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Re: Inaccuracies [message #5309 is a reply to message #5303]

Tue, 14 November 1995 00:00

thompson
Messages: 584
Registered: August 1991

Senior Member

Andy Loughe <afl@cdc.noaa.gov> writes:

> Ok, I am sure this has been discussed before, but let
> me start this thread again. I wish to create a 15-element
> vector which contains the numbers -1.4 to 1.4 by an increment
> of 0.2 I also wish the sum of these elements to be zero
> (No, this isn't the new math). Here is what I tried...

> TRIAL #1
> ========
> IDL> a = findgen(15)*.2 - 1.4
> IDL> print, total(a)
> 7.15256e-07

> Hmmm! Not so good.

> Maybe I am missing something here, but this kind of behavior
> makes IDL a bit problematical for scientific use. With only 15
> numbers and double precision arithmetic, I can't believe this
> would fail in FORTRAN or C!

Here's a FORTRAN program I tried this on.

program test
c
total = 0
do i = 1,15
a = (i-1)*0.2 - 1.4
total = total + a
enddo
write (*,*) total
c
end

and the result of running this program?

> a.out
7.1525574E-07

Exactly the same answer as IDL gives! If instead I do it in double precision,
I get

> a.out
4.440892098500626E-015

Again, exactly the same answer as IDL! It appears that IDL is working
correctly within the confines of the floating point arithmetic of the computer.

Interestingly enough, the same problem done in IDL on an OpenVMS computer gives
exactly zero when done in single precision, but 8.8817842e-16 in double
precision. VMS uses a different floating point format than the standard IEEE
representation used in most modern computers.

The bottom line is that all computers are subject to round-off errors when
doing floating point arithmetic. This will occur no matter what software
package is used.

Bill Thompson

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[Message index]

		Re: Inaccuracies By: C R Shaw on Thu, 16 November 1995 00:00
		Re: Inaccuracies By: Hermann Mannstein on Thu, 16 November 1995 00:00
		Re: Inaccuracies By: wclodius on Wed, 15 November 1995 00:00
		Re: Inaccuracies By: Andy Loughe on Wed, 15 November 1995 00:00
		Re: Inaccuracies By: thompson on Wed, 15 November 1995 00:00
		Re: Inaccuracies By: hahn on Tue, 14 November 1995 00:00
		Re: Inaccuracies By: lpmix on Tue, 14 November 1995 00:00
		Re: Inaccuracies By: Andy Loughe on Tue, 14 November 1995 00:00
		Re: Inaccuracies By: wclodius on Tue, 14 November 1995 00:00
		Re: Inaccuracies By: thompson on Tue, 14 November 1995 00:00
		Re: Inaccuracies By: Jackel on Tue, 14 November 1995 00:00

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