0_rational_intermediate.rb

#!/usr/bin/env ruby
def lesseq(a, b, c, d)
  return a * d <= c * b
end

lower_numer = 2
lower_denom = 1
upper_numer = 3
upper_denom = 1

step = 0

loop do
  left_numer = 0
  left_denom = 1
  right_numer = 1
  right_denom = 0

  loop do
    mediant_numer = left_numer + right_numer
    mediant_denom = left_denom + right_denom
    if lesseq(mediant_numer, mediant_denom, lower_numer, lower_denom)
      left_numer = mediant_numer
      left_denom = mediant_denom
    elsif lesseq(upper_numer, upper_denom, mediant_numer, mediant_denom)
      right_numer = mediant_numer
      right_denom = mediant_denom
    else
      puts "#{step} #{mediant_numer}/#{mediant_denom} #{mediant_numer.to_f/mediant_denom.to_f}"

      # Alternate between inserting above/below
      if step % 2 == 0
        lower_numer = mediant_numer
        lower_denom = mediant_denom
      else
        upper_numer = mediant_numer
        upper_denom = mediant_denom
      end
      step += 1
      break
    end

    # Stop if numerator/denominator exceeds 32 bits
    exit if Math.log2(mediant_numer) >= 32
    exit if Math.log2(mediant_denom) >= 32
  end
end

1_output.txt

0 5/2 2.5
1 8/3 2.6666666666666665
2 13/5 2.6
3 21/8 2.625
4 34/13 2.6153846153846154
5 55/21 2.619047619047619
6 89/34 2.6176470588235294
7 144/55 2.618181818181818
8 233/89 2.6179775280898876
9 377/144 2.6180555555555554
10 610/233 2.6180257510729614
11 987/377 2.618037135278515
12 1597/610 2.6180327868852458
13 2584/987 2.6180344478216817
14 4181/1597 2.618033813400125
15 6765/2584 2.6180340557275543
16 10946/4181 2.6180339631667064
17 17711/6765 2.6180339985218035
18 28657/10946 2.618033985017358
19 46368/17711 2.618033990175597
20 75025/28657 2.618033988205325
21 121393/46368 2.618033988957902
22 196418/75025 2.6180339886704433
23 317811/121393 2.6180339887802426
24 514229/196418 2.618033988738303
25 832040/317811 2.6180339887543225
26 1346269/514229 2.618033988748204
27 2178309/832040 2.618033988750541
28 3524578/1346269 2.618033988749648
29 5702887/2178309 2.618033988749989
30 9227465/3524578 2.618033988749859
31 14930352/5702887 2.6180339887499087
32 24157817/9227465 2.6180339887498896
33 39088169/14930352 2.6180339887498967
34 63245986/24157817 2.618033988749894
35 102334155/39088169 2.6180339887498953
36 165580141/63245986 2.618033988749895
37 267914296/102334155 2.618033988749895
38 433494437/165580141 2.618033988749895
39 701408733/267914296 2.618033988749895
40 1134903170/433494437 2.618033988749895
41 1836311903/701408733 2.618033988749895
42 2971215073/1134903170 2.618033988749895
43 4807526976/1836311903 2.618033988749895