Fibonacci and decimal representation bounds

[std10093]

No, I was reffering to the GMP, but yes, I can say for sure that this is a buggy code of mine. Couldn't get a really good approach and the last thing I tried was something like this:

double test_dig(double a) {// LOG (Phi^1000/√5)
  double phi = 1.618033;
  double sqrt_5 = 2.2360679775;
  //return (a*phi - (0.34948500216));
  std::cout << pow(phi, a) << std::endl;
  return log10(pow(phi, a)/sqrt_5);
}

int main() {
        double aa = 1000;
        
        std::cout << "1 = " << test_dig(aa) << std::endl;
        std::cout <<"2 = " << test_dig(2) << std::endl;
        std::cout <<"3 = " << test_dig(3) << std::endl;
        std::cout <<"5 = " << test_dig(5) << std::endl;
        std::cout <<"8 = " << test_dig(8) << std::endl;
        std::cout <<"13 = " << test_dig(13) << std::endl;
        aa = 21;
        std::cout << aa << " = " << test_dig(aa) << std::endl;
        aa = 34;
        return 0;
}

However, I did face the same fact as anduril:
""Tuning" it to be more accurate would be fun if I had the time, but probably also goes beyond my current math skills (which have degraded significantly since I finished school)."

[brewbuck]

Well, the Fibonacci sequence grows polynomially (specifically, quadratically), therefore the number of digits is going to be proportional to log(k). I am too lazy to put tighter bounds than that...

[std10093]

Well, the Fibonacci sequence grows polynomially (specifically, quadratically), therefore the number of digits is going to be proportional to log(k). I am too lazy to put tighter bounds than that...

The link of Epy provides a better-ready one, based on this thought and mine (the relation with phi)

[Epy]

Well, the Fibonacci sequence grows polynomially (specifically, quadratically), therefore the number of digits is going to be proportional to log(k). I am too lazy to put tighter bounds than that...

It grows exponentially and so the digits are proportional to k.

[phantomotap]

It grows exponentially and so the digits are proportional to k.

O_o

The growth "trends" but is never constant.

The secondary "term"--not mathematics guy--is a constant `log(φ)'.

The tertiary "term" is also a constant `log(5)/2'.

As it grows, the measure is more "geometric" with "n".

Soma

[brewbuck]

It grows exponentially and so the digits are proportional to k.

You're right. That wrong piece of information has been in my head for a very long time...

[phantomotap]

O_o

So this latest post shows up and I spend ten minutes trying to figure out how the it could have actual exponential growth.

*derp*

I got muddled up in thinking about `floor(log10(fib(n)))'.

Soma