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# Fibonacci Without Loops or Recursion

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

## Introduction

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.

## 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.

## UPDATE

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.

## Share

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 First Prev Next
 Thoughts PIEBALDconsult8-Sep-13 14:55 PIEBALDconsult 8-Sep-13 14:55
 Re: Thoughts Andrew Rissing10-Sep-13 6:08 Andrew Rissing 10-Sep-13 6:08
 formula's missing part Member 33856988-Sep-13 12:30 Member 3385698 8-Sep-13 12:30
 Re: formula's missing part Andrew Rissing10-Sep-13 6:06 Andrew Rissing 10-Sep-13 6:06
 Re: formula's missing part Yuksel YILDIRIM14-Oct-13 16:56 Yuksel YILDIRIM 14-Oct-13 16:56
 My vote of 2 YvesDaoust17-Dec-12 2:57 YvesDaoust 17-Dec-12 2:57
 Can do better YvesDaoust17-Dec-12 2:51 YvesDaoust 17-Dec-12 2:51
 Re: Can do better Andrew Rissing17-Dec-12 5:48 Andrew Rissing 17-Dec-12 5:48
 Re: Can do better Andrew Rissing17-Dec-12 6:04 Andrew Rissing 17-Dec-12 6:04
 Re: Can do better YvesDaoust17-Dec-12 6:32 YvesDaoust 17-Dec-12 6:32
 Re: Can do better Andrew Rissing17-Dec-12 13:04 Andrew Rissing 17-Dec-12 13:04
 Re: Can do better YvesDaoust17-Dec-12 21:34 YvesDaoust 17-Dec-12 21:34
 Re: Can do better Andrew Rissing18-Dec-12 5:24 Andrew Rissing 18-Dec-12 5:24
 My vote of 5 Manish Choudhary .NET expert14-Dec-12 19:50 Manish Choudhary .NET expert 14-Dec-12 19:50
 This is correct only for n up to 70 Matt T Heffron13-Dec-12 13:12 Matt T Heffron 13-Dec-12 13:12
 Re: This is correct only for n up to 70 Andrew Rissing13-Dec-12 13:45 Andrew Rissing 13-Dec-12 13:45
 Interesting. I tested the values only up to 50, guess I was shooting too low there.I'll double check somethings on the timing, but it looks like you're dead on.I was initially worried that the overuse of Pow/Division/etc. would outweigh the cost of just looping through additions quickly. I guess my fears were valid and should have been checked.I'll let you know otherwise if my timing shows something different.Thanks for the post.
 Re: This is correct only for n up to 70 Andrew Rissing17-Dec-12 13:05 Andrew Rissing 17-Dec-12 13:05
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