From: ptkwt@... (Phil Tomson)
Date: 2005-06-26T07:05:39+09:00
Subject: Re: [ANN] FixedPt-0.0.1

In article <d9kfk2$55j$1@sea.gmane.org>,
Florian Gro�  <florgro@gmail.com> wrote:
>Phil Tomson wrote:
>
>> Constuction with Strings is not currently supported, but that's a 
>> thought.  Practically speaking, I'm not sure how big of a problem this 
>> is, I doubt I'd really need to have a FixedPt number with more 
>> precision than Ruby has.
>> 
>> I did some experimenting in irb to find out where the cutoff is:
>> 
>> irb(main):027:0> x = 9.0000000000001
>> => 9.0000000000001
>> irb(main):028:0> x = 9.00000000000001
>> => 9.00000000000001
>> irb(main):029:0> x = 9.000000000000001
>> => 9.0
>> 
>> It happens at 15 digits to the right of the decimal point.  (When you 
>> go the other way by increasing the size of the number you automatically 
>> convert to a Bignum - however we don't have a 'Smallnum' equivilent when the 
>> numbers get very small.)
>
>BigDecimal would work, but does AFAIK not automatically take care of the 
>precision that would be needed to avoid data loss. Keeping numbers 
>around as Rational and converting to a BigDecimal on output might work 
>in that cases.

I'll look into this.

>
>> That would be about 50 fractional bits in a 
>> binary fixed point number - practically speaking, you usually (where 
>> 'usually' probably covers 99.999% of the cases ) don't need that kind of 
>> precision in a hardware implementation of an algorithm.  
>
>Ah, I'm not sure how frequently such accurate numbers are used (I'm not 
>experienced at hardware design), but it might still be worth 
>considering. After all 1.1 will not be accurately presented (the first 
>error occurs at the 15th digit) either.
>
>> [...]
>> 
>> I implemented a model of a Support Vector Machine (kind of like a 
>> Perceptron, a type of artificial neuron) using FixedPt and an exp(-x) 
>> lookup table and came up with the following results:
>> 
>> 1) I needed 9 fractional bits at a minimum.
>> 2) The value of x for which exp(-x) = 0.0 was -12.25.
>> 3) The number of entries in the exp(-x) lookup table was 128 (7 bits of 
>> address) which was surprisingly small.
>
>Thank you for the detailed description of the process where this library 
>would be involved. It was very interesting for me -- always nice to see 
>where Ruby can be used in the real world where you might not have 
>expected it to be at first. Perhaps this is an interesting enough use 
>case for it to be added to the RealWorldRuby page of the rubygarden.org 
>Wiki? If you can name the company you are doing this for then even 
>better. :)

It was for a University project, so I'm not sure it qualifies as a 
'RealWorld' application ;-)  Actually, I spent last winter 
working on this project as a visiting researcher at the University of 
Genova, Italy.

>
>Anyway, I think you are likely right in that this will rarely be much of 
>a problem -- but having the possibility in the next release (there will 
>be one anyway, won't there? ;)) might still be a good thing -- even if 
>just getting users in the habit of being careful with Floats. Yours will 
>probably know anyway, but allowing for such a style consistently through 
>all libraries should keep confusion low.
>
>

Hopefully there will be other releases: I certainly hope to implement 
more methods in C to speed things up.   I'll keep your suggestion in 
mind.  Thanks.


Phil