require "bigdecimal"

testvalues = [[100000000000000.01,           100000000000000.011],
              [100.01,                       100.011],
              [10000000000000.001 / 10000.0, 1000000000.0000001000],
              [0.001,                        0.0010000001],
              [0.000000000000000000000101,   0.0],
              [(2**0.5) * (2**0.5),            2.0],
              [-(2**0.5) * (2**0.5),          -2.0],
              [BigDecimal("3.14159265358979323846"),       3.14159265358979324],
              [Float::NAN, Float::NAN,],
              [Float::INFINITY, Float::INFINITY],
               ]

class  Numeric
  def close_to?(num, tol = Float::EPSILON)
    return true  if self == num
    return false if (self.to_f.nan? or num.to_f.nan?)        # NaN is not even close to itself
    return false if [self, num].count( Float::INFINITY) == 1 # Infinity is only close to itself
    return false if [self, num].count(-Float::INFINITY) == 1
    (self-num).abs <= tol * ([self.abs, num.abs].max)
  end
end

testvalues.each do |a,b|
  puts "#{a} #{a.close_to?(b) ? '≈' : '≉'} #{b}"
end