From: Eleanor McHugh <eleanor@...>
Date: 2009-11-16T11:22:47+09:00
Subject: Re: Trajectories

On 16 Nov 2009, at 01:12, Todd Benson wrote:
> On Sun, Nov 15, 2009 at 5:32 PM, Eleanor McHugh
>> The physical limitations imposed on arbitrary-precision decimal  
>> computation
>> by binary representation are something you should know *before*  
>> arguing that
>> one representation is better than another.
>
> I think Marnen originally was suggesting that the imprecisions will
> stack, like an arrow at a target going more and more off course during
> its flight, of course depending on the application.  For some apps,
> it's totally reasonable to see something go chaotic because of these
> things.

This isn't an issue of chaotic behaviour (that has a very fixed  
meaning mathematically) but of unnoticeable error. The difference  
between 1e10-13 and 2e10-13 matters a lot when working on a system  
which needs to be accurate to a resolution of 1e10-14 but not when  
working to a resolution of 1e10-4. The additional nine decimal places  
tell us nothing meaningful in this latter case as we'll still end up  
rounding the result to zero.

> For a short and unimportant game I'm playing, I wouldn't be upset.
> But, for a game that takes 10's of hours and have it ride my butt
> later at a crucial moment, I might just call that a bug.

That's not a bug but a fundamental outcome of the nature of binary  
coded non-integral numbers. Many rational non-integral numbers cannot  
be expressed accurately in binary representations, whilst binary coded  
decimal brings a whole host of other problems: lower information  
density, higher memory usage, and heavier processing load. BCD also  
does nothing to resolve the problem of how to represent irrational  
numbers such as π.

> Does the imprecision in the calculation stack in ballistic calcs?  A
> virtual magic bullet as it were?  I'm not sure, but I'm guessing it
> doesn't to great effect.


The imprecision can indeed stack for complex ballistics systems,  
depending on the complexity of the forces involved. However to the  
extent of the precision chosen for performing these calculations the  
resultant inaccuracy is irrelevant.

http://en.wikipedia.org/wiki/Accuracy_and_precision explains all of  
this in reasonable detail.


Ellie

Eleanor McHugh
Games With Brains
http://slides.games-with-brains.net
----
raise ArgumentError unless @reality.responds_to? :reason