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Subject: RE: GISList: ArcView3x: math malfunction
Date:  07/30/2003 07:15:01 PM
From:  Irving, David




This is a direct consequence of the limited precision of computer arithmeti=
c, and is not exclusive to ArcView. You should get similar results from pro=
grams written in C, FORTRAN, BASIC, ... on any computer (the results will d=
iffer between computer architectures, but not generally between languages).=
There is an excellent treatment of this in Knuth, or in any elementary tex=
t on numerical analysis.

To repeat, it is _not_ a malfunction.

David Irving
Technical Systems Analyst
Innovation Team

Santos Ltd
91 King William St
Adelaide SA 5000

Ph : +61 8 8224 7810
Fax: +61 8 8218 5960
email: david.irving@santos.com


-----Original Message-----
From: S=F6ren Alsleben [mailto:GIS_mail@web.de]=0D
Sent: Wednesday, 30 July 2003 20:51
To: GIS-List
Subject: GISList: ArcView3x: math malfunction

Just FYI

While calculating and relating attributes of a feature table using some
Number-Requests, I encountered a strange phenomenon:

10/3 is NOT equal to (1/3) * 10

Ok, I always guessed that my math teacher was a liar. But seriously,
this bug seems to be caused by some internal AV-limitations dealing with
numbers. Any value that consists of more than 16 digits (plus radix and
leading zeros for values ranged from 1 to -1) seems to be stripped after
the 16th digit. Then AV adds a final digit that usually is not a result
of traditional rounding.

Two scripts demonstrating this misbehaviour are appended. As far as I
know this error occurs on any plattform and AV version. Assuming that a
lot of AVs functions / requests should be based on similar arithmetics
makes me shiver...

Cheers,
S=F6ren



' --- SCRIPT1: START ---
' Precision of Numbers
n =3D -10
valstr =3D "10^n / 3"+nl
for each i in 1..30
val =3D (10^n/3).SetFormatPrecision (30)
valstr =3D valstr+nl+(10^n).AsString+" / 3 =3D "+val.AsString
n =3D n + 1
end
n =3D -10
valstr =3D valstr+nl+nl+nl+"(9 * (10^n)) / 10"+nl
for each i in 1..30
val =3D ((9 * (10^n)) / 10).SetFormatPrecision (30)
valstr =3D valstr+nl+((9 * (10^n))).AsString+" / 10 =3D "+val.AsString
n =3D n + 1
end
MsgBox.Report (valstr, "Precision of Numbers")
' --- SCRIPT1: END ---


' --- SCRIPT2: START ---
' Relating Numbers
val1 =3D (10 / 3)
val2 =3D (1 / 3) * (10)
if (val1 =3D val2) then
aBool =3D true
else
aBool =3D false
end
msgbox.info (val1.AsString+" =3D "+val2.AsString+nl+"is
"+aBool.AsString.UCase, "Relating Numbers: 10/3 =3D (1/3)*10 ?!?")
' --- SCRIPT2: END ---




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Disclaimer: The information contained in this email is intended only for th=
e use of the
person(s) to whom it is addressed and may be confidential or contain
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notified that any perusal, use, distribution, copying or disclosure is stri=
ctly
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advise us by return email and delete the email without making a copy.


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