Newton Fibonacci

calc_fiboncci.rb

require 'benchmark'

def is_fibonacci?(i)
  a,b=0,1
    until b >= i
        a,b=b,a+b
        return true if b == i
    end
end

puts Benchmark.measure {is_fibonacci?(28657)}
puts Benchmark.measure {is_fibonacci?(638817435613190341905763972389505493)}


#Results :
# 0.000000   0.000000   0.000000 (  0.000012)
# 0.000000   0.000000   0.000000 (  0.000085)

newton_fibonacci.rb

require 'benchmark'

def is_fibonacci?(i)
  x, x1 = 5 * (i * i) + 4, 5 * (i * i) - 4
  y, y1 = (newton_root(5 * (i * i) + 4)).to_i, (newton_root(5 * (i * i) - 4)).to_i 
  (y**2) == x || (y1**2) == x1 ? true : false
end

def newton_root(n)
  guess1 = (Math.sqrt(n)).to_i
while n > 0
  guess2 = (n/guess1 + guess1)/2
  return guess2 if guess1 - guess2 < 0.5
  guess1 = guess2
end
  return guess2
end

puts Benchmark.measure {is_fibonacci?(28657)}
puts Benchmark.measure {is_fibonacci?(638817435613190341905763972389505493)}

# Results : 
# 0.000000   0.000000   0.000000 (  0.000032)
# 0.000000   0.000000   0.000000 (  0.000057)