[R] Integer bit size and the modulus operator

Duncan Murdoch murdoch at stats.uwo.ca
Mon Jan 30 19:50:01 CET 2006

On 1/30/2006 1:39 PM, Ionut Florescu wrote:
> Thank you for the quick reply, I will look into the R packages.
> For crashing R try this:
> generator.zp=function(x,p)
> {a=1:(p-1); b=x^a%%p;
> if(all(b[1:(p-2)]!=1)&&(b[p-1]==1)){return(x, " Good ")}
> else{return(x, " No Good, try another integer ")}
> }

Thanks, I can reproduce the crash using

for (x in 10:100) generator.zp(x, 41)

I'll see if I can track down what's going wrong.  By the way, you're not 
supposed to use two arguments to return():  that's not supposed to be 
allowed any more.  I'm somewhat surprised you don't get an error from 
it.  But that's not the cause of the crash.

Duncan Murdoch

> This checks if element x is a generator of the group Z_p. If you try 
> this function for p = 41 and x various increasing values eventually it 
> will crash R. That is what I meant by random, at first I started x=2,3 
> so on, when I got to 8, R crashed. Now apparently I can get to 15. When 
> I tried again I got to 20.
> Ionut Florescu
> Duncan Murdoch wrote:
>> On 1/30/2006 11:32 AM, Ionut Florescu wrote:
>>> I am a statistician and I come up to an interesting problem in 
>>> cryptography. I would like to use R since there are some statistical 
>>> procedures that I need to use.
>>> However, I run into a problem when using the modulus operator %%.
>>> I am using R 2.2.1 and when I calculate modulus for large numbers 
>>> (that I need with my problem) R gives me warnings. For instance if 
>>> one does:
>>> a=1:40;
>>> 8^a %% 41
>>> one obtains zeros which is not possible since 8 to any power is not a 
>>> multiple of 41.
>>> In addition when working with numbers larger that this and with the 
>>> mod operator R crashes randomly.
>> Could you keep a record of the random crashes, and see if you can make 
>> any of them repeatable?  R shouldn't crash.  If you can find a 
>> repeatable way to make it crash, then that's a bug that needs to be 
>> fixed.  (If it crashes at random it should still be fixed, but it's so 
>> much harder to fix that it's unlikely to happen unless the cases are 
>> ones that look likely to come up in normal situations.)
>>> I believe this is because R stores large integers as real numbers 
>>> thus there may be lack of accuracy when applying the modulus operator 
>>> and converting back to integers.
>>> So my question is this: Is it possible to increase the size of memory 
>>> used for storing integers? Say from 32 bits to 512 bits (Typical size 
>>> of integers in cryptography).
>> No, but there is at least one contributed package that does multiple 
>> precision integer arithmetic.  I can't remember the name of it right 
>> now, but Google should be able to find it for you...
>> Duncan Murdoch
>>> Thank you, any help would be greatly appreciated.
>>> Ionut Florescu
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