another newbie question

Hello guys... I need to finish my genethic algorithm today and i found
some little problem, I'm doing:

(+ (* 2 0.0001) 4.1)

my interpreter prints this:
4.1001997

Why??? shouldn't it be just 4.1002 ? 
if If substitute 4.1 for 3.1 it prints the correct result, but for
4.1, 5.1, 6.1 it screws it up.

I'm desperate, i need to finish this quick :(

Re: another newbie question

On Jul 22, 2005, at 8:56 AM, Carlos Bruguera wrote:

> Hello guys... I need to finish my genethic algorithm today and i found
> some little problem, I'm doing:
>
> (+ (* 2 0.0001) 4.1)
>
> my interpreter prints this:
> 4.1001997
>
> Why??? shouldn't it be just 4.1002 ?

The accuracy of floating point numbers is limited. For example, when  
you evaluate 0.0001 you get a number which is close to 0.0001, but  
not exacly 0.0001.

Google for

     floating point computation

or

     what every computer scientist should know about floating point

Re: another newbie question

Carlos Bruguera <cbruguera@gmail.com> writes:

> Hello guys... I need to finish my genethic algorithm today and i found
> some little problem, I'm doing:
>
> (+ (* 2 0.0001) 4.1)
>
> my interpreter prints this:
> 4.1001997
>
> Why??? shouldn't it be just 4.1002 ? 

Read Goldberg's 'What every computer scientist should know about
floating point'. If you really need the exact results, use rationals.

-- 
"a totalitarian ideology that hates freedom, rejects tolerance, 
and despises all dissent."    --- Bush describing his religious 
constituency^W^W^Wthe Iraqi resistance

Re: another newbie question

On Jul 22, 2005, at 2:56 AM, Carlos Bruguera wrote:

> Hello guys... I need to finish my genethic algorithm today and i found
> some little problem, I'm doing:
>
> (+ (* 2 0.0001) 4.1)
>
> my interpreter prints this:
> 4.1001997
>
> Why??? shouldn't it be just 4.1002 ?
> if If substitute 4.1 for 3.1 it prints the correct result, but for
> 4.1, 5.1, 6.1 it screws it up.
>
> I'm desperate, i need to finish this quick :(

It is doing the right thing, just not what you want. As others have 
pointed out, floating point numbers are approximations (any numerical 
analysis book will cover this in detail) and using them will result in 
approximate results. To illustrate (it is nice to have CL around to see 
this kind of stuff):

(list (+ (* 2 0.0001) 4.1)
       (+ ( * 2 1/10000) 41/10)
       (float (+ ( * 2 1/10000) 41/10))
       (rational 4.1)
       (+ (* 2 (rational 0.0001)) (rational 4.1))
       (float (+ (* 2 (rational 0.0001)) (rational 4.1))))

produces:

(4.1001997 20501/5000 4.1002 8598323/2097152 281763591959/68719476736 
4.1001997)

The trouble begins when you let the lisp reader handle the '4.1'.

And, if you control the display of the number:

(format nil "~,4f" (+ (* 2 0.0001) 4.1)) --> "4.1002"

and, just for fun:

(format nil "~,4f" (+ ( * 2 1/10000) 41/10)) --> "4.1002"

The error is in the 7th decimal place, do you really care about that, 
and if so why? The 'why' will help you decide between ignoring the 
issue, controlling the display of numbers, increasing the precision of 
the floats to double or long, using rational numbers instead, 
controlling errors, changing algorithms, or some other even more 
desperate measure.

----
Bob Hutchison          -- blogs at <http://www.recursive.ca/hutch/>
Recursive Design Inc.  -- <http://www.recursive.ca/>

Re: another newbie question

thank you very much for your help... I suppose I could use a little reading :D