计算第 1 百万个斐波那契数

Question

I am trying to compute the 1 millionth fibonacci number using the Big Int Library since the number is more than 200,000 digits. I can't seem to fix this problem I am having when taking the sqrt or pow, Big Int can't be assigned to pow or sqrt.

BigInteger Phi = (sqrt(5) + 1) / 2;

BigInteger phi = (sqrt(5) - 1) / 2;

BigInteger PhiSquared = pow(Phi, n);
BigInteger phiSquared = pow(phi, n);

Answer 1

If you want to use a library that can handle big integers, the simplest thing is to get the boost library and use the cpp_int type in the multiprecision library.

Since the multiprecision library is header-file only, this would be one of the simplest ones to use right out-of-box with minimal setup.

Here is a simple, straightforward implementation that computes the 1 millionth Fibonacci number without using floating point (which could yield inexact results):

#include <boost/multiprecision/cpp_int.hpp>
#include <iostream>
 
int main() {
    using Int = boost::multiprecision::cpp_int;
    Int n1 = 0, n2 = 1;
    Int n3;
    for (int i = 1; i <= 1000000; ++i)
    {
        n3 = n1 + n2;
        n1 = n2;
        n2 = n3;
    }
    std::cout << n3;
}

This took around 40 seconds to complete on an Intel I7 laptop, using Visual Studio 2019 in release mode.

The resulting number is a 208988 digit number.