Kahan sum

kahan.rb

# Reduces numerical error when adding a sequence of floats.
# http://en.wikipedia.org/wiki/Kahan_summation_algorithm
#
# Examples:
#
# Sums all given arguments:
# KahanSum.new([3.14159265358979323846 , 2.71828182845904523536], 1.41421356237309504880)
# => #<KahanSum:0x007fd218984120 @sum=7.274088044421934, @c=2.220446049250313e-16>
#
# Incremental summation:
# sum = KahanSum.new
# sum+3.14159265358979323846
# sum+2.71828182845904523536
# sum+1.41421356237309504880
# => 7.274088044421934
class KahanSum
  def initialize(*args)
    @sum = 0.0
    @c = 0.0
    args.each { |arg| Array(arg).each {|n| self+n } }
  end

  def +(n)
    y = n - @c
    t = @sum + y
    @c = (t - @sum) - y
    @sum = t
  end

  def to_f
    @sum
  end
end