June 2018 Update

Task/Bernoulli-numbers/Crystal/bernoulli-numbers.crystal

@@ -1,62 +1,27 @@
-# Taken from the 'Ada 99' project, https://marquisdegeek.com/code_ada99
+require "big"
 
-class Fraction
-  def initialize(n : Int64, d : Int64)
-    @numerator = n
-    @denominator = d
+class Bernoulli
+  include Iterator(Tuple(Int32, BigRational))
+
+  def initialize
+    @a = [] of BigRational
+    @m = 0
   end
 
-  def numerator
-    @numerator
-  end
-
-  def denominator
-    @denominator
-  end
-
-  def subtract(rhs_fraction)
-    rhs_numerator = rhs_fraction.numerator * @denominator
-    rhs_denominator = rhs_fraction.denominator * @denominator
-    @numerator *= rhs_fraction.denominator
-    @denominator *= rhs_fraction.denominator
-    @numerator -= rhs_numerator
-    self.reduce
-  end
-
-  def multiply(value)
-    @numerator *= value
-  end
-
-  def reduce
-    gcd = gcd(@numerator, @denominator)
-    @numerator /= gcd
-    @denominator /= gcd
-  end
-
-  def to_s
-    @numerator == 0 ? 0 : @numerator.to_s + '/' + @denominator.to_s
+  def next
+    @a << BigRational.new(1, @m+1)
+    @m.downto(1) { |j| @a[j-1] = j*(@a[j-1] - @a[j]) }
+    v = @m.odd? && @m != 1 ? BigRational.new(0, 1) : @a.first
+    return {@m, v}
+  ensure
+    @m += 1
   end
 end
 
-def gcd(a, b)
-  # we need b>0 because b on its own isn't considered true
-  b > 0 ? gcd(b, a % b) : a
-end
+b = Bernoulli.new
+bn = b.first(61).to_a
 
-def calculate_bernoulli(bern)
-  row = [] of Fraction
-  0_i64.step(bern) do |m|
-    row << Fraction.new(1_i64, m + 1)
-    m.step(1, -1) do |j|
-      row[j - 1].subtract(row[j])
-      row[j - 1].multiply(j)
-      row[j - 1].reduce
-    end
-  end
-
-  row[0]
-end
-
-1_i64.step(30_i64) do |bern|
-  puts "#{bern} : #{calculate_bernoulli(bern).to_s}"
+max_width = bn.map { |_, v| v.numerator.to_s.size }.max
+bn.reject { |i, v| v.zero? }.each do |i, v|
+  puts "B(%2i) = %*i/%i" % [i, max_width, v.numerator, v.denominator]
 end