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All digits of Fibonacci number using implicit calculation method

  • To: mathgroup at smc.vnet.net
  • Subject: [mg16736] All digits of Fibonacci number using implicit calculation method
  • From: Alex Vinokur <alexander.vinokur at telrad.co.il>
  • Date: Wed, 24 Mar 1999 02:23:50 -0500
  • Sender: owner-wri-mathgroup at wolfram.com

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Hi,

Here's is function written on C++ language and
based on implicit formula of Fibonacci#n calculation.
//##################################
//######### C++ function ###########
//##################################
#include <string>
#include <math.h>

double Fib (int n)
{
double  R5 = sqrt (5);
double  Phi = (1+R5)/2;
double  Psi = (1-R5)/2;
        return ((pow (Phi, n) - pow (Psi, n))/R5);
}
//##################################



Here are the calculation results.
//##################################
//######### Results ################
//##################################
Fib [0] = 0
Fib [1] = 1
Fib [2] = 1
Fib [3] = 2
Fib [4] = 3
Fib [5] = 5
Fib [6] = 8
Fib [7] = 13
Fib [8] = 21
Fib [9] = 34
Fib [10] = 55
[snip]
Fib [28] = 317811
Fib [29] = 514229
Fib [30] = 832040
Fib [31] = 1.34627e+06
Fib [32] = 2.17831e+06
Fib [33] = 3.52458e+06
[snip]
Fib [1472] = 1.90687e+307
Fib [1473] = 3.08538e+307
Fib [1474] = 4.99225e+307
Fib [1475] = Infinity
Fib [1476] = Infinity
Fib [1477] = Infinity
...
//##################################

What do we have to do to get (using this formula)
        all decimal digits of large Fibonacci number?
How do we have to change this algorithm?

        Thanks in advance,
        Alex


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