What is the fastest way to split a number into parts?

Question

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?

You're aware of Mod[]'s partner Quotient[], aren't you? For that matter, have you seen QuotientRemainder[]? — J. M.'s missing motivation, Nov 24 '12 at 10:32

Mohsen Afshin · Answer 1 · 2012-11-24T13:21:53.917

2

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.

edited Nov 24 '12 at 13:21

answered Nov 24 '12 at 10:56

Mohsen Afshin

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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]. – J. M.'s missing motivation Nov 24 '12 at 12:27
Quotient[] and QuotientRemainder[] are two different functions, see... – J. M.'s missing motivation Nov 24 '12 at 13:11
Oh sorry, I mistyped it – Mohsen Afshin Nov 24 '12 at 13:22

What is the fastest way to split a number into parts?

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