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In the following Mathematica compiled program, 3 persons take turns in a fair Russian Roulette Game with 1 bullet in the 6th chamber and we find the probabilities of each person being killed after 1,000,000 repetitions of the experiment,

The program: 

  p = 3; n = 1000000.; arg = Table[0, n]; Roulette = 
  Compile[{i}, Module[{c = 1}, While[RandomInteger[{1, 6}]
  != 6, c++]; m = Mod[c, p]; If[m != 0, m, p]], 
  RuntimeAttributes -> {Listable}, Parallelization -> True, 
  RuntimeOptions -> "Speed"]; 
  Counts[Roulette[arg]]/n // AbsoluteTiming

with Parallelization -> True, gives nonsense whereas without:

  p = 3; n = 1000000.; arg = Table[0, n]; Roulette = 
  Compile[{i}, Module[{c = 1}, While[RandomInteger[{1, 6}]
  != 6, c++]; m = Mod[c, p]; If[m != 0, m, p]], 
  RuntimeAttributes -> {Listable},  
  RuntimeOptions -> "Speed"]; 
  Counts[Roulette[arg]]/n // AbsoluteTiming

gives correct answer.

By including local variable m in the module as in:

  p = 3; n = 1000000.; arg = Table[0, n]; Roulette = 
  Compile[{i}, Module[{m = 1,c = 1}, While[RandomInteger[{1, 6}]
  != 6, c++]; m = Mod[c, p]; If[m != 0, m, p]], 
  RuntimeAttributes -> {Listable}, Parallelization -> True, 
  RuntimeOptions -> "Speed"]; 
  Counts[Roulette[arg]]/n // AbsoluteTiming

we take the correct answer this time, but parallelization still fails.

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  • $\begingroup$ The function is changing a global variable m and using it in the result, so that could be a problem. $\endgroup$
    – Daniel Lichtblau
    Commented Jun 23, 2019 at 15:22
  • $\begingroup$ I have tried initialization {c = 1,m = 1} inside module, no avail. Also, do not forget to use first program with Parallelization -> True, not the second one. $\endgroup$
    – dimachaerus
    Commented Jun 23, 2019 at 17:11
  • $\begingroup$ In V12 on macOS, the first program gives me an error "Instruction 10 in CompiledFunction[...] calls ordinary code that can be evaluated on only one thread at a time." Also, I get some probability that person 0 will be killed. Is that what you mean by it gives nonsense? $\endgroup$
    – MassDefect
    Commented Jun 23, 2019 at 18:52
  • $\begingroup$ Yes, there is no 0 person by definition of: m = Mod[c, p]; If[m != 0, m, p] $\endgroup$
    – dimachaerus
    Commented Jun 23, 2019 at 19:19
  • 1
    $\begingroup$ (1) I cannot get the bad behavior on my office Linux machine. Yet I saw it on my Windows laptop. Very strange. (2) Return Mod[c,p,1] from the Module-- it's faster that way. $\endgroup$
    – Daniel Lichtblau
    Commented Jun 23, 2019 at 21:18

1 Answer 1

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Program needs all variables p, c, m to be local inside the module:

n = 1000000.; arg = Table[0, n]; Roulette = 
Compile[{i}, Module[{p = 3,m = 1,c = 1}, While[RandomInteger[{1, 6}]
!= 6, c++]; m = Mod[c, p]; If[m != 0, m, p]], 
RuntimeAttributes -> {Listable}, Parallelization -> True, 
RuntimeOptions -> "Speed"]; 
Counts[Roulette[arg]]/n // AbsoluteTiming

There is no bug!

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