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Re: Not sure this limit is right...

  • To: mathgroup at smc.vnet.net
  • Subject: [mg131126] Re: Not sure this limit is right...
  • From: Bill Rowe <readnews at sbcglobal.net>
  • Date: Thu, 13 Jun 2013 02:37:55 -0400 (EDT)
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On 6/12/13 at 5:38 AM, readnews at sbcglobal.net (Bill Rowe) wrote:

>On 6/11/13 at 2:32 AM, bernardsarman at gmail.com (Bernard Sarman)
>wrote:
>
>>Yes, that's what I meant.
>>
>>I have another, related question: 9^-9^9 seems to explode on my
>>machine. The memory jumps to over 1 GB, and I have to abort the
>>evaluation. I have no idea why Mathematica would require so much
>>memory to evaluate this expression.

>9^9 evaluates to 387420489. That is you are computing an *exact*
>value with a bit less than 400 million digits. You should expect
>each digit to take require at least 4 bytes (assumes 32 bit
>integers). So the number you are computing requires around 1 GB to

The computation above is overly simplistic and not correct.
Optimal storage of the numerator would require

In[5]:= 9^9 Log[8, 9] // N

Out[5]= 4.093646313840355*^8

bytes. But this has to be a low estimate of the memory required.
That is I am sure the method Mathematica uses to store large
integers that cannot be represented in native machine format
will have some overhead, possibly storing the pieces as an
array. So, it should not be all that surprising the total memory
required starts to look like 1GB or possibly more.




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