#### Fibonacci Large

```/**
* @file
* @brief Computes N^th Fibonacci number given as
* input argument. Uses custom build arbitrary integers library
* to perform additions and other operations.
*
* Took 0.608246 seconds to compute 50,000^th Fibonacci
* number that contains 10450 digits!
*
* \author [Krishna Vedala](https://github.com/kvedala)
* @see fibonacci.cpp, fibonacci_fast.cpp, string_fibonacci.cpp
*/

#include <cinttypes>
#include <ctime>
#include <iostream>

#include "./large_number.h"

/** Compute fibonacci numbers using the relation
* \f[f(n)=f(n-1)+f(n-2)\f]
* and returns the result as a large_number type.
*/
large_number fib(uint64_t n) {
large_number f0(1);
large_number f1(1);

do {
large_number f2 = f1;
f1 += f0;
f0 = f2;
n--;
} while (n > 2);  // since we start from 2

return f1;
}

int main(int argc, char *argv[]) {
uint64_t N;
if (argc == 2) {
N = strtoull(argv[1], NULL, 10);
} else {
std::cout << "Enter N: ";
std::cin >> N;
}

clock_t start_time = std::clock();
large_number result = fib(N);
clock_t end_time = std::clock();
double time_taken = static_cast<double>(end_time - start_time) /
static_cast<double>(CLOCKS_PER_SEC);

std::cout << std::endl
<< N << "^th Fibonacci number: " << result << std::endl
<< "Number of digits: " << result.num_digits() << std::endl
<< "Time taken: " << std::scientific << time_taken << " s"
<< std::endl;

N = 5000;
if (fib(N) ==
large_number(
"387896845438832563370191630832590531208212771464624510616059721489"
"555013904403709701082291646221066947929345285888297381348310200895"
"498294036143015691147893836421656394410691021450563413370655865623"
"825465670071252592990385493381392883637834751890876297071203333705"
"292310769300851809384980180384781399674888176555465378829164426891"
"298038461377896902150229308247566634622492307188332480328037503913"
"035290330450584270114763524227021093463769910400671417488329842289"
"149127310405432875329804427367682297724498774987455569190770388063"
"704683279481135897373999311010621930814901857081539785437919530561"
"751076105307568878376603366735544525884488624161921055345749367589"
"784902798823435102359984466393485325641195222185956306047536464547"
"076033090242080638258492915645287629157575914234380914230291749108"
"898415520985443248659407979357131684169286803954530954538869811466"
"508206686289742063932343848846524098874239587380197699382031717420"
"893226546887936400263079778005875912967138963421425257911687275560"
"0360311370547754724604639987588046985178408674382863125"))
std::cout << "Test for " << N << "^th Fibonacci number passed!"
<< std::endl;
else
std::cerr << "Test for " << N << "^th Fibonacci number failed!"
<< std::endl;

return 0;
}
```