From: "trans.  (T. Onoma)" <transami@...>
Date: 2004-10-28T06:34:28+09:00
Subject: Re: Rounding error, (100.0 * 9.95).to_i == 994

On Wednesday 27 October 2004 04:54 pm, Hal Fulton wrote:
| trans. (T. Onoma) wrote:
| > On Wednesday 27 October 2004 04:36 pm, Hal Fulton wrote:
| > | Jason DiCioccio wrote:
| > | > I'm confused now..  100.0 * 9.95 is clearly 995.  So what exactly is
| > | > the issue with floating point numbers is making this come out to
| > | > 994.999999999983 (or wahtever ;))?  If every language is plagued by
| > | > this problem, then I'd be curious to know the history behind it..
| > | >
| > | :) It's not history, it's math.
| > |
| > | Here's the short explanation.
| > |
| > | Remember repeating decimals, which you learned about in elementary
| > | school? For example, 1/3 = 0.33333... can't be expressed in a finite
| > | number of digits.
| >
| > Not exactly, '1/3' is finite. Rational numbers can be expressed.
| > Irrationals cannot. But current standards do not attempt to deal with
| > repeating decimals, even though they could. The reason for this seems to
| > be a matter of history related to an ability to test inequalities
| > quickly.
|
| Expressed as a single number in either base 10 or 2, 0.333... requires an
| infinite number of digits (which is all I said).
|
| Knowing that it is rational, you could separately store the two numbers
| expressing that ratio. But that is completely different from traditional
| floating-point storage, and the simple traditional methods of (e.g.)
| addition and subtraction would not work.
|
| > IEEE754 is now 20 years old, and is showing its age. I have actually been
| > thinking of working on a improved version myself. But there's many
| > details to deal with, so who knows... maybe.
|
| Good idea, go for it.

Well, some group in San Fran is busy screwing it up (IEEE-754r) and have been 
doing so since 2000 with plans to complete the screw-up in Decemeber of 2005. 
I shouldn't be so harsh. But from reading it over it becomes clear that they 
are simply cowing to current systems, rather then setting a high-mark 
standard. Plan example:

  "Decimal arithmetic, compatible with that used in Java, C#, PL/I, COBOL, 
REXX, etc.,"

I thought languages were built to meet standards, not the other way around. 
BTW: They've added a new decimal specification and compressed decimal format.

T.