Here are some variations.

  1. To generate fibonacci-numbers sequentially. 
    my $x = 1/sqrt(5); for my $n (0 .. 28) { print int($x + 0.5), " "; $x 
+*= (sqrt(5) + 1)/2; } print "\n";

    [download]
    or 
    my($x, $y) = (1, 0); for my $n (0 .. 28) { print $y, " "; ($x, $y) = (
+$y, $x + $y); } print "\n";

    [download]
  2. To generate the nth fibonacci number directly: 
    my $n = 28; $x = int(((1 + sqrt(5))/2)**$n / sqrt(5) + 0.5); print $x,
+ "\n";

    [download]
    or 
    my $n = 28; my($a, $b, $c, $d, $x, $y) = (0, 1, 1, 1, 1, 0); { 0 != ($
+n & 1) and ($x, $y) = ($a*$x + $b*$y, $c*$x + $d*$y); $n <= 1 and las
+t; $n >>= 1; ($a, $b, $c, $d) = ($a*$a + $b*$c, $a*$b + $b*$d, $c*$a 
++ $d*$c, $c*$b + $d*$d); redo} print $y, "\n";

    [download]
    (Update: I wonder whether I really need all seven variables for this)

    Update: of course not, $b and $c are the same, so you can omit one of them like this: 

    my $n = 28;
my($a, $b, $d, $x, $y) = (0, 1, 1, 1, 0);
{
        0 != ($n & 1) and ($x, $y) = ($a*$x + $b*$y, $b*$x + $d*$y);
        $n <= 1 and last;
        $n >>= 1;
        ($a, $b, $d) = ($a*$a + $b*$b, $a*$b + $b*$d, $b*$b + $d*$d);
redo}
print $y, "\n";

    [download]
    also I've updated the above code to have $n = 28 instead of $n = '$n'

Update 2006 nov 15: another interesting way for sequentially generating the numbers is this (all four are equivalent). 

perl -le'$==1;1while print$==(1+$=+$=*sqrt 5)/2'
perl -le'$==1;1while print$==(1+sqrt 5)*$=/2+.5'
perl -le'$==1;1while print$==$=*1.6180339887+.5'
perl -le'for ($x = 1; $x = int(0.5 + $x * (sqrt(5) + 1)/2); ) { print 
+$x; }'

[download]

See also Re: Fibonacci numbers (again).

In reply to Re: Fibonacci Numbers by ambrus
in thread Fibonacci Numbers by dReKurCe

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