newbie question: floating point addition operation

[hajovonta]

Can someone explain this:

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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 ?

[Konfusius]

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:

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(format t "~,5f" (+ 2.32 0.001))
-> 2.32100

[hajovonta]

Thanks, that suits for me.

[marcoxa]

... and, BTW

http://docs.oracle.com/cd/E19957-01/806-3568/ncg_math.html

Cheers

MA

[hajovonta]

Maybe it was my high expectations

[Kompottkin]

Maybe it was my high expectations

If you want exact rationals, use exact rationals.

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CL-USER> (+ 232/100 1/1000)
2321/1000

[hajovonta]

ok, but then I want to display the result in floating point format...

[Konfusius]

You can convert rationals to floats:

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(float (+ 232/100 1/1000))
-> 2.321

[Kompottkin]

You can convert rationals to floats:

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(float (+ 232/100 1/1000))
-> 2.321

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

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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:

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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.