From: Yohanes Santoso <ysantoso@...>
Date: 2002-12-28T18:08:55+09:00
Subject: Re: 1210 / 100 = 12? what?

Tom Sawyer <transami@transami.net> writes:

> mathmatical computing that are 100% accurate. granted they are
> comupationally intense and must indeed keep 2/3 as 2/3 and never
> approximate to .6666. and at some points require a set degree of
> accuracy to return, least the

As an aside note, the result of a floating point operation must be
treated carefully, since the underlying representation of the real
number cannot fully represent certain numbers.

For example:

> 2.4/0.2 == 12
false

How come? Because 2.4 and 0.2 are some of the numbers that cannot be
represented fully in IEEE floating point format:

> "%.20f" % 2.4
"2.39999999999999991118"
> "%.20f" % 0.2
"0.20000000000000001110"

Thus, in performing a floating point operation, the only guarantee
that you will have is that the result will be within a certain range
(tolerance) from the actual, correct result.

If you do any meaningful floating point operation, it will be useful
if you have something like this:

class Float
  @@tolerance = 1E-6  #adjust this as needed
  def around?(other)
    other = other.to_f unless other.is_a? Float
    (other-self).abs < @@tolerance
  end
end

> (2.4/0.2).around? 12
true

Which is as we expected.

YS.