       Re: The most efficient Fibonacci algorithim?

• To: mathgroup at smc.vnet.net
• Subject: [mg23405] Re: The most efficient Fibonacci algorithim?
• From: "Peter Tolksdorf" <Peter.Tolksdorf at gmx.de>
• Date: Sat, 6 May 2000 19:14:14 -0400 (EDT)
• References: <8er92l\$hdq@smc.vnet.net>
• Sender: owner-wri-mathgroup at wolfram.com

```Try http://www.freenet.de/Tolksdorf

<zeno at magicnet.net> schrieb in im Newsbeitrag: 8er92l\$hdq at smc.vnet.net...
> On page 128 of the book "The Mathematica Programmer" by Roman Maeder (the
> Mathematic 2.2 edition) is this Mathematica program to compute Fibonacci
> numbers...
>
> fibj[n_]:=
> Module[{r11=1,r12=0,r22=1,digits=IntegerDigits[n-1,2],i,t},
> Do[If[digits[[i]]==1,
> {r11,r22}={r11(r11+2r12),r12(r11+r22)};
> r12=r11-r22,
> t=r12(r11+r22);
> {r11,r12}={r11(r11+2r12)-t,t};
> r22=r11-r12],
> {i,Length[digits]-1}];
> If[digits[[-1]]==1,
> r11(r11+2r12),
> r11(r11+r22)-(-1)^((n-1)/2)]]
>
> The book says this is the most efficient one of a few mentioned in the
book.
> Does anyone know of any other programs that are faster? This one really
> screams...I am curious if anyone has done anything even better.
>

```

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