newbie question: floating point addition operation

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newbie question: floating point addition operation

Postby hajovonta » Tue Mar 05, 2013 12:35 am

Can someone explain this:

Code: Select all
CG-USER(9): (+ 2.32 0.001)
2.3209999


I have Allegro Common Lisp, 9.0, Windows 7 machine.

What is the proper way to correctly display 2.321 ?
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Re: newbie question: floating point addition operation

Postby Konfusius » Tue Mar 05, 2013 2:30 am

Since floating point numbers are represented internally as numbers by the base of two there isn't a way to represent 0.001 exactly. There will always be rounding errors. This isn't a problem of Lisp but of floating point arithmetic in general. The only way around it is to print it rounded:
Code: Select all
(format t "~,5f" (+ 2.32 0.001))
-> 2.32100
Last edited by Konfusius on Tue Mar 05, 2013 5:23 am, edited 1 time in total.
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Re: newbie question: floating point addition operation

Postby hajovonta » Tue Mar 05, 2013 3:35 am

Thanks, that suits for me.
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Re: newbie question: floating point addition operation

Postby marcoxa » Wed Mar 06, 2013 7:14 am

Marco Antoniotti
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Re: newbie question: floating point addition operation

Postby hajovonta » Wed Mar 06, 2013 11:58 am

Maybe it was my high expectations :)
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Re: newbie question: floating point addition operation

Postby Kompottkin » Thu Mar 07, 2013 10:22 am

hajovonta wrote:Maybe it was my high expectations :)


If you want exact rationals, use exact rationals. :)

Code: Select all
CL-USER> (+ 232/100 1/1000)
2321/1000
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Re: newbie question: floating point addition operation

Postby hajovonta » Thu Mar 07, 2013 2:13 pm

ok, but then I want to display the result in floating point format...
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Re: newbie question: floating point addition operation

Postby Konfusius » Fri Mar 08, 2013 4:56 am

You can convert rationals to floats:
Code: Select all
(float (+ 232/100 1/1000))
-> 2.321
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Re: newbie question: floating point addition operation

Postby Kompottkin » Sat Mar 09, 2013 3:42 am

Konfusius wrote:You can convert rationals to floats:
Code: Select all
(float (+ 232/100 1/1000))
-> 2.321


Technically, that (somewhat) reintroduces the problem...

Code: Select all
L> (format t "~E" (float (+ 232/100 1/1000)))
2.3210001e+0
NIL
L> (= 2.3210001 (float (+ 232/100 1/1000)))
T


The Right Thing[TM] would be to use something like Wu-Decimal:

Code: Select all
L> (ql:quickload "wu-decimal")
; Loading "wu-decimal"
[package wu-decimal]...
("wu-decimal")
L> (wu-decimal:enable-decimal-printing-for-ratios)
NIL
L> (format t "~A" (+ 232/100 1/1000))
2.321
NIL


Of course, I'm nitpicking. If you're just hacking something together to quickly visualize something, using floating point and rounding the results isn't so bad.
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