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Fibonacci Without Loops or Recursion

, 17 Dec 2012 CPOL 10.4K 8
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A method for calculating a Fibonacci number without using loops or recursion.


While reading one of our Insider News posts which linked to Evan Miller's site,  he mentioned a mathematical means of producing a Fibonacci number without using loops or recursion.   I decided to post the C# version of it here, but in no way do I claim credit to creating this.   I thought it was interesting enough to share for those who might not read the Insider News articles.  

You can read more about this closed-form solution on wiki.

The Code

public static long Fibonacci(long n)
    return (long)Math.Round(0.44721359549995682d * Math.Pow(1.6180339887498949d, n));

NOTE: Due to limits of precision, the preceding formula is only accurate up to n = 77. 


Based on YvesDaoust's recommendation, I've updated the formula to use a simpler version of the closed form solution (also found on Wiki), as it proves to be faster and more compact.

Furthermore, I've adjusted the constants slightly to improve the function's accuracy.


This article, along with any associated source code and files, is licensed under The Code Project Open License (CPOL)


About the Author

Andrew Rissing
Software Developer (Senior)
United States United States
Since I've begun my profession as a software developer, I've learned one important fact - change is inevitable. Requirements change, code changes, and life changes.

So..If you're not moving forward, you're moving backwards.

Comments and Discussions

GeneralMy vote of 5 Pin
Manish Choudhary .NET expert14-Dec-12 19:50
memberManish Choudhary .NET expert14-Dec-12 19:50 
BugThis is correct only for n up to 70 Pin
Matt T Heffron13-Dec-12 13:12
memberMatt T Heffron13-Dec-12 13:12 
GeneralRe: This is correct only for n up to 70 Pin
Andrew Rissing13-Dec-12 13:45
memberAndrew Rissing13-Dec-12 13:45 
GeneralRe: This is correct only for n up to 70 Pin
Andrew Rissing17-Dec-12 13:05
memberAndrew Rissing17-Dec-12 13:05 
Btw, with the recent changes, I've improved the accuracy (up to n = 77) and the performance a bit. Feel free to try it out.

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