Ben Nadel
On User Experience (UX) Design, JavaScript, ColdFusion, Node.js, Life, and Love.
I am the chief technical officer at InVision App, Inc - a prototyping and collaboration platform for designers, built by designers. I also rock out in JavaScript and ColdFusion 24x7.
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Comparing ColdFusion Number Randomization Algorithms

By Ben Nadel on
Tags: ColdFusion

The other week, I posted about how I didn't feel like ColdFusion always did a great job of random number generation. When using ColdFusion's RandRange() method, I just pass in the two required integers. After posting this, Dustin told me that ColdFusion MX7 introduced a third argument for the RandRange() method, which was the algorithm by which the random numbers were generated. By default, ColdFusion uses the CFMX_COMPAT algorithm. Apparently (and this is stated directly in the documentation), the alternate algorithm, SHA1PRNG, will do a much better job of randomizing numbers.

To explore these two algorithms, I first wanted to start out graphing them, to see if I could see any obvious trends. In the following example, I am looping over the two algorithms and then using ColdFusion's CFChart tag to charge 50 random numbers between the values 1 and 50.

  • <!---
  • Loop over the two algorithms, the default
  • CFMX_COMPAT and then the SHA1PRNG. We are
  • going to chart some random numbers to see
  • what they look like.
  • --->
  • <cfloop
  • index="strAlgorithm"
  • list="CFMX_COMPAT,SHA1PRNG"
  • delimiters=",">
  •  
  • <!---
  • Create a line graph of this randomly
  • selected numbers.
  • --->
  • <cfchart
  • format="png"
  • chartheight="500"
  • chartwidth="545"
  • labelformat="number"
  • xaxistitle="Iteration"
  • yaxistitle="Random Number">
  •  
  • <cfchartseries type="line">
  •  
  • <!---
  • Create each data item by randomly generating
  • a number using one of the algorithms.
  • --->
  • <cfloop
  • index="intI"
  • from="1"
  • to="50"
  • step="1">
  •  
  • <cfchartdata
  • item="#intI#"
  • value="#RandRange( 1, 50, strAlgorithm )#"
  • />
  •  
  • </cfloop>
  •  
  • </cfchartseries>
  •  
  • </cfchart>
  •  
  • </cfloop>

From the above code, we get the following graphs:

Algorithm: CFMX_COMPAT (ColdFusion's Default)


 
 
 

 
 ColdFusion RandRange() With CFMX_COMPAT  
 
 
 

Algorithm: SHA1PRNG (Added in ColdFusion MX7)


 
 
 

 
 ColdFusion RandRange() With SHA1PRNG  
 
 
 

Now, I look at these two graphs, and frankly, they don't mean anything to me. I don't see trends, and even if I do see some trends, I don't understand the significance. Both of these graphics look like a nice randomized set of numbers.

But more than that, this is not a useful test case for me. My issues with randomness rarely involve generating a ton of numbers right in a row; my scenarios usually involve manually refreshing a page to see if something is rotating "properly" (think advertisements or header images). In that case, there is a big delay between random number generation (compared the delay between CFLoop iterations). In my next experiment, I am using a META tag refresh to put a uniform delay between my page refreshes as this will most closely mimic me sitting there and hitting the browser's refresh button:

  • <!--- Param the list of random numbers. --->
  • <cfparam
  • name="URL.numbers"
  • type="string"
  • default=""
  • />
  •  
  • <!---
  • Create a random number using one of the
  • two algorithms, CFMX_COMPAT or SHA1PRNG.
  • --->
  • <cfset intNumber = RandRange( 1, 10, "SHA1PRNG" ) />
  •  
  • <!--- Add it to the list of numbers. --->
  • <cfset URL.numbers = ListAppend( URL.numbers, intNumber ) />
  •  
  •  
  • <!---
  • Check to see if we have generated enough numbers.
  • We want to generate 20. If have less than 20, let
  • provide the refresh link. If we have 20, just output
  • the numbers.
  • --->
  • <cfif (ListLen( URL.numbers ) LT 20)>
  •  
  • <!---
  • Provide meta-drive refresh. This is to ensure
  • that the timing of the refresh is similar for
  • each page refresh.
  • --->
  • <meta
  • http-equiv="refresh"
  • content=".5; url=#CGI.script_name#?numbers=#URL.numbers#"
  • />
  •  
  • <cfelse>
  •  
  • <!--- We have all the numbers, so output them. --->
  • #URL.numbers#
  •  
  • </cfif>

I ran the above code three times for each algorithm and here are the number lists that were generated:

Algorithm: CFMX_COMPAT (ColdFusion's Default)

  • 9,7,7,7,7,7,7,6,6,6,6,9,9,8,9,8,8,8,8,8
  • 3,6,6,6,5,6,6,5,5,4,4,5,2,3,2,2,2,2,2,2
  • 5,8,8,7,7,6,7,7,6,6,9,10,9,9,8,8,9,8,8,8

Algorithm: SHA1PRNG (Added in ColdFusion MX7)

  • 6,8,9,6,4,5,5,9,8,4,10,5,7,4,4,8,10,2,6,1
  • 6,6,8,9,8,1,8,9,9,3,7,3,3,5,6,7,7,3,4,5
  • 4,8,2,8,4,1,4,4,3,3,9,10,2,10,6,6,4,4,5,2

Just looking at these numbers, I can clearly see grouping in the CFMX_COMPAT algorithm. There is some grouping in the SHA1PRNG algorithm, but to a much much lesser degree. I don't know how the timing of the random number generation affects things, but it seems to have some sort of a link to the seemingly effective nature of the outcome. Now, I say "seemingly" because, remember, I am really more concerned about an even distribution of numbers and less so about the actual randomization of the numbers. Randomization or not, the SHA1PRNG seems to have a better distribution of numbers.




Reader Comments

Here's the mathematical proof for the variance (http://en.wikipedia.org/wiki/Variance) of the above results.

CFMX_COMPAT - variance - standard dev
test 1 - 1.05 - 1.0246
test 2 - 2.69 - 1.6401
test 3 - 1.5275 - 1.2359

SHA1PRNG - variance - standard dev
test 1 - 6.1475 - 2.4794
test 2 - 5.4275 - 2.3296
test 3 - 7.1475 - 2.6734

As the numbers get larger, the more variance the test set has present. A standard deviation of 2 means you should be hitting ~95% of your population, where 1 is only ~68%. The proof is in the pudding so to speak (sorry for the math pun).

I used this UDF to calculate the variance: http://www.cflib.org/udf.cfm?ID=256

Reply to this Comment

@Dustin,

It's been a million years since I took a statistics class (and didn't do so well in it). From what it looks like, a bigger standard deviation is a Good thing since, if you think about the Bell Curve, you are covering more ground (as you say, I think). Thanks for doing the testing.

Reply to this Comment

Yeah, it has been a long time for me as well. In fact I forgot about normal vs. random distributions when talking about standard deviation. The confidence levels stated (~95% and ~64%) are for a normal distribution, which we aren't dealing with. For a random distribution it is ~75% for 2 stddevs and ~50% for 1.41 stddevs.

I'm beginning to remember why I didn't particularity care for the class.

Reply to this Comment

Yeah, if I never hear about a z-test or t-square test (or something like that) again, I will quite content. My brain just doesn't seem to like that sort of thing.

Reply to this Comment

Thanks Ben,

I was complaining about the default behavior of randrange to a colleague only 2 days ago when observing the behavior of an online competition application we were running.

Little did I know that this behavior could be changed!

All goes to show I should RTFM!

Reply to this Comment

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