.0).
    

idea seems working. i think i will give some time for it. it deserves deeper study, and some more deeper tests.
Cheers,
Very Happy

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Post 30 Oct 2013, 12:48
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revolution
When all else fails, read the source


Joined: 24 Aug 2004
Posts: 17658
Location: In your JS exploiting you and your system
revolution
Indeed PI was proved irrational a long time ago so would be fine for generating PRNG sequences. But it suffers from the problem of generation difficulty. If you want some significant amount of numbers then you need to compute PI to very large precision.
Post 30 Oct 2013, 13:26
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