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I have very large numbers (million digits).

number = A*10^partlen + B

As of now, I split the numbers by this way:

 TotalLen = IntegerLength[a]; 
 partlen = IntegerPart[TotalLen/2];
 Print[First[Timing[A = IntegerPart[number/(10^partlen )]]]];
 Print[First[Timing[B = Mod[number, 10^partlen ]]]]

And the timings for a 6 million digits number are:

4.703

0.36

Converting the number to strings and rebuilding the parts is even slower than this.

Is there any faster way?

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    $\begingroup$ You're aware of Mod[]'s partner Quotient[], aren't you? For that matter, have you seen QuotientRemainder[]? $\endgroup$
    – J. M.'s eventual burnout ♦
    Nov 24, 2012 at 10:32

1 Answer 1

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Per J.M. suggestion, I've got a ten fold increase in speed:

TotalLen = IntegerLength[a]; 

RightLen = Quotient[TotalLen, 2]; 

Print[First[Timing[{A, B} = QuotientRemainder[a, (10^RightLen)]]]];

Timing:

0.344

Although the time decreased but it is yet so large just for pre-processing.

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  • $\begingroup$ You didn't totally take my suggestion. Try RightLen = Quotient[TotalLen, 2]; Also, Mathematica is perfectly capable of parallel assignment: {A, B} = QuotientRemainder[number, 10^RightLen]. $\endgroup$
    – J. M.'s eventual burnout ♦
    Nov 24, 2012 at 12:27
  • $\begingroup$ Quotient[] and QuotientRemainder[] are two different functions, see... $\endgroup$
    – J. M.'s eventual burnout ♦
    Nov 24, 2012 at 13:11
  • $\begingroup$ Oh sorry, I mistyped it $\endgroup$
    – Mohsen Afshin
    Nov 24, 2012 at 13:22

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