From: David Masover <ninja@...>
Date: 2009-11-22T16:14:28+09:00
Subject: Re: really crazy about this (do/while)

On Saturday 21 November 2009 09:21:59 pm Florian Frank wrote:
> Welcome to the wonderful world of floating point numbers:
>  >> 98.4 + 0.1 + 0.1 < 98.6
> 
>  # => false
> 
>  >> 98.3 + 0.1 + 0.1 + 0.1 < 98.6
> 
>  # => true

If you want accuracy, and don't care about performance, you could always use 
rationals (fractions):

>> Rational(983,10) + Rational(1,10) + Rational(1,10) + Rational(1,10) < 
Rational(986,10)
=> false

Of course, beware of trying to convert from floats to rationals:

>> Rational(98.3)
=> (6917247552664371/70368744177664)

If you look carefully:

>> Rational(98.3).denominator == 2**46
=> true

That also explains why floats behave strangely in general, for the newbies out 
there. When we see 98.3, we see 98 and 3/10ths. But the computer doesn't use 
10ths any more than it uses 10s, 100s, etc. It uses binary, powers of two. So 
it converts those 3/10ths to some fraction of a power of two.

Unless, of course, you're on a mainframe. Then you can do packed decimal 
arithmetic... But it'll be slower and perversely hard to work with for other 
reasons.

So my compromise is, when I want to work with some fraction of a number, and I 
want it to be as precise as possible (with no regard for performance), I make 
it a Rational as long as I can get away with. I can always call to_f on the 
end result.

I might be Doing It Wrong, though. Maybe BigDecimal is the way to go?