#!/usr/bin/perl
use strict;
use warnings;
use bignum;

print "Fibonnaci Fun\n\n";

print "Pick a number that represents which value of the Fibonnaci sequence you want to start with\n";
print "ie: 1 would be 1, and 2 would be 1, and 3 would be 2 and so on.\n"; 
print "Your choice: ";
chomp (my $start = <>);

print "\nNow pick a number to repesent the range you want.\n";
print "If you want to use values 1 through 10 you you need only enter 10,\n";
print "assuming of course you entered 1 above.\n";
print "Your choice: ";
chomp(my $range = <>);
print "\n";

for my $fibNum ($start .. $start + $range){
  my $fibValue1 = fib($fibNum);
  my $fibValue2 = fib($fibNum - 1);
  my $phiApprox = $fibNum <= 1 ? '***' : $fibValue1 / $fibValue2;

  print "$fibValue1 / $fibValue2 = $phiApprox\n";
}


my %cache;

sub fib {
    my ($n) = @_;
    return $n if $n < 2;
    
    --$n;
    return ($cache{$n} ||= fib($n)) + ($cache{$n - 1} ||= fib($n - 1));
}

##</code><code>##

Fibonnaci Fun

Pick a number that represents which value of the Fibonnaci sequence you want to start with
ie: 1 would be 1, and 2 would be 1, and 3 would be 2 and so on.
Your choice: 90

Now pick a number to repesent the range you want.
If you want to use values 1 through 10 you you need only enter 10,
assuming of course you entered 1 above.
Your choice: 10

2880067194370816120 / 1779979416004714189 = 1.618033988749894848204586834365638117579
4660046610375530309 / 2880067194370816120 = 1.618033988749894848204586834365638117774
7540113804746346429 / 4660046610375530309 = 1.6180339887498948482045868343656381177
12200160415121876738 / 7540113804746346429 = 1.618033988749894848204586834365638117728
19740274219868223167 / 12200160415121876738 = 1.618033988749894848204586834365638117717
31940434634990099905 / 19740274219868223167 = 1.618033988749894848204586834365638117721
51680708854858323072 / 31940434634990099905 = 1.61803398874989484820458683436563811772
83621143489848422977 / 51680708854858323072 = 1.61803398874989484820458683436563811772
135301852344706746049 / 83621143489848422977 = 1.61803398874989484820458683436563811772
218922995834555169026 / 135301852344706746049 = 1.61803398874989484820458683436563811772
354224848179261915075 / 218922995834555169026 = 1.61803398874989484820458683436563811772