# Have the Random functions changed?

I re-ran a program I wrote for Mathematica v8, now on v9, and it appears to generate different RandomInteger numbers, even though I use the same SeedRandom at the beginning.
Have Random functions changed in v9?

• To give a particular example, what does BlockRandom[SeedRandom[42, Method -> "ExtendedCA"]; RandomInteger[{-9, 9}, 10]] return on version 9? – J. M. is away Jun 22 '13 at 7:54
• @J. M. - {4, -5, -7, -8, -3, -9, -5, -6, -1, 3} – stevenvh Jun 22 '13 at 7:57
• hmmm. both v8 and v9 produce the same sequence for me... – Stefan Jun 22 '13 at 7:58
• You might find ArrayReshape better fitting your needs. There is an adequate example in its documentation. – Artes Dec 4 '13 at 17:29
• @Artes - Thanks, I'll look at it. Any reason why it's better than Partition (which works now)? – stevenvh Dec 4 '13 at 17:44

The default random number generation method has changed from version 8 to version 9.

The default methods for version 8 and version 9 are:

PRNG                |     v8           |  v9
-----------------------------------------------------
RandomInteger[]     |    ExtendedCA    |  Rule30CA
RandomReal[]        |    ExtendedCA    |  Rule30CA


The following does produce the same results for both versions:

methods = {
"Congruential",
"ExtendedCA",
"Legacy",
"MersenneTwister",
"MKL",
"ParallelGenerator",
"ParallelMersenneTwister",
"Rule30CA"
};

Table[BlockRandom[SeedRandom[42, Method -> m];
Print[m <> ": ", RandomInteger[{-9, 9}, 10]];
RandomInteger[{-9, 9}, 10]], {m, methods}];

Congruential: {-9, 0, 3, -7, -9, -3, 5, -1, 7, 4}

ExtendedCA: {4, -5, -7, -8, -3, -9, -5, -6, -1, 3}

Legacy: {9, -9, 0, 5, 7, -5, 9, 8, -1, 0}

MersenneTwister: {7, 6, 5, 2, 0, -3, 4, 4, -1, 8}

MKL: {-5, 2, -8, -3, -3, -5, 1, 1, 3, -5}

ParallelGenerator: {-2, 2, 3, 0, -6, -7, 3, -7, -9, -1}

ParallelMersenneTwister: {-4, -4, -1, -2, 0, -9, 0, -8, -9, -8}

Rule30CA: {9, -9, 0, 5, 7, -5, 9, 8, -1, 0}


If you use the default method, you indeed get different results:

BlockRandom[SeedRandom[42]; RandomInteger[{-9, 9}, 10]]


v8:

{4, -5, -7, -8, -3, -9, -5, -6, -1, 3}


v9:

{9, -9, 0, 5, 7, -5, 9, 8, -1, 0}


If they claim that the default is "ExtendedCA", than this is not true for version 9. For version 9, the default is "Rule30CA", while on version 8 it uses "ExtendedCA".

So if you want to produce the same random numbers on version 9, you have to explicitly set the method to "ExtendedCA".

Incidentally, the reason why "Legacy" and "Rule30CA" gave the same results for RandomInteger is that the legacy method does use the rule 30 generator in the integer case.

Now, let's test if this holds for RandomReal as well:

Table[BlockRandom[SeedRandom[42, Method -> m];
Print[m <> ": ", InputForm @ RandomReal[10, 10]]], {m, methods}];

Congruential: {3.8461335440024715, 3.354304567149635, 4.51935934053208,
8.850230228014308, 3.6248509154618356, 8.157875428939777,
2.4513895134473387, 5.818949583945838, 4.969467831268059,
0.03347488955145989}

ExtendedCA:   {4.259052837159626, 3.910231598741685, 3.4706935350965935,
4.53740630685645, 5.5596334203812, 2.8916925336738952,
2.9684806264504378, 2.064076444638916, 3.251697057830391,
9.733246886114031}

Legacy:       {8.9572216046609, 4.970307857530802, 5.435846534404246,
7.085955661473399, 6.776487260106322, 8.054379667584591,
0.7094411741824413, 8.968322445752152, 8.901306909526046,
0.7502088503156987}

MersenneTwister: {5.153950855950999, 0.6727671698455833, 4.524316138874237,
9.921991209186388, 0.5443991248015738, 8.437734478961886,
6.959208913527714, 9.091869760437504, 2.310061068071903,
8.976972757532419}

MKL:          {2.2010771720728672, 5.882083584870089, 0.7266383901861087,
3.3726500591458435, 3.3079876451216217, 2.488652193017376,
5.6151582821198005, 5.305289374386305, 6.735427495488978,
2.29022838609706}

ParallelGenerator: {2.8013742426114714, 8.147026088771263, 3.8405810263728526,
2.5308472947817595, 9.400530227458631, 9.054157508803371,
9.449607002369156, 4.3141703917759315, 6.087645635734276,
6.8637216165050745}

ParallelMersenneTwister: {9.999076480701376, 9.830697737962758, 8.382728461259866,
9.292582323124666, 0.487553230365652, 5.914364713788565,
1.6141971841606058, 1.4211558070777137, 9.501590480279376,
2.6447011005402707}

Rule30CA:     {5.633636625848604, 0.19140585740303528, 6.149388826993686,
1.9144953965106026, 2.9253076004819345, 0.55162786941208,
1.995816904778028, 9.427477798414383, 0.39607049447435116,
1.8220850707267502}


Both lists are identical between version 8 and version 9.

Let's use the default method for RandomReal:

v8:

BlockRandom[SeedRandom[42]; InputForm @ RandomReal[10, 10]]

{4.259052837159626, 3.910231598741685, 3.4706935350965935,
4.53740630685645, 5.5596334203812, 2.8916925336738952,
2.9684806264504378, 2.064076444638916, 3.251697057830391,
9.733246886114031}


So the default method for version 8 is "ExtendedCA".

v9:

BlockRandom[SeedRandom[42]; InputForm @ RandomReal[10, 10]]

{5.633636625848604, 0.19140585740303528, 6.149388826993686,
1.9144953965106026, 2.9253076004819345, 0.55162786941208,
1.995816904778028, 9.427477798414383, 0.39607049447435116,
1.8220850707267502}


And the default method for version 9 is "Rule30CA".

• Huh, that's a step back. Here I thought they replaced the legacy generator with the newer CA-based ones precisely because the legacy method had not too good statistical properties... – J. M. is away Jun 22 '13 at 8:39
• I've hade the same 'yikes!' moment...in chess something like this would've been called a blunder. – Stefan Jun 22 '13 at 8:50
• Well, for completeness' sake, could you also do tests replacing RandomInteger[{-9, 9}, 10] with RandomReal[1, 10]? Maybe use InputForm[] so that all the digits of the random variates are displayed... BTW, to cover the default method in the results of the Table[], you can use the setting Method -> Automatic. – J. M. is away Jun 22 '13 at 9:19
• @J. M. done. if you want to have a look at it and feel free to improve things. btw. i've used coloured Grid's in my notebook, but it seems to be impossible to paste this here in SE, that's why i've used Table. – Stefan Jun 22 '13 at 10:03
• @"Now we wait for somebody from WRI to explain this switch..." Well, there was no switch. – ilian Jul 27 '18 at 21:19

The default random number generation method has been the same for the last 12 years (in terms of releases, since V6).

It has not changed, certainly not between V8 and version V9, or more recently.

Both version 8 and version 9 should be using "ExtendedCA" as documented.

On my machine, both of the following results are as expected

In[1]:= \$Version

(* 9.0 for Linux x86 (64-bit) (November 20, 2012) *)

In[2]:= BlockRandom[SeedRandom[42]; RandomInteger[{-9, 9}, 10]]

(* {4, -5, -7, -8, -3, -9, -5, -6, -1, 3} *)

In[3]:= BlockRandom[SeedRandom[42]; InputForm @ RandomReal[10, 10]]

(* {4.259052837159626, 3.910231598741685, 3.4706935350965935,
4.53740630685645, 5.5596334203812, 2.8916925336738952,
2.9684806264504378, 2.064076444638916, 3.251697057830391, 9.733246886114031} *)


I have tried the other platforms as well.

No idea what was happening in the earlier answer which claims "Rule30CA" was the default in V9, but it doesn't even seem possible.

I would think either a (mysterious!) bug, or some user initialization code switching the method.