1 left shift by n

Question

in this equation

#define mod 1000000007
int n;
int num = ((1<<n)%mod)+2;

I have to left shift 1 by any value of n and then perform mod operation to contain the result within the range of int. But the 1<<n is not showing correct value for bigger values of n such as 1000 or 10000. How to do it ?

It does not give correct output because after 31 shifts overflow happens — Ashwani, Oct 08 '14 at 12:06
Related (possibly even a duplicate): http://stackoverflow.com/questions/11289495/what-is-the-fastest-way-to-compute-large-power-of-2-modulo-a-number — Paul R, Oct 08 '14 at 12:08

score 2 · Answer 1 · answered Oct 08 '14 at 11:59

The maximum you can left-shift 1 by is CHAR_BIT * sizeof(int) - 2. Any larger amount causes undefined behaviour.

If you want to work with numbers like 2¹⁰⁰⁰⁰ you are going to have to use a big integer library (or write your own) , there are no built-in data types that can handle that sort of number accurately.

Another option is to use a smarter algorithm for modular exponentiation.

1 left shift by n

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