Fast Fibonacci method

ruby-talk
1

The fastest pure-Ruby Fibonacci method I have been able to come up with is a
copy of the GMP algorithm described at
http://www.swox.com/gmp/manual/Fibonacci-Numbers-Algorithm.html

Is there a Ruby implementation that gets better time results for the
millionth Fibonacci number (timing code included at bottom) ?

class Integer
  FibonacciCache = Hash.new do |hash, key|
    subkey = key.div(2)
    case key.modulo(4)
      when 1
        hash[key] = (2*hash[subkey] + hash[subkey - 1])*(2*hash[subkey] -
hash[subkey - 1]) + 2
      when 3
        hash[key] = (2*hash[subkey] + hash[subkey - 1])*(2*hash[subkey] -
hash[subkey - 1]) - 2
      else
        hash[key] = hash[subkey] * (hash[subkey] + 2*hash[subkey - 1])
    end
  end
  FibonacciCache[0] = 0
  FibonacciCache[1] = 1

  def fib
    return FibonacciCache[self]
  end

  def fib_uncached
    return FibonacciCache.dup[self]
  end
end

start_time = Time.now
1_000_000.fib
p Time.now - start_time
puts "Doesn't work !" unless (1..10).map { |i| i.fib } == [1, 1, 2, 3, 5, 8,
13, 21, 34, 55]

2

A slightly faster method :

class Integer
  FibonacciCache = Hash.new do |hash, key|
    if hash.has_key?(key - 1) and hash.has_key?(key - 2)
      hash[key] = hash[key - 1] + hash[key - 2]
    elsif hash.has_key?(key + 1) and hash.has_key?(key + 2)
      hash[key] = hash[key + 2] - hash[key + 1]
    else
      subkey = key.div(2)
      case key.modulo(4)
        when 1
          hash[key] = (2*hash[subkey] + hash[subkey - 1])*(2*hash[subkey] -
hash[subkey - 1]) + 2
        when 3
          hash[key] = (2*hash[subkey] + hash[subkey - 1])*(2*hash[subkey] -
hash[subkey - 1]) - 2
        else
          hash[key] = hash[subkey] * (hash[subkey] + 2*hash[subkey - 1])
      end
    end
  end
  FibonacciCache[0] = 0
  FibonacciCache[1] = 1

  def fib
    return FibonacciCache[self]
  end

  def fib_uncached
    return FibonacciCache.dup[self]
  end
end

start_time = Time.now
1_000_000.fib
p Time.now - start_time
puts "Doesn't work !" unless (1..10).map { |i| i.fib } == [1, 1, 2, 3, 5, 8,
13, 21, 34, 55]

3

Other suggesgtions (untested, i.e. unmeasured)

- use shift operator instead of *2 and /2

- put your 4 alternatives (i.e. key % 4) as lambdas into another hash
and then do
   algo[key % 4][subkey]

Kind regards

robert

4

Thanks for your suggestions. I tried both, but could only get the same
speed.

···

On 27/05/06, Robert Klemme <shortcutter@googlemail.com> wrote:

Other suggesgtions (untested, i.e. unmeasured)

- use shift operator instead of *2 and /2

- put your 4 alternatives (i.e. key % 4) as lambdas into another hash
and then do
   algo[key % 4][subkey]

Kind regards

robert