I browsed old threads and found this. Choosing better algorithm for calculating Fibonacci numbers can make a lot bigger difference than choosing better optimizing compiler.

Here is an example using 8th programming language that calculates Fibonacci(4784969) using fast doubling with result of million digits. Luckily 8th can calculate using big numbers with ease…

```
\
\ Fibonacci with million digits
\
: bits? \ n -- nbits-1
n:ln 2 n:ln n:/ n:int ;
: fibo-loop
-rot 2dup 2 n:*
over n:- n:* -rot
n:sqr swap n:sqr n:+
rot r@ swap n:shr 1 n:band if
dup rot n:+
then ;
: fibo \ n -- fibo(n)
>r F0 F1
' fibo-loop 1 r@ bits? loop-
r> 1 n:band if
n:sqr swap n:sqr n:+
else
2 n:* over n:- n:*
then ;
: app:main
1m n#
d:msec
4784969 fibo
d:msec rot n:- swap
"%.f" strfmt
s:len "digits: %d\n" s:strfmt .
dup 40 s:lsub "%s first 40 digits.\n" s:strfmt .
40 s:rsub "%s last 40 digits.\n" s:strfmt .
"Took: %d msecs\n" s:strfmt . ;
```

What about speed? It’s not bad:

```
C:\temp>8th fibo.8th
digits: 1000000
1072739564180047722936481359622500432190 first 40 digits.
3407167474856539211500699706378405156269 last 40 digits.
Took: 107 msecs
```