Calculating large power of a number

Question

#include<iostream>
#include<cstdio>
#define M 1000000007
using namespace std;

long long int power(int a,int b)
{
    if(b==0)
        return 1;
    else if(b==1)
        return a;
    else if(b%2==0)
        return power((a*a)%M,b/2);
    else
        return (power((a*a)%M,b/2)*a)%M;
}

In this function when I pass a=2, b>31, it always returns 0.for b=31 i got 147483634.can you tell where the problem is?

or can you tell another method for calculating large powers of a number.

Answer 1

In (a*a)%M, a*a probably overflows before computing the remainder. And starting with 2, the overflow producing 0 doesn't surprise me. You need to work with a type able to represent (M-1)*(M-1), i.e. 1000000012000000036 while int is commonly limited to 2147483647. long long (standard in C since 99 and C++ since 11, common extension elsewhere) is guaranteed to work.

Answer 2

Under <cmath> there's pow(x,y) in which x is the base and y is the exponent. x^y.

Reference here

Answer 3

When a is an int, a*a uses int-sized arithmetic. Try a*(long long)a instead, to use wider arithmetic that won't overflow.