Float approximations in ruby

float_approximative_equality_key.rb

class Float
  ExponentBits                  = 11 # 11 bits for exponent
  SignificandBits               = 52 # 52 bits for significand
  ApproximativeEqualityDefault  = 37 # precise to about 5 decimal places, which should be good for anything non-scientific
  ApproximativeMaxExponent      = 1<<ExponentBits
  ApproximativeMaxSignificand   = 1<<SignificandBits
  ApproximativeMask1            = (1<<11)-1
  ApproximativeMask2            = (1<<20)-1
  ApproximativeMask3            = (1<<32)-1

  def components
    a,b = *[self].pack("G").unpack("NN") # sadly there's no unpack unsigned 64bit int in network order
    [a[31], (a >> 20) &  ApproximativeMask1, ((a & ApproximativeMask2) << 32) | b] # [bit 0, bits 1-11, bits 12-63]
  end

  def approximative_equality_key(e=ApproximativeEqualityDefault)
    raise ArgumentError, "e must be a positive integer between 1 and 51" unless e.is_a?(Integer) && e.between?(1,51)
    return self if nan? || infinite?

    sign, exponent, significand = *components
    factor        = 1<<e
    significand2  = significand.fdiv(factor).round*factor
    if significand2 >= ApproximativeMaxSignificand then
      significand2  = 0
      exponent     += 1
      if exponent >= ApproximativeMaxExponent then
        return Float::MAX # ugly, happy about nice refactors, bring it on :)
      end
    end
    integers = [(sign<<31) | (exponent<<20) | ((significand2 >> 32) & ApproximativeMask2), (significand2 & ApproximativeMask3)]
    binary   = integers.pack("NN")

    binary.unpack("G").first
  end

  def close?(other, e=ApproximativeEqualityDefault)
    approximative_equality_key(e) == other.to_f.approximative_equality_key(e)
  end
end

## Example:
if __FILE__ == $0 then
  p [1.0, 1.0+Float::EPSILON, 2.0-Float::EPSILON, 2.0, 4.0].map { |v| v.approximative_equality_key }.uniq
  # => [1.0, 2.0, 4.0]
end