Binet's Formula and Fibonacci Numbers

binet.rb

#!/usr/bin/env ruby

=begin
Ref. Python implementation from this answer on StackOverflow:
http://stackoverflow.com/a/7843192/195964
=end

include Math

=begin
Phi, as defined by Binet's formula:
http://en.wikipedia.org/wiki/Jacques_Philippe_Marie_Binet
=end
PHI = ( 1 + 5 ** 0.5 ) / 2

=begin
Yields first n Fibonacci numbers.
Only yields correct result for n < 70, due to floating-point rounding errors.
=end
def fib( n )
  ( ( PHI ** n - ( 1 - PHI ) ** n ) / 5 ** 0.5 ).round
end

=begin
Rounding eliminates error introduced by modification to Binet's formula.
Does not verify that number given actually is a Fibonacci number.
Can be used to find Fibonacci number closest to a given number.
=end
def fib_inverse( n )
  n < 2 ? n : ( log( n * 5 ** 0.5 ) / log( PHI ) ).round
end

(1..10).each do |n|
  puts "#{n}: #{fib(n)} - #{fib_inverse(n)}"
end