Foreword
If you studied how PC usually generate random number, you know that it's impossible to create a real random number. A PC is a machine extremely rigid, it doesn't possess any device to obtain something absolutely random.On the other side, mathematicians and software expert concluded that it's very near to a random number the "result of a calculus that you can't forecast". What does it mean?
It means that you ask to a PC to make a calculus that you can't forecast (but another PC can forecast), for you seem random. Every PC with any software works this way.
Let's make a real world example:
>> now/time/precise
== 13:55:05.015
the command now/time/precise return the time with milliseconds precision. If you want just the millisecond, you can type:
>> next parse to-string now/precise/time "."
== ["484"]
Every time you'll send the command, the result will be different, because you can't know or calculate the milliseconds of the time of your request; but another PC can calculate when "he" requests and can exactly forecast the result.
The problem is that the result depends always on the time of the request, a machine will give you always the same results in the same conditions.
Numbers generated this way are called pseudo-random
Mathematical approach
The majority of situation don't need to know "how much random" is the result, but some scientific tasks require that the random distribution of the results are similar to specific mathematical distributions.Fortunately there is the randomr.r library for this purpose.
Here a script that shows how it works:
The randomr.r lib contains the following distributions:
UNIFORM:
- uniform law on
- exponential law
- exponential law with a l degree
- normal law
- normal polar law
- logarithmic normal law
- gamma law
- geometric law in a disc
- geometric law in a rectangle
- χ2 law (chi square)
- Erlang law
- Student law
- Fisher law
- Laplace Law
- beta law
- weibull law
- Rayleigh law
- Bernouilli law
- binomial law
- binomial negative law
- geometric law
- Poisson law
Here the source:
REBOL [
File: %demorandom.r
Date: 17-June-2009
Title: "Random Number Generator Demo"
Version: 1.0
Author: "François Jouen."
Rights: {Copyright © EPHE 2009}
Purpose: {Some examples how to use randomr lib}
]
; load random library
if not exists? %randomr.r [write %randomr.r (read http://www.rebol.org/download-a-script.r?script-name=randomr.r )]
do %randomr.r
; some variables
psample: 500
baseline: 250
xpas: 1
yscale: 40
col: yellow
xy1: 0x59
xy2: 500x59
plot: copy [pen col line]
plot2: copy [pen col line]
; for fun
app-styles: stylize [
app_btn: button 60 edge [size: 1x1 color: 0.0.0 ] font [style: none colors/1: black shadow: none]
]
; update slider
fix_slider: does [
either 0 = length? calc/data [calc/sld/redrag 1]
[calc/sld/redrag calc/lc / length? calc/data]
]
Clear_Screen: does [
x: 0
plot: copy [pen col line]
append clear visu/effect reduce ['draw plot]
plot2: copy [pen white line xy1 xy2 pen col line-width 2 line]
append clear visu2/effect reduce ['draw plot2]
show [visu visu2]
]
; Data visualization
show_law: func [lawname] [
Clear_Screen
buffer: copy calc/data
n: length? calc/data
normalized: copy []
; calculate mean
sigma: 0
for i 1 n 1 [v: pick buffer i sigma: sigma + v]
m: round/to sigma / n .001
; calculate variance and SD
sigma: 0
for i 1 n 1 [v: pick buffer i sigma: sigma + power (v - m) 2]
variance: round/to sigma / (n - 1) .001
sd: round/to square-root variance .001
; show data in normal reduced law (x - m /sd)
for i 1 n 1 [x: x + xpas v: ((pick buffer i) - m ) / sd y: baseline - ( yscale * v)
append plot to-pair compose [(x) (y)]
append normalized v]
str: join lawname [newline " mean: " m newline "variance: " variance newline " SD: " sd]
visu/text: str
buffer: copy sort normalized
x: 0
;now show random value distribution in second window
visu2/text: "Sorted Normalized Data [(x-m)/sd]"
for i 1 n 1 [
x: x + xpas v: pick buffer i y: 59 - ( 29 * v)
append plot2 to-pair compose [(x) (y)]
]
show [visu visu2]
]
MainWin: layout/size [
styles app-styles
origin 5x5
space 2x2
across
at 5x2 box 875x30 bevel
at 95x2 text "Parameters" text "Sample" fsample: field 50 to-string psample [
if error? try [psample: to-integer fsample/text][psample: 320]]
; //CONTINUOUS LAWS//
at 5x35 app_btn 90 "Exponential" [if error? try [clear calc/data
for i 1 psample 1 [append calc/data rand_exp]
fix_slider show calc show_law face/text]
[Alert "Error in processing"]
]
at 5x60 app_btn 90 "Exp with L°" [if error? try [clear calc/data
for i 1 psample 1 [append calc/data rand_expm to-decimal expmp/text]
fix_slider show calc show_law face/text]
[Alert "Error in processing"]
]
expmp: field 35 "1.0"
at 5x85 app_btn 90 "Normal" [if error? try [clear calc/data
for i 1 psample 1 [append calc/data rand_norm to-decimal normp/text]
fix_slider show calc show_law face/text]
[Alert "Error in processing"]
]
normp: field 35 "1.0"
at 5x110 app_btn 90 "Gamma" [if error? try [clear calc/data
for i 1 psample 1 [append calc/data rand_gamma to-integer gamp1/text to-decimal gamp2/text]
fix_slider show calc show_law face/text]
[Alert "Error in processing"]
]
gamp1: field 35 "1" gamp2: field 35 "1.0"
at 5x135 app_btn 90 "Chi-2" [if error? try [clear calc/data
for i 1 psample 1 [append calc/data rand_chi2 to-integer chip/text]
fix_slider show calc show_law face/text]
[Alert "Error in processing"]
]
chip: field 35 "2"
at 5x160 app_btn 90 "Erlang" [if error? try [clear calc/data
for i 1 psample 1 [ append calc/data rand_erlang to-integer erp/text]
fix_slider show calc show_law face/text]
[Alert "Error in processing"]
]
erp: field 35 "1"
at 5x185 app_btn 90 "Student" [if error? try [clear calc/data
for i 1 psample 1 [append calc/data rand_student to-integer stud/text to-decimal stud2/text]
fix_slider show calc show_law face/text]
[Alert "Error in processing"]
]
stud: field 35 "3" stud2: field 35 "1.0"
at 5x210 app_btn 90 "Fischer" [if error? try [clear calc/data
for i 1 psample 1 [append calc/data rand_fischer to-integer fisc1/text to-integer fisc2/text ]
fix_slider show calc show_law face/text]
[Alert "Error in processing"]
]
fisc1: field 35 "1" fisc2: field 35 "1"
at 5x235 app_btn 90 "Laplace" [if error? try [ clear calc/data
for i 1 psample 1 [ append calc/data rand_laplace to-decimal lp/text]
fix_slider show calc show_law face/text ]
[Alert "Error in processing"]
]
lp: field 35 "1.0"
at 5x260 app_btn 90 "Beta" [if error? try [clear calc/data
for i 1 psample 1 [ append calc/data rand_beta to-integer beta1/text to-integer beta2/text]
fix_slider show calc show_law face/text ]
[Alert "Error in processing"]
]
beta1: field 35 "1" beta2: field 35 "1"
at 5x285 app_btn 90 "Weibull" [if error? try [clear calc/data
for i 1 psample 1 [ append calc/data rand_weibull to-decimal a/text to-decimal lambda/text]
fix_slider show calc show_law face/text ]
[Alert "Error in processing"]
]
a: field 35 "1.0" lambda: field 35 "1.0"
at 5x310 app_btn 90 "Rayleigh" [if error? try [clear calc/data
for i 1 psample 1 [ append calc/data rand_rayleigh to-decimal ra/text to-decimal rb/text]
fix_slider show calc show_law face/text ]
[Alert "Error in processing"]
]
ra: field 35 "1.0" rb: field 35 "1.0"
; DISCRETE LAWS
at 5x335 app_btn 90 "Bernouilli" [if error? try [clear calc/data
for i 1 psample 1 [ append calc/data rand_bernouilli to-decimal bp/text]
fix_slider show calc show_law face/text ]
[Alert "Error in processing"]
]
bp: field 35 "0.5"
at 5x360 app_btn 90 "Binomial" [if error? try [clear calc/data
for i 1 psample 1 [ append calc/data rand_binomial to-integer ob/text to-decimal bpp/text]
fix_slider show calc show_law face/text ]
[Alert "Error in processing"]
]
ob: field 35 "1" bpp: field 35 "0.5"
at 5x385 app_btn 90 "NegBinomial" [if error? try [clear calc/data
for i 1 psample 1 [ append calc/data rand_binomialneg to-integer onb/text to-decimal nbpp/text]
fix_slider show calc show_law face/text ]
[Alert "Error in processing"]
]
onb: field 35 "1" nbpp: field 35 "0.5"
at 5x410 app_btn 90 "Geometric" [if error? try [clear calc/data
for i 1 psample 1 [ append calc/data rand_geo to-decimal geop/text]
fix_slider show calc show_law face/text ]
[Alert "Error in processing"]
]
geop: field 35 "0.25"
at 5x435 app_btn 90 "Poisson" [if error? try [clear calc/data
for i 1 psample 1 [ append calc/data rand_poisson to-decimal pp/text]
fix_slider show calc show_law face/text ]
[Alert "Error in processing"]
]
pp: field 35 "1.5"
; REBOL LAWS
at 5x460 app_btn 90 "Rebol Rand" [if error? try [clear calc/data
for i 1 psample 1 [ append calc/data random to-integer rpp/text]
fix_slider show calc show_law face/text ]
[Alert "Error in processing"]
]
rpp: field 35 "10"
at 5x485 app_btn 90 "Rebol Real" [if error? try [clear calc/data
for i 1 psample 1 [ append calc/data rand_real]
fix_slider show calc show_law face/text ]
[Alert "Error in processing"]
]
at 175x35 calc: text-list 200x475
pad 5 visu: box blue + 100 500x350 font [valign: 'top] frame navy
at 382x390 visu2: box blue + 100 500x118 font [valign: 'top] frame navy
at 370x2 text "X Step" fxpas: field 50 to-string xpas [if error? try
[xpas: to-integer fxpas/text]
[xpas: 1 fxpas/text: "1"]]
pad 5 text "Y Scale" fyscale: field 50 to-string yscale [if error? try
[yscale: to-integer fyscale/text]
[yscale: 40 fyscale/text: to-string yscale]]
pad 200 app_btn 90 "Quit" [Quit]
]885x520
view center-face MainWin
Practical approach
Another way is getting number from the site www.random.org, this site extract random numbers form radio wave noise. Nobody can predict the exact amount of radio wave used every day, so the noise is totally random.Here the source of the script:
REBOL[
File: %random-org.r
Date: 17-6-2008
Title: "Random.org"
Purpose: "Get really random numbers (come from atmospheric noise) from http://random.org"
]
random-org: func [
"Get block of random numbers from http://random.org"
/size "Size of block (default = 100)"
siz
/interval "Number interval (default = 1 - 100)"
min max
/base "Numerical base - 2, 8, 10, 16 (default = 10)"
base-num
][
if not size [siz: 100]
if not interval [min: 1 max: 100]
if not base [base-num: 10]
load read rejoin [http://random.org/integers/?num= siz "&min=" min "&max=" max "&col=1&base=" base-num "&format=plain&rnd=new"]
]
It usually get a casual list numbers from the site, but if you want just a number or two between 1 and 10:
>> random-org/size/interval 1 1 10
== 9
>> random-org/size/interval 2 1 10
== [2 6 ]
As usual for more information digit:
? random-orgHere a web app from random.org:
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